{
  "schema": "apeiron-ap1-m1-junction-convergence-pilot-v1.1",
  "updated_utc": "2026-09-02T17:55:53Z",
  "classification": "M1_EXACT_INITIAL_JUNCTION_PILOT_COMPLETE_TOLERANCE_FREEZE_OPEN",
  "config": {
    "prefix_intervals": 256,
    "temporal_strides": [
      16,
      8,
      4,
      2
    ],
    "curvature_tail_strides": [
      4,
      2,
      1
    ],
    "temporal_mode_nodes": 64,
    "momentum_nodes": [
      24,
      32,
      48,
      64
    ],
    "decimal_digits": 80,
    "roundoff_digits": 60,
    "held_out_momentum_nodes": 96,
    "physical_N_lower": -100.0,
    "physical_N_upper": 0.0
  },
  "authority_sha256": {
    "HANDOFF/CURRENT_STATE_LATEST.npz": "26473f1ce826f7272af22bea2ce92d313f914b7b8ca9601d5f7047e79de9c81f",
    "AP1/APEIRON_AP1_M1_BACKGROUND_SPEC_LATEST.md": "9a565aef648f4a7229941bf9efa5c51a754fd4763dd11e59e8032701d6ed0259",
    "AP1/APEIRON_AP1_R2C_G22_PASS_CHECKPOINT_20260902T151240Z.json": "13cb421bc457a59c149ae68840829b867f3637f92acfdff533ce665ff6f26c6e",
    "AP1/CODE/ap1_m1_background_preflight.py": "8b5754bd0c89f6b6ec77fa7a8e042ac153168ac445ba932d862b142254718475",
    "AP1/CODE/planck2018_neutrino_closure.py": "ccd3158930dcb9ab74d7634ed06f2eaa00745ac95e2883f9fe02d9039a056acc",
    "AP1/CODE/chi_background_closure.py": "1097888c72fbe9152e1905a2a3ab37c15df9ca681639571b87d76de6ddf072a7",
    "AP1/CODE/ap1_r2c_mode_inheritance.py": "221d3f111eb0eb1435d64c62cc4de117a5464052a9345281d98c42f7fccff1cb",
    "AP1/CODE/ap1_r2c_high_precision_modes.py": "3b76dc1bba339fc7576381661b7a0099501231154f45cf9bb2eba3db16f0d484",
    "AP1/CODE/ap1_r2c_self_consistent_candidate.py": "2c22454f69817ecdc40d38dacad0efaa72fdddcfa50c9c00a48478d610ed8cb0"
  },
  "junction_rule": {
    "rule": "use exact stored HARD-PASS index 0; determine the physical-N offset by Friedmann inversion; test Raychaudhuri independently against a pre-frozen pilot-derived tolerance",
    "rationale": "implements the specified earliest junction without interpolation or mode reinitialization, maximizes distance from the tachyonic onset, and avoids ill-conditioned interpolated-root families",
    "frozen_before_held_out_evaluation": true
  },
  "exploratory_root_scan_role": "independent diagnostic only; no interpolated root is a candidate, checkpoint, or seed",
  "Hdot_sampling_rule": "differentiate the complete frozen 15361-point H(N) cubic spline once and sample that single derivative on every nested prefix grid",
  "local_curvature_tail_sampling_rule": "evaluate adiabatic orders 2+4 once on the complete frozen trajectory and sample the same local values on every nested prefix grid",
  "temporal_pilot": {
    "levels": [
      {
        "prefix_intervals": 256,
        "stride": 16,
        "nodes": 17,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 8,
        "simultaneous_sign_change_brackets": 2,
        "positive_frequency_brackets": 2,
        "selected_earliest_admissible": {
          "left_index": 0,
          "right_index": 1,
          "fraction": 0.2389246633386148,
          "N_local": 2.5600787611229337e-05,
          "N_physical": -57.19042820930391,
          "H_Mpl": 4.2969118436844693e-07,
          "required_standard_density_Mpl4": 8.971016944645801e-25,
          "vacuum_frequency_margin_Mpl2": 6.2991147616090845e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "right_raychaudhuri_residual_Mpl2": 2.1322986241320927e-20,
          "left_normalized_residual": -3.625504617408686e-08,
          "right_normalized_residual": 1.1548755161722298e-07,
          "bracket_width_N_local": 0.00010715004158003876
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684877974411396e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 1.4e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 0,
            "right_index": 1,
            "fraction": 0.2389246633386148,
            "N_local": 2.5600787611229337e-05,
            "N_physical": -57.19042820930391,
            "H_Mpl": 4.2969118436844693e-07,
            "required_standard_density_Mpl4": 8.971016944645801e-25,
            "vacuum_frequency_margin_Mpl2": 6.2991147616090845e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
            "right_raychaudhuri_residual_Mpl2": 2.1322986241320927e-20,
            "left_normalized_residual": -3.625504617408686e-08,
            "right_normalized_residual": 1.1548755161722298e-07,
            "bracket_width_N_local": 0.00010715004158003876
          },
          {
            "left_index": 7,
            "right_index": 8,
            "fraction": 0.5125383542602964,
            "N_local": 0.0008049685138940012,
            "N_physical": -58.545008917127184,
            "H_Mpl": 4.2969075751002307e-07,
            "required_standard_density_Mpl4": 5.1815535846900007e-23,
            "vacuum_frequency_margin_Mpl2": 6.292389381100096e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.6796724828776285e-19,
            "right_raychaudhuri_residual_Mpl2": -3.4996389818969277e-19,
            "left_normalized_residual": 1.9929528767051913e-06,
            "right_normalized_residual": -1.895445606724159e-06,
            "bracket_width_N_local": 0.00010714993713190697
          }
        ]
      },
      {
        "prefix_intervals": 256,
        "stride": 8,
        "nodes": 33,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 17,
        "simultaneous_sign_change_brackets": 6,
        "positive_frequency_brackets": 6,
        "selected_earliest_admissible": {
          "left_index": 4,
          "right_index": 5,
          "fraction": 0.19713372233297785,
          "N_local": 0.00022486151846154903,
          "N_physical": -57.85984272726989,
          "H_Mpl": 4.296911321989055e-07,
          "required_standard_density_Mpl4": 3.192490724842452e-24,
          "vacuum_frequency_margin_Mpl2": 6.297901730430278e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 3.3015329464327498e-21,
          "right_raychaudhuri_residual_Mpl2": -1.3446149324062516e-20,
          "left_normalized_residual": 1.7881454663836803e-08,
          "right_normalized_residual": -7.282578574053697e-08,
          "bracket_width_N_local": 5.35750142480713e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684877974411396e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 1.9e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 4,
            "right_index": 5,
            "fraction": 0.19713372233297785,
            "N_local": 0.00022486151846154903,
            "N_physical": -57.85984272726989,
            "H_Mpl": 4.296911321989055e-07,
            "required_standard_density_Mpl4": 3.192490724842452e-24,
            "vacuum_frequency_margin_Mpl2": 6.297901730430278e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.3015329464327498e-21,
            "right_raychaudhuri_residual_Mpl2": -1.3446149324062516e-20,
            "left_normalized_residual": 1.7881454663836803e-08,
            "right_normalized_residual": -7.282578574053697e-08,
            "bracket_width_N_local": 5.35750142480713e-05
          },
          {
            "left_index": 9,
            "right_index": 10,
            "fraction": 0.2313970905559262,
            "N_local": 0.0004945722175807385,
            "N_physical": -58.206600757904695,
            "H_Mpl": 4.296910057186836e-07,
            "required_standard_density_Mpl4": 1.273520487599976e-23,
            "vacuum_frequency_margin_Mpl2": 6.295704288334817e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.4640458643115948e-20,
            "right_raychaudhuri_residual_Mpl2": -4.862938890744133e-20,
            "left_normalized_residual": 7.929433117249363e-08,
            "right_normalized_residual": -2.633821493761483e-07,
            "bracket_width_N_local": 5.357499809610964e-05
          },
          {
            "left_index": 14,
            "right_index": 15,
            "fraction": 0.1556321235521632,
            "N_local": 0.0007583880481021679,
            "N_physical": -58.210756104638605,
            "H_Mpl": 4.296908042374688e-07,
            "required_standard_density_Mpl4": 1.3120956344050313e-23,
            "vacuum_frequency_margin_Mpl2": 6.292948971033842e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.107971034158618e-21,
            "right_raychaudhuri_residual_Mpl2": -4.9414465248771756e-20,
            "left_normalized_residual": 4.93298171452441e-08,
            "right_normalized_residual": -2.6763448281566777e-07,
            "bracket_width_N_local": 5.357497189231546e-05
          },
          {
            "left_index": 18,
            "right_index": 19,
            "fraction": 0.4042402435454371,
            "N_local": 0.0009860070546045092,
            "N_physical": -58.01984478417415,
            "H_Mpl": 4.2969055370109867e-07,
            "required_standard_density_Mpl4": 6.006079761752605e-24,
            "vacuum_frequency_margin_Mpl2": 6.290088190327468e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 2.2621480118584816e-20,
            "right_raychaudhuri_residual_Mpl2": -3.333900496370298e-20,
            "left_normalized_residual": 1.2252066589498114e-07,
            "right_normalized_residual": -1.8056813151282398e-07,
            "bracket_width_N_local": 5.3574942043365325e-05
          },
          {
            "left_index": 23,
            "right_index": 24,
            "fraction": 0.46234447758658476,
            "N_local": 0.0012569945774579263,
            "N_physical": -58.237170492432675,
            "H_Mpl": 4.2969014459562973e-07,
            "required_standard_density_Mpl4": 1.4195987701764072e-23,
            "vacuum_frequency_margin_Mpl2": 6.286102713327417e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 2.148239780679478e-20,
            "right_raychaudhuri_residual_Mpl2": -2.4981654103010287e-20,
            "left_normalized_residual": 1.1635147168848291e-07,
            "right_normalized_residual": -1.353039600398865e-07,
            "bracket_width_N_local": 5.357489142292552e-05
          },
          {
            "left_index": 29,
            "right_index": 30,
            "fraction": 0.4636231942165903,
            "N_local": 0.0015785121985867814,
            "N_physical": -58.414563220474,
            "H_Mpl": 4.296894761163382e-07,
            "required_standard_density_Mpl4": 2.886184737641129e-23,
            "vacuum_frequency_margin_Mpl2": 6.280555888819153e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.328844598922267e-20,
            "right_raychaudhuri_residual_Mpl2": -7.321992282990996e-20,
            "left_normalized_residual": 3.4277952773081286e-07,
            "right_normalized_residual": -3.9657010581675964e-07,
            "bracket_width_N_local": 5.357480793830179e-05
          }
        ]
      },
      {
        "prefix_intervals": 256,
        "stride": 4,
        "nodes": 65,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 37,
        "simultaneous_sign_change_brackets": 8,
        "positive_frequency_brackets": 8,
        "selected_earliest_admissible": {
          "left_index": 0,
          "right_index": 1,
          "fraction": 0.8632324457891232,
          "N_local": 2.312384855992946e-05,
          "N_physical": -56.6976375885845,
          "H_Mpl": 4.29691185507547e-07,
          "required_standard_density_Mpl4": 3.412099966100508e-26,
          "vacuum_frequency_margin_Mpl2": 6.299136419648466e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "right_raychaudhuri_residual_Mpl2": 1.0605635231637947e-21,
          "left_normalized_residual": -3.625504617408686e-08,
          "right_normalized_residual": 5.7441238821214645e-09,
          "bracket_width_N_local": 2.6787510910564553e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684877974411396e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 2.66e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 0,
            "right_index": 1,
            "fraction": 0.8632324457891232,
            "N_local": 2.312384855992946e-05,
            "N_physical": -56.6976375885845,
            "H_Mpl": 4.29691185507547e-07,
            "required_standard_density_Mpl4": 3.412099966100508e-26,
            "vacuum_frequency_margin_Mpl2": 6.299136419648466e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
            "right_raychaudhuri_residual_Mpl2": 1.0605635231637947e-21,
            "left_normalized_residual": -3.625504617408686e-08,
            "right_normalized_residual": 5.7441238821214645e-09,
            "bracket_width_N_local": 2.6787510910564553e-05
          },
          {
            "left_index": 1,
            "right_index": 2,
            "fraction": 0.4176267988019817,
            "N_local": 3.7974693204736606e-05,
            "N_physical": -56.77324059787477,
            "H_Mpl": 4.2969118256130796e-07,
            "required_standard_density_Mpl4": 4.769444971403199e-26,
            "vacuum_frequency_margin_Mpl2": 6.299057240007356e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.0605635231637947e-21,
            "right_raychaudhuri_residual_Mpl2": -1.4789371176144381e-21,
            "left_normalized_residual": 5.7441238821214645e-09,
            "right_normalized_residual": -8.010079591204404e-09,
            "bracket_width_N_local": 2.6787510586638554e-05
          },
          {
            "left_index": 2,
            "right_index": 3,
            "fraction": 0.9471510110491417,
            "N_local": 7.894683889822794e-05,
            "N_physical": -56.50429276484271,
            "H_Mpl": 4.29691173803596e-07,
            "required_standard_density_Mpl4": 1.6090248246726008e-26,
            "vacuum_frequency_margin_Mpl2": 6.298830582892971e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.4789371176144381e-21,
            "right_raychaudhuri_residual_Mpl2": 8.252150974451569e-23,
            "left_normalized_residual": -8.010079591204404e-09,
            "right_normalized_residual": 4.4694522258375654e-10,
            "bracket_width_N_local": 2.6787510233369172e-05
          },
          {
            "left_index": 19,
            "right_index": 20,
            "fraction": 0.007638168303973431,
            "N_local": 0.0005091672258829547,
            "N_physical": -57.5934939536956,
            "H_Mpl": 4.2969099707355565e-07,
            "required_standard_density_Mpl4": 1.0820020372566283e-24,
            "vacuum_frequency_margin_Mpl2": 6.295569674597359e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.266135340648734e-23,
            "right_raychaudhuri_residual_Mpl2": -4.243410095490058e-21,
            "left_normalized_residual": 1.76897488804341e-10,
            "right_normalized_residual": -2.2982778454441895e-08,
            "bracket_width_N_local": 2.6787498530129843e-05
          },
          {
            "left_index": 27,
            "right_index": 28,
            "fraction": 0.8845278546894976,
            "N_local": 0.0007469568527177559,
            "N_physical": -57.59851573952742,
            "H_Mpl": 4.2969081501533915e-07,
            "required_standard_density_Mpl4": 1.1057368483832954e-24,
            "vacuum_frequency_margin_Mpl2": 6.293082119959009e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.7137595793568124e-21,
            "right_raychaudhuri_residual_Mpl2": -4.848188596008633e-22,
            "left_normalized_residual": 2.0114146132611605e-08,
            "right_normalized_residual": -2.625834623647953e-09,
            "bracket_width_N_local": 2.6787488283394308e-05
          },
          {
            "left_index": 36,
            "right_index": 37,
            "fraction": 0.4601799812748327,
            "N_local": 0.0009766769653917582,
            "N_physical": -57.46579690120138,
            "H_Mpl": 4.29690565959171e-07,
            "required_standard_density_Mpl4": 6.492305976100202e-25,
            "vacuum_frequency_margin_Mpl2": 6.2902163682582095e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 2.1584613903132106e-21,
            "right_raychaudhuri_residual_Mpl2": -2.5320107687182262e-21,
            "left_normalized_residual": 1.169048733608354e-08,
            "right_normalized_residual": -1.371367800220852e-08,
            "bracket_width_N_local": 2.6787472094379227e-05
          },
          {
            "left_index": 47,
            "right_index": 48,
            "fraction": 0.6337227771767194,
            "N_local": 0.0012759877830101041,
            "N_physical": -57.59198253967035,
            "H_Mpl": 4.29690111455864e-07,
            "required_standard_density_Mpl4": 1.0794374755478793e-24,
            "vacuum_frequency_margin_Mpl2": 6.285802061997425e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5332291390270095e-21,
            "right_raychaudhuri_residual_Mpl2": -8.861712585058924e-22,
            "left_normalized_residual": 8.304171019385809e-09,
            "right_normalized_residual": -4.799621356334806e-09,
            "bracket_width_N_local": 2.6787444243539862e-05
          },
          {
            "left_index": 58,
            "right_index": 59,
            "fraction": 0.7790192277207105,
            "N_local": 0.001574541579328561,
            "N_physical": -57.81993460498142,
            "H_Mpl": 4.296894863548347e-07,
            "required_standard_density_Mpl4": 2.6785378051041187e-24,
            "vacuum_frequency_margin_Mpl2": 6.280632332380778e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.603107325810176e-21,
            "right_raychaudhuri_residual_Mpl2": -1.0220767487245555e-21,
            "left_normalized_residual": 1.9514958981848967e-08,
            "right_normalized_residual": -5.5357195807729475e-09,
            "bracket_width_N_local": 2.6787405990904645e-05
          }
        ]
      },
      {
        "prefix_intervals": 256,
        "stride": 2,
        "nodes": 129,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 89,
        "simultaneous_sign_change_brackets": 46,
        "positive_frequency_brackets": 46,
        "selected_earliest_admissible": {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878425339991634,
          "N_local": 7.752094659454906e-05,
          "N_physical": -56.69916548500461,
          "H_Mpl": 4.296911741311535e-07,
          "required_standard_density_Mpl4": 3.022613588034913e-26,
          "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
          "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
          "left_normalized_residual": -2.5565397212652397e-09,
          "right_normalized_residual": 6.884484820267378e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684877974411396e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 3.86e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 5,
            "right_index": 6,
            "fraction": 0.7878425339991634,
            "N_local": 7.752094659454906e-05,
            "N_physical": -56.69916548500461,
            "H_Mpl": 4.296911741311535e-07,
            "required_standard_density_Mpl4": 3.022613588034913e-26,
            "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
            "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
            "left_normalized_residual": -2.5565397212652397e-09,
            "right_normalized_residual": 6.884484820267378e-10,
            "bracket_width_N_local": 1.339375507064178e-05
          },
          {
            "left_index": 6,
            "right_index": 7,
            "fraction": 0.3642274780348604,
            "N_local": 8.524090532641941e-05,
            "N_physical": -56.74707739119948,
            "H_Mpl": 4.2969117234716105e-07,
            "required_standard_density_Mpl4": 3.779356413779906e-26,
            "vacuum_frequency_margin_Mpl2": 6.29879436356012e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
            "right_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
            "left_normalized_residual": 6.884484820267378e-10,
            "right_normalized_residual": -1.2017122827262556e-09,
            "bracket_width_N_local": 1.3393754974687068e-05
          },
          {
            "left_index": 7,
            "right_index": 8,
            "fraction": 0.21241430411053652,
            "N_local": 9.660131182641272e-05,
            "N_physical": -56.70112291800134,
            "H_Mpl": 4.296911696555098e-07,
            "required_standard_density_Mpl4": 4.096999558168485e-26,
            "vacuum_frequency_margin_Mpl2": 6.298728217567521e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
            "right_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
            "left_normalized_residual": -1.2017122827262556e-09,
            "right_normalized_residual": 4.455685895618096e-09,
            "bracket_width_N_local": 1.339375487477941e-05
          },
          {
            "left_index": 8,
            "right_index": 9,
            "fraction": 0.6065846174498755,
            "N_local": 0.00011527448719392336,
            "N_physical": -56.223771979203654,
            "H_Mpl": 4.296911650179105e-07,
            "required_standard_density_Mpl4": 4.513930388941858e-27,
            "vacuum_frequency_margin_Mpl2": 6.298616934764003e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
            "right_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
            "left_normalized_residual": 4.455685895618096e-09,
            "right_normalized_residual": -2.8898447940549242e-09,
            "bracket_width_N_local": 1.3393754770835335e-05
          },
          {
            "left_index": 9,
            "right_index": 10,
            "fraction": 0.2574202995656594,
            "N_local": 0.00012399162068847292,
            "N_physical": -56.32060338324056,
            "H_Mpl": 4.296911627704443e-07,
            "required_standard_density_Mpl4": 8.69484844629573e-27,
            "vacuum_frequency_margin_Mpl2": 6.298564016845657e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
            "left_normalized_residual": -2.8898447940549242e-09,
            "right_normalized_residual": 8.336328255348749e-09,
            "bracket_width_N_local": 1.3393754662768595e-05
          },
          {
            "left_index": 10,
            "right_index": 11,
            "fraction": 0.9413398149808291,
            "N_local": 0.0001465456254441022,
            "N_physical": -56.85173446217978,
            "H_Mpl": 4.2969115669102096e-07,
            "required_standard_density_Mpl4": 5.690277456177136e-26,
            "vacuum_frequency_margin_Mpl2": 6.2984240669508886e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
            "right_raychaudhuri_residual_Mpl2": -9.591458369669014e-23,
            "left_normalized_residual": 8.336328255348749e-09,
            "right_normalized_residual": -5.194835684323147e-10,
            "bracket_width_N_local": 1.3393754550492778e-05
          },
          {
            "left_index": 14,
            "right_index": 15,
            "fraction": 0.11548721003307255,
            "N_local": 0.00018905937578647347,
            "N_physical": -56.96006244393786,
            "H_Mpl": 4.2969114412597683e-07,
            "required_standard_density_Mpl4": 8.828292126183686e-26,
            "vacuum_frequency_margin_Mpl2": 6.298148090172184e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5513916356533313e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1882058139512706e-21,
            "left_normalized_residual": 8.402502271818305e-10,
            "right_normalized_residual": -6.4354493210886855e-09,
            "bracket_width_N_local": 1.3393754057482415e-05
          },
          {
            "left_index": 17,
            "right_index": 18,
            "fraction": 0.08744038024700374,
            "N_local": 0.00022886498517327977,
            "N_physical": -56.789232006461916,
            "H_Mpl": 4.296911310119382e-07,
            "required_standard_density_Mpl4": 4.568037874804944e-26,
            "vacuum_frequency_margin_Mpl2": 6.2978756030892115e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.106238344959863e-23,
            "right_raychaudhuri_residual_Mpl2": 6.372692486534195e-22,
            "left_normalized_residual": -3.307203902435353e-10,
            "right_normalized_residual": 3.4515183868669134e-09,
            "bracket_width_N_local": 1.339375363908614e-05
          },
          {
            "left_index": 22,
            "right_index": 23,
            "fraction": 0.3109410910174016,
            "N_local": 0.0002988272650373031,
            "N_physical": -56.70810397507022,
            "H_Mpl": 4.296911045649456e-07,
            "required_standard_density_Mpl4": 3.7581961073256013e-26,
            "vacuum_frequency_margin_Mpl2": 6.297363409473673e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.99856639440169e-22,
            "right_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
            "left_normalized_residual": -1.624055774041247e-09,
            "right_normalized_residual": 3.5989779442597223e-09,
            "bracket_width_N_local": 1.3393752842742138e-05
          },
          {
            "left_index": 23,
            "right_index": 24,
            "fraction": 0.564706651707065,
            "N_local": 0.0003156198909813086,
            "N_physical": -56.69531183159522,
            "H_Mpl": 4.29691097551177e-07,
            "required_standard_density_Mpl4": 4.0136158997550725e-26,
            "vacuum_frequency_margin_Mpl2": 6.297234186260923e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
            "right_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "left_normalized_residual": 3.5989779442597223e-09,
            "right_normalized_residual": -2.774203555973799e-09,
            "bracket_width_N_local": 1.3393752668113652e-05
          },
          {
            "left_index": 24,
            "right_index": 25,
            "fraction": 0.7238164271918855,
            "N_local": 0.0003311447204991803,
            "N_physical": -56.67592240321177,
            "H_Mpl": 4.2969109083978294e-07,
            "required_standard_density_Mpl4": 3.1800670545861125e-26,
            "vacuum_frequency_margin_Mpl2": 6.2971126129239e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
            "left_normalized_residual": -2.774203555973799e-09,
            "right_normalized_residual": 1.058541146449756e-09,
            "bracket_width_N_local": 1.3393752488282513e-05
          },
          {
            "left_index": 25,
            "right_index": 26,
            "fraction": 0.10861082179822887,
            "N_local": 0.00033629856135931695,
            "N_physical": -56.6223775919006,
            "H_Mpl": 4.2969108856934607e-07,
            "required_standard_density_Mpl4": 2.3340453548590064e-26,
            "vacuum_frequency_margin_Mpl2": 6.297071862011722e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
            "right_raychaudhuri_residual_Mpl2": -1.6040381628345865e-21,
            "left_normalized_residual": 1.058541146449756e-09,
            "right_normalized_residual": -8.687643951565464e-09,
            "bracket_width_N_local": 1.3393752303225248e-05
          },
          {
            "left_index": 30,
            "right_index": 31,
            "fraction": 0.8427289524142231,
            "N_local": 0.00041309991647547526,
            "N_physical": -56.65091948474018,
            "H_Mpl": 4.296910516217719e-07,
            "required_standard_density_Mpl4": 3.344055246552905e-26,
            "vacuum_frequency_margin_Mpl2": 6.296436238913727e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.2235941124756778e-21,
            "right_raychaudhuri_residual_Mpl2": 4.1496969396006417e-22,
            "left_normalized_residual": -1.204322734204436e-08,
            "right_normalized_residual": 2.24752102750371e-09,
            "bracket_width_N_local": 1.3393751298504256e-05
          },
          {
            "left_index": 32,
            "right_index": 33,
            "fraction": 0.8794008590948205,
            "N_local": 0.0004403785928661611,
            "N_physical": -56.60458670710162,
            "H_Mpl": 4.2969103711929483e-07,
            "required_standard_density_Mpl4": 2.422318717846245e-26,
            "vacuum_frequency_margin_Mpl2": 6.29619826252337e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7113735259912426e-21,
            "right_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
            "left_normalized_residual": 9.268985585911212e-09,
            "right_normalized_residual": -1.2711287745714935e-09,
            "bracket_width_N_local": 1.3393750858574967e-05
          },
          {
            "left_index": 33,
            "right_index": 34,
            "fraction": 0.13927695721182692,
            "N_local": 0.00044385930854661996,
            "N_physical": -56.65083941813677,
            "H_Mpl": 4.2969103521278307e-07,
            "required_standard_density_Mpl4": 2.5408554787641562e-26,
            "vacuum_frequency_margin_Mpl2": 6.296167422194674e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
            "right_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
            "left_normalized_residual": -1.2711287745714935e-09,
            "right_normalized_residual": 7.855498040187442e-09,
            "bracket_width_N_local": 1.3393750630116873e-05
          },
          {
            "left_index": 34,
            "right_index": 35,
            "fraction": 0.5055229316221608,
            "N_local": 0.0004621584663088393,
            "N_physical": -56.674236408190716,
            "H_Mpl": 4.2969102497707594e-07,
            "required_standard_density_Mpl4": 3.27358524823297e-26,
            "vacuum_frequency_margin_Mpl2": 6.296003522723821e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
            "right_raychaudhuri_residual_Mpl2": -1.418703344144049e-21,
            "left_normalized_residual": 7.855498040187442e-09,
            "right_normalized_residual": -7.683852771421306e-09,
            "bracket_width_N_local": 1.3393750395837372e-05
          },
          {
            "left_index": 37,
            "right_index": 38,
            "fraction": 0.2761316055719378,
            "N_local": 0.0004992673064013667,
            "N_physical": -56.95940617049714,
            "H_Mpl": 4.29691003142314e-07,
            "required_standard_density_Mpl4": 8.683488899909805e-26,
            "vacuum_frequency_margin_Mpl2": 6.295662530107288e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.891666530020456e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
            "left_normalized_residual": -3.1909913874787536e-09,
            "right_normalized_residual": 8.365061636851863e-09,
            "bracket_width_N_local": 1.3393749656707803e-05
          },
          {
            "left_index": 38,
            "right_index": 39,
            "fraction": 0.6120451497427785,
            "N_local": 0.0005171601978165187,
            "N_physical": -57.01135998833373,
            "H_Mpl": 4.29690992056104e-07,
            "required_standard_density_Mpl4": 1.1305188629660545e-25,
            "vacuum_frequency_margin_Mpl2": 6.295493822700022e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
            "right_raychaudhuri_residual_Mpl2": -9.789925335806768e-22,
            "left_normalized_residual": 8.365061636851863e-09,
            "right_normalized_residual": -5.302331638639811e-09,
            "bracket_width_N_local": 1.3393749397776797e-05
          },
          {
            "left_index": 43,
            "right_index": 44,
            "fraction": 0.3686707670589538,
            "N_local": 0.0005808692460792936,
            "N_physical": -56.38768208111163,
            "H_Mpl": 4.296909495232809e-07,
            "required_standard_density_Mpl4": 1.3813187640175078e-26,
            "vacuum_frequency_margin_Mpl2": 6.294870827937082e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -8.89864129001246e-22,
            "right_raychaudhuri_residual_Mpl2": 1.523845360633848e-21,
            "left_normalized_residual": -4.819603162500771e-09,
            "right_normalized_residual": 8.253316438136793e-09,
            "bracket_width_N_local": 1.3393748003819256e-05
          },
          {
            "left_index": 51,
            "right_index": 52,
            "fraction": 0.5175748228717203,
            "N_local": 0.0006900136034076554,
            "N_physical": -56.791632190308796,
            "H_Mpl": 4.296908650774768e-07,
            "required_standard_density_Mpl4": 4.3752395393722416e-26,
            "vacuum_frequency_margin_Mpl2": 6.293722225867458e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2188561560037294e-21,
            "right_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
            "left_normalized_residual": 6.6014631197392056e-09,
            "right_normalized_residual": -6.153143547955088e-09,
            "bracket_width_N_local": 1.3393745416623716e-05
          },
          {
            "left_index": 52,
            "right_index": 53,
            "fraction": 0.6057309951478642,
            "N_local": 0.0007045880899376551,
            "N_physical": -56.94035089498465,
            "H_Mpl": 4.296908526724755e-07,
            "required_standard_density_Mpl4": 8.792718649026132e-26,
            "vacuum_frequency_margin_Mpl2": 6.293561091423428e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
            "right_raychaudhuri_residual_Mpl2": 7.394726529583393e-22,
            "left_normalized_residual": -6.153143547955088e-09,
            "right_normalized_residual": 4.005068145222769e-09,
            "bracket_width_N_local": 1.3393745061689535e-05
          },
          {
            "left_index": 55,
            "right_index": 56,
            "fraction": 0.42134239853141464,
            "N_local": 0.000742299669706633,
            "N_physical": -57.03203966644007,
            "H_Mpl": 4.2969081928852725e-07,
            "required_standard_density_Mpl4": 1.2125725238328269e-25,
            "vacuum_frequency_margin_Mpl2": 6.293135637750973e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.1467529397916027e-22,
            "right_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
            "left_normalized_residual": 2.2459288888163688e-09,
            "right_normalized_residual": -3.084484025960798e-09,
            "bracket_width_N_local": 1.3393743953274851e-05
          },
          {
            "left_index": 56,
            "right_index": 57,
            "fraction": 0.7437193655246365,
            "N_local": 0.000760011247926384,
            "N_physical": -56.906387415728744,
            "H_Mpl": 4.2969080296152854e-07,
            "required_standard_density_Mpl4": 6.934448839336835e-26,
            "vacuum_frequency_margin_Mpl2": 6.292931635524838e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
            "left_normalized_residual": -3.084484025960798e-09,
            "right_normalized_residual": 1.0628922758579984e-09,
            "bracket_width_N_local": 1.3393743568903388e-05
          },
          {
            "left_index": 57,
            "right_index": 58,
            "fraction": 0.4513855429535026,
            "N_local": 0.000769489547062301,
            "N_physical": -56.953879584273736,
            "H_Mpl": 4.2969079403720936e-07,
            "required_standard_density_Mpl4": 8.628654545432148e-26,
            "vacuum_frequency_margin_Mpl2": 6.2928212886367955e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
            "right_raychaudhuri_residual_Mpl2": -2.3851789262401107e-22,
            "left_normalized_residual": 1.0628922758579984e-09,
            "right_normalized_residual": -1.2918404507906814e-09,
            "bracket_width_N_local": 1.3393743176885482e-05
          },
          {
            "left_index": 60,
            "right_index": 61,
            "fraction": 0.6625296414804297,
            "N_local": 0.0008124987844043409,
            "N_physical": -56.72634788093764,
            "H_Mpl": 4.2969075199085846e-07,
            "required_standard_density_Mpl4": 3.487610598278128e-26,
            "vacuum_frequency_margin_Mpl2": 6.292311072168803e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.0632820781371679e-21,
            "right_raychaudhuri_residual_Mpl2": 5.416001966562323e-22,
            "left_normalized_residual": -5.7588592254670335e-09,
            "right_normalized_residual": 2.9333697507287355e-09,
            "bracket_width_N_local": 1.339374195376004e-05
          },
          {
            "left_index": 62,
            "right_index": 63,
            "fraction": 0.2828776488502654,
            "N_local": 0.0008342013068245111,
            "N_physical": -56.42416066977023,
            "H_Mpl": 4.2969072976349885e-07,
            "required_standard_density_Mpl4": 1.0516148238801056e-26,
            "vacuum_frequency_margin_Mpl2": 6.292047577098258e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.5493257717780747e-22,
            "right_raychaudhuri_residual_Mpl2": -8.997886021744807e-22,
            "left_normalized_residual": 1.922356303387535e-09,
            "right_normalized_residual": -4.873360505520376e-09,
            "bracket_width_N_local": 1.3393741098036778e-05
          },
          {
            "left_index": 70,
            "right_index": 71,
            "fraction": 0.047099575065959104,
            "N_local": 0.0009381932721551563,
            "N_physical": -56.635079275733936,
            "H_Mpl": 4.296906134321862e-07,
            "required_standard_density_Mpl4": 2.4692151081577868e-26,
            "vacuum_frequency_margin_Mpl2": 6.290728777635009e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 5.890382125923059e-23,
            "right_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
            "left_normalized_residual": 3.190301549322586e-10,
            "right_normalized_residual": -6.454495453235951e-09,
            "bracket_width_N_local": 1.3393737338068313e-05
          },
          {
            "left_index": 71,
            "right_index": 72,
            "fraction": 0.5614620610416048,
            "N_local": 0.0009584762452410652,
            "N_physical": -56.95618282563535,
            "H_Mpl": 4.296905887515237e-07,
            "required_standard_density_Mpl4": 8.467609511956364e-26,
            "vacuum_frequency_margin_Mpl2": 6.290460528983634e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
            "right_raychaudhuri_residual_Mpl2": 9.308093924205628e-22,
            "left_normalized_residual": -6.454495453235951e-09,
            "right_normalized_residual": 5.041375983482935e-09,
            "bracket_width_N_local": 1.339373682891006e-05
          },
          {
            "left_index": 73,
            "right_index": 74,
            "fraction": 0.4348853540070985,
            "N_local": 0.0009835683828234758,
            "N_physical": -56.62021285300039,
            "H_Mpl": 4.2969055733943505e-07,
            "required_standard_density_Mpl4": 3.015939093992669e-26,
            "vacuum_frequency_margin_Mpl2": 6.2901239722949215e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.194690813740266e-21,
            "right_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
            "left_normalized_residual": 6.47059010702358e-09,
            "right_normalized_residual": -8.408251725070025e-09,
            "bracket_width_N_local": 1.3393735783597243e-05
          },
          {
            "left_index": 74,
            "right_index": 75,
            "fraction": 0.5675920042901169,
            "N_local": 0.0009987395561132746,
            "N_physical": -55.832306400564924,
            "H_Mpl": 4.296905378492746e-07,
            "required_standard_density_Mpl4": 3.66165402285607e-27,
            "vacuum_frequency_margin_Mpl2": 6.289917856371982e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
            "right_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
            "left_normalized_residual": -8.408251725070025e-09,
            "right_normalized_residual": 6.405649730889708e-09,
            "bracket_width_N_local": 1.3393735247269316e-05
          },
          {
            "left_index": 75,
            "right_index": 76,
            "fraction": 0.46870607498227307,
            "N_local": 0.0010108088391480106,
            "N_physical": -55.995256347003696,
            "H_Mpl": 4.296905220722735e-07,
            "required_standard_density_Mpl4": 1.1627710255761945e-26,
            "vacuum_frequency_margin_Mpl2": 6.289752465737699e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
            "right_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
            "left_normalized_residual": 6.405649730889708e-09,
            "right_normalized_residual": -7.261017616518347e-09,
            "bracket_width_N_local": 1.3393734701716781e-05
          },
          {
            "left_index": 76,
            "right_index": 77,
            "fraction": 0.9123702377387957,
            "N_local": 0.001030144893436112,
            "N_physical": -56.94665879344938,
            "H_Mpl": 4.296904963167453e-07,
            "required_standard_density_Mpl4": 8.540104780800767e-26,
            "vacuum_frequency_margin_Mpl2": 6.289485018541246e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
            "right_raychaudhuri_residual_Mpl2": 1.2876254256938986e-22,
            "left_normalized_residual": -7.261017616518347e-09,
            "right_normalized_residual": 6.973937491092083e-10,
            "bracket_width_N_local": 1.3393734146858972e-05
          },
          {
            "left_index": 89,
            "right_index": 90,
            "fraction": 0.9686572376319323,
            "N_local": 0.0012050172758680136,
            "N_physical": -56.82090151317981,
            "H_Mpl": 4.296902338903307e-07,
            "required_standard_density_Mpl4": 4.95451873713127e-26,
            "vacuum_frequency_margin_Mpl2": 6.286919107523303e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3204165946425948e-21,
            "right_raychaudhuri_residual_Mpl2": 4.272461087877763e-23,
            "left_normalized_residual": -7.1515464632206394e-09,
            "right_normalized_residual": 2.3140202296214582e-10,
            "bracket_width_N_local": 1.3393726058015575e-05
          },
          {
            "left_index": 92,
            "right_index": 93,
            "fraction": 0.024259324250412394,
            "N_local": 0.0012325494449634913,
            "N_physical": -56.850344980674116,
            "H_Mpl": 4.296901875854801e-07,
            "required_standard_density_Mpl4": 5.534209017110175e-26,
            "vacuum_frequency_margin_Mpl2": 6.28649117473157e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.0142619240537e-23,
            "right_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
            "left_normalized_residual": 2.1741766762132975e-10,
            "right_normalized_residual": -8.7448142610148e-09,
            "bracket_width_N_local": 1.3393723951315778e-05
          },
          {
            "left_index": 93,
            "right_index": 94,
            "fraction": 0.4848703013313575,
            "N_local": 0.0012521124648400947,
            "N_physical": -56.9863466284211,
            "H_Mpl": 4.2969015377855907e-07,
            "required_standard_density_Mpl4": 1.053735996171995e-25,
            "vacuum_frequency_margin_Mpl2": 6.286182970155485e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
            "right_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
            "left_normalized_residual": -8.7448142610148e-09,
            "right_normalized_residual": 9.290554634716903e-09,
            "bracket_width_N_local": 1.3393723228069879e-05
          },
          {
            "left_index": 94,
            "right_index": 95,
            "fraction": 0.4549072309281898,
            "N_local": 0.0012651048706622495,
            "N_physical": -56.997242900768406,
            "H_Mpl": 4.296901309484704e-07,
            "required_standard_density_Mpl4": 1.1016369238939384e-25,
            "vacuum_frequency_margin_Mpl2": 6.285976581984483e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
            "right_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
            "left_normalized_residual": 9.290554634716903e-09,
            "right_normalized_residual": -1.113241198825085e-08,
            "bracket_width_N_local": 1.3393722494135915e-05
          },
          {
            "left_index": 95,
            "right_index": 96,
            "fraction": 0.7538644082141279,
            "N_local": 0.0012825027420651565,
            "N_physical": -56.88732829339666,
            "H_Mpl": 4.2969009987700475e-07,
            "required_standard_density_Mpl4": 6.420356596172189e-26,
            "vacuum_frequency_margin_Mpl2": 6.2856979866767695e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
            "right_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
            "left_normalized_residual": -1.113241198825085e-08,
            "right_normalized_residual": 3.634716123765566e-09,
            "bracket_width_N_local": 1.3393721749403948e-05
          },
          {
            "left_index": 96,
            "right_index": 97,
            "fraction": 0.7092775479346664,
            "N_local": 0.001295299279278346,
            "N_physical": -56.97299511970861,
            "H_Mpl": 4.296900766345335e-07,
            "required_standard_density_Mpl4": 9.217305944021855e-26,
            "vacuum_frequency_margin_Mpl2": 6.285491362413646e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
            "right_raychaudhuri_residual_Mpl2": -2.75070198710292e-22,
            "left_normalized_residual": 3.634716123765566e-09,
            "right_normalized_residual": -1.4898169372979586e-09,
            "bracket_width_N_local": 1.3393720993773364e-05
          },
          {
            "left_index": 98,
            "right_index": 99,
            "fraction": 0.4569399285322861,
            "N_local": 0.0013187069801230823,
            "N_physical": -56.82730406410569,
            "H_Mpl": 4.29690033281348e-07,
            "required_standard_density_Mpl4": 6.073586449968256e-26,
            "vacuum_frequency_margin_Mpl2": 6.285109757800073e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.944762113653646e-22,
            "right_raychaudhuri_residual_Mpl2": 1.1819066111200154e-21,
            "left_normalized_residual": -5.386216613824514e-09,
            "right_normalized_residual": 6.4013655597193205e-09,
            "bracket_width_N_local": 1.3393719449427549e-05
          },
          {
            "left_index": 101,
            "right_index": 102,
            "fraction": 0.4981349024957319,
            "N_local": 0.001359439888821723,
            "N_physical": -56.70056065100801,
            "H_Mpl": 4.2968995523825917e-07,
            "required_standard_density_Mpl4": 3.1665149012667346e-26,
            "vacuum_frequency_margin_Mpl2": 6.284434543407456e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.0692527777417256e-21,
            "right_raychaudhuri_residual_Mpl2": -1.0772596878265491e-21,
            "left_normalized_residual": 5.791218593121455e-09,
            "right_normalized_residual": -5.83458581994365e-09,
            "bracket_width_N_local": 1.3393717048993748e-05
          },
          {
            "left_index": 114,
            "right_index": 115,
            "fraction": 0.8582876521016599,
            "N_local": 0.0015383819170730285,
            "N_physical": -57.02543001641031,
            "H_Mpl": 4.296895721023366e-07,
            "required_standard_density_Mpl4": 1.1146909461019985e-25,
            "vacuum_frequency_margin_Mpl2": 6.281299647025049e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2661559056265394e-21,
            "right_raychaudhuri_residual_Mpl2": -2.0905570032648377e-22,
            "left_normalized_residual": 6.857684532074395e-09,
            "right_normalized_residual": -1.1322762412690418e-09,
            "bracket_width_N_local": 1.3393705454777492e-05
          },
          {
            "left_index": 116,
            "right_index": 117,
            "fraction": 0.43422312123954604,
            "N_local": 0.001559489530737296,
            "N_physical": -57.1789623682144,
            "H_Mpl": 4.2968952243814917e-07,
            "required_standard_density_Mpl4": 2.0622346831073145e-25,
            "vacuum_frequency_margin_Mpl2": 6.280911635012511e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -7.285056987183484e-22,
            "right_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
            "left_normalized_residual": -3.9456939643992105e-09,
            "right_normalized_residual": 5.141095987972354e-09,
            "bracket_width_N_local": 1.3393703494664864e-05
          },
          {
            "left_index": 117,
            "right_index": 118,
            "fraction": 0.9878589932033509,
            "N_local": 0.001580298467958751,
            "N_physical": -57.16308991401113,
            "H_Mpl": 4.2968947258953135e-07,
            "required_standard_density_Mpl4": 1.9334187724532636e-25,
            "vacuum_frequency_margin_Mpl2": 6.280525645903106e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1666079949267927e-23,
            "left_normalized_residual": 5.141095987972354e-09,
            "right_normalized_residual": -6.318522291659054e-11,
            "bracket_width_N_local": 1.339370249623978e-05
          },
          {
            "left_index": 119,
            "right_index": 120,
            "fraction": 0.8428465471001942,
            "N_local": 0.0016051436166644778,
            "N_physical": -57.16339033749111,
            "H_Mpl": 4.296894117252259e-07,
            "required_standard_density_Mpl4": 1.9369378485244054e-25,
            "vacuum_frequency_margin_Mpl2": 6.280059616028694e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.306399063187383e-22,
            "right_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "left_normalized_residual": -2.8740250373060523e-09,
            "right_normalized_residual": 5.358781255435093e-10,
            "bracket_width_N_local": 1.3393700462002202e-05
          },
          {
            "left_index": 120,
            "right_index": 121,
            "fraction": 0.09178239976574161,
            "N_local": 0.001608477788814241,
            "N_physical": -57.15354798384819,
            "H_Mpl": 4.296894034642662e-07,
            "required_standard_density_Mpl4": 1.8655455109898024e-25,
            "vacuum_frequency_margin_Mpl2": 6.279996722973984e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "right_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
            "left_normalized_residual": 5.358781255435093e-10,
            "right_normalized_residual": -5.302694440333927e-09,
            "bracket_width_N_local": 1.3393699425939256e-05
          },
          {
            "left_index": 121,
            "right_index": 122,
            "fraction": 0.5318905792781098,
            "N_local": 0.0016277661643535953,
            "N_physical": -56.998728930731936,
            "H_Mpl": 4.2968935508388884e-07,
            "required_standard_density_Mpl4": 1.0699821571821313e-25,
            "vacuum_frequency_margin_Mpl2": 6.279630665950597e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
            "right_raychaudhuri_residual_Mpl2": 8.616500379152947e-22,
            "left_normalized_residual": -5.302694440333927e-09,
            "right_normalized_residual": 4.666827559239031e-09,
            "bracket_width_N_local": 1.3393698377093784e-05
          }
        ]
      }
    ],
    "successive_exact_initial_probe_deltas": [
      {
        "abs_delta_N_physical": 0.0,
        "relative_delta_required_standard_density": 0.0,
        "abs_delta_quantum_rho_over_H2": 0.0,
        "abs_delta_quantum_pressure_over_H2": 0.0,
        "abs_delta_quantum_chi2_over_scale": 0.0,
        "abs_delta_friedmann_normalized": 0.0,
        "abs_delta_raychaudhuri_normalized": 0.0,
        "coarse_nodes": 17,
        "fine_nodes": 33,
        "coarse_stride": 16,
        "fine_stride": 8,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64
      },
      {
        "abs_delta_N_physical": 0.0,
        "relative_delta_required_standard_density": 0.0,
        "abs_delta_quantum_rho_over_H2": 0.0,
        "abs_delta_quantum_pressure_over_H2": 0.0,
        "abs_delta_quantum_chi2_over_scale": 0.0,
        "abs_delta_friedmann_normalized": 0.0,
        "abs_delta_raychaudhuri_normalized": 0.0,
        "coarse_nodes": 33,
        "fine_nodes": 65,
        "coarse_stride": 8,
        "fine_stride": 4,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64
      },
      {
        "abs_delta_N_physical": 0.0,
        "relative_delta_required_standard_density": 0.0,
        "abs_delta_quantum_rho_over_H2": 0.0,
        "abs_delta_quantum_pressure_over_H2": 0.0,
        "abs_delta_quantum_chi2_over_scale": 0.0,
        "abs_delta_friedmann_normalized": 0.0,
        "abs_delta_raychaudhuri_normalized": 0.0,
        "coarse_nodes": 65,
        "fine_nodes": 129,
        "coarse_stride": 4,
        "fine_stride": 2,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64
      }
    ],
    "root_scan_diagnostic_successive_selection_deltas": [
      {
        "coarse_nodes": 17,
        "fine_nodes": 33,
        "coarse_stride": 16,
        "fine_stride": 8,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64,
        "abs_delta_N_local": 0.0001992607308503197,
        "abs_delta_N_physical": 0.6694145179659827,
        "relative_delta_H": 1.2141172459484253e-07,
        "relative_delta_required_standard_density": 0.7189963035808501
      },
      {
        "coarse_nodes": 33,
        "fine_nodes": 65,
        "coarse_stride": 8,
        "fine_stride": 4,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64,
        "abs_delta_N_local": 0.00020173766990161957,
        "abs_delta_N_physical": 1.162205138685394,
        "relative_delta_H": 1.2406268332517664e-07,
        "relative_delta_required_standard_density": 92.56380986958494
      },
      {
        "coarse_nodes": 65,
        "fine_nodes": 129,
        "coarse_stride": 4,
        "fine_stride": 2,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64,
        "abs_delta_N_local": 5.4397098034619594e-05,
        "abs_delta_N_physical": 0.0015278964201144163,
        "relative_delta_H": 2.6475743886615266e-08,
        "relative_delta_required_standard_density": 0.12885748267902528
      }
    ]
  },
  "curvature_tail_time_pilot": {
    "levels": [
      {
        "stride": 4,
        "nodes": 3841,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "Hdot0_Mpl2": -7.610360106610851e-17,
        "curvature_tail_initial": {
          "rho": -6.551101685815108e-21,
          "pressure": 8.6775629393721e-21,
          "chi2": 1.7722849653064216e-15
        },
        "last_octave_rho_over_total": 8.322855368349601e-07,
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97495610793557,
          "N_offset_physical_minus_local": -56.97495610793557,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.108904253367216e-26,
          "standard_pressure_Mpl4": 3.0363014177890724e-26,
          "quantum_rho_Mpl4": 2.5653537420603665e-21,
          "quantum_pressure_Mpl4": 5.840734297337593e-21,
          "quantum_chi2_Mpl2": 1.7722866157723746e-15,
          "friedmann_residual_Mpl4": 0.0,
          "friedmann_normalized": 0.0,
          "raychaudhuri_residual_Mpl2": -6.7505291496701305e-21,
          "raychaudhuri_normalized": -3.6561576899567873e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        }
      },
      {
        "stride": 2,
        "nodes": 7681,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "Hdot0_Mpl2": -7.610360106610851e-17,
        "curvature_tail_initial": {
          "rho": -6.551102839031144e-21,
          "pressure": 8.623565723413397e-21,
          "chi2": 1.771701022782825e-15
        },
        "last_octave_rho_over_total": 9.552119372810032e-07,
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97810131892663,
          "N_offset_physical_minus_local": -56.97810131892663,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.224225856949213e-26,
          "standard_pressure_Mpl4": 3.074741952316392e-26,
          "quantum_rho_Mpl4": 2.5653525888443307e-21,
          "quantum_pressure_Mpl4": 5.78673708137889e-21,
          "quantum_chi2_Mpl2": 1.771702673248778e-15,
          "friedmann_residual_Mpl4": 3.7882142165171375e-40,
          "friedmann_normalized": 6.839122401537743e-28,
          "raychaudhuri_residual_Mpl2": -6.777527565437822e-21,
          "raychaudhuri_normalized": -3.67078031630757e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        }
      },
      {
        "stride": 1,
        "nodes": 15361,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "Hdot0_Mpl2": -7.610360106610851e-17,
        "curvature_tail_initial": {
          "rho": -6.551100775796261e-21,
          "pressure": 8.790755548572385e-21,
          "chi2": 1.7684861469751866e-15
        },
        "last_octave_rho_over_total": 1.157141718655048e-06,
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537878e-21,
          "quantum_chi2_Mpl2": 1.7684877974411396e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        }
      }
    ],
    "successive_exact_initial_probe_deltas": [
      {
        "abs_delta_N_physical": 0.003145210991064573,
        "relative_delta_required_standard_density": 0.01250203598333592,
        "abs_delta_quantum_rho_over_H2": 6.245939516831339e-15,
        "abs_delta_quantum_pressure_over_H2": 2.924546090928536e-10,
        "abs_delta_quantum_chi2_over_scale": 9.018550662002347e-12,
        "abs_delta_friedmann_normalized": 6.839122401537743e-28,
        "abs_delta_raychaudhuri_normalized": 1.462262635078266e-10,
        "coarse_nodes": 3841,
        "fine_nodes": 7681,
        "coarse_stride": 4,
        "fine_stride": 2,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64
      },
      {
        "abs_delta_N_physical": 0.005655378697845492,
        "relative_delta_required_standard_density": 0.022879321580293828,
        "abs_delta_quantum_rho_over_H2": 1.1174697442845654e-14,
        "abs_delta_quantum_pressure_over_H2": 9.055177029602703e-10,
        "abs_delta_quantum_chi2_over_scale": 4.965132555282514e-11,
        "abs_delta_friedmann_normalized": 1.5750706136874802e-27,
        "abs_delta_raychaudhuri_normalized": 4.5275698898883915e-10,
        "coarse_nodes": 7681,
        "fine_nodes": 15361,
        "coarse_stride": 2,
        "fine_stride": 1,
        "coarse_mode_nodes": 64,
        "fine_mode_nodes": 64
      }
    ]
  },
  "momentum_pilot": {
    "levels": [
      {
        "prefix_intervals": 256,
        "stride": 2,
        "nodes": 129,
        "mode_nodes": 24,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 82,
        "simultaneous_sign_change_brackets": 38,
        "positive_frequency_brackets": 38,
        "selected_earliest_admissible": {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878218636318041,
          "N_local": 7.752066974071143e-05,
          "N_physical": -56.632994026199036,
          "H_Mpl": 4.296911741312159e-07,
          "required_standard_density_Mpl4": 2.3197704838882924e-26,
          "vacuum_frequency_margin_Mpl2": 6.298838762390164e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720130737462458e-22,
          "right_raychaudhuri_residual_Mpl2": 1.2712373056926067e-22,
          "left_normalized_residual": -2.5564726820888543e-09,
          "right_normalized_residual": 6.885155668002273e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.952040483060934,
          "N_offset_physical_minus_local": -56.952040483060934,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 8.311082997598541e-26,
          "standard_pressure_Mpl4": 2.770360999199491e-26,
          "quantum_rho_Mpl4": 2.565361720272924e-21,
          "quantum_pressure_Mpl4": 5.953953967622372e-21,
          "quantum_chi2_Mpl2": 1.756705185333028e-15,
          "friedmann_residual_Mpl4": 6.658073471454363e-40,
          "friedmann_normalized": 1.2020275736036033e-27,
          "raychaudhuri_residual_Mpl2": -6.693920644224442e-21,
          "raychaudhuri_normalized": -3.625497927156958e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693920644224442e-21,
        "initial_normalized_residual": -3.625497927156958e-08,
        "wronskian_relative_error": 3.52e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 5,
            "right_index": 6,
            "fraction": 0.7878218636318041,
            "N_local": 7.752066974071143e-05,
            "N_physical": -56.632994026199036,
            "H_Mpl": 4.296911741312159e-07,
            "required_standard_density_Mpl4": 2.3197704838882924e-26,
            "vacuum_frequency_margin_Mpl2": 6.298838762390164e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -4.720130737462458e-22,
            "right_raychaudhuri_residual_Mpl2": 1.2712373056926067e-22,
            "left_normalized_residual": -2.5564726820888543e-09,
            "right_normalized_residual": 6.885155668002273e-10,
            "bracket_width_N_local": 1.339375507064178e-05
          },
          {
            "left_index": 6,
            "right_index": 7,
            "fraction": 0.3642629608311855,
            "N_local": 8.524138057429921e-05,
            "N_physical": -56.69164260233723,
            "H_Mpl": 4.296911723470496e-07,
            "required_standard_density_Mpl4": 3.0758191989938875e-26,
            "vacuum_frequency_margin_Mpl2": 6.298794360806752e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2712373056926067e-22,
            "right_raychaudhuri_residual_Mpl2": -2.2186517096271547e-22,
            "left_normalized_residual": 6.885155668002273e-10,
            "right_normalized_residual": -1.2016452434811902e-09,
            "bracket_width_N_local": 1.3393754974687068e-05
          },
          {
            "left_index": 10,
            "right_index": 11,
            "fraction": 0.9413473893081634,
            "N_local": 0.0001465457268927834,
            "N_physical": -56.81600680180519,
            "H_Mpl": 4.2969115669099316e-07,
            "required_standard_density_Mpl4": 4.9885357821205014e-26,
            "vacuum_frequency_margin_Mpl2": 6.298424066316216e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5391861027143146e-21,
            "right_raychaudhuri_residual_Mpl2": -9.590219752044633e-23,
            "left_normalized_residual": 8.336395203337908e-09,
            "right_normalized_residual": -5.194164835867535e-10,
            "bracket_width_N_local": 1.3393754550492778e-05
          },
          {
            "left_index": 14,
            "right_index": 15,
            "fraction": 0.11549642969064501,
            "N_local": 0.0001890594992722995,
            "N_physical": -56.93756461944729,
            "H_Mpl": 4.296911441259377e-07,
            "required_standard_density_Mpl4": 8.125889404914153e-26,
            "vacuum_frequency_margin_Mpl2": 6.2981480893425384e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5515154971692504e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1881934362059777e-21,
            "left_normalized_residual": 8.403173118975775e-10,
            "right_normalized_residual": -6.435382281901024e-09,
            "bracket_width_N_local": 1.3393754057482415e-05
          },
          {
            "left_index": 17,
            "right_index": 18,
            "fraction": 0.08742267958427188,
            "N_local": 0.0002288647480949639,
            "N_physical": -56.74338278240312,
            "H_Mpl": 4.296911310120215e-07,
            "required_standard_density_Mpl4": 3.8661461595514955e-26,
            "vacuum_frequency_margin_Mpl2": 6.29787560476425e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.105002251690378e-23,
            "right_raychaudhuri_residual_Mpl2": 6.372816095861143e-22,
            "left_normalized_residual": -3.306534421119088e-10,
            "right_normalized_residual": 3.4515853350000067e-09,
            "bracket_width_N_local": 1.339375363908614e-05
          },
          {
            "left_index": 22,
            "right_index": 23,
            "fraction": 0.3109282551228123,
            "N_local": 0.00029882709311650343,
            "N_physical": -56.60763462682718,
            "H_Mpl": 4.296911045650164e-07,
            "required_standard_density_Mpl4": 3.0564741764923325e-26,
            "vacuum_frequency_margin_Mpl2": 6.297363410787697e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.998442532639252e-22,
            "right_raychaudhuri_residual_Mpl2": 6.6450764568295855e-22,
            "left_normalized_residual": -1.6239886891800126e-09,
            "right_normalized_residual": 3.599044892267386e-09,
            "bracket_width_N_local": 1.3393752842742138e-05
          },
          {
            "left_index": 23,
            "right_index": 24,
            "fraction": 0.5647171563519481,
            "N_local": 0.00031562003167792403,
            "N_physical": -56.574739330514966,
            "H_Mpl": 4.2969109755111726e-07,
            "required_standard_density_Mpl4": 3.311898651682732e-26,
            "vacuum_frequency_margin_Mpl2": 6.297234185169295e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.6450764568295855e-22,
            "right_raychaudhuri_residual_Mpl2": -5.122011512936614e-22,
            "left_normalized_residual": 3.599044892267386e-09,
            "right_normalized_residual": -2.7741366079643636e-09,
            "bracket_width_N_local": 1.3393752668113652e-05
          },
          {
            "left_index": 24,
            "right_index": 25,
            "fraction": 0.7237989598114215,
            "N_local": 0.0003311444865454097,
            "N_physical": -56.590319578811446,
            "H_Mpl": 4.2969109083988517e-07,
            "required_standard_density_Mpl4": 2.4783699219937013e-26,
            "vacuum_frequency_margin_Mpl2": 6.29711261476612e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.122011512936614e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9545550439856322e-22,
            "left_normalized_residual": -2.7741366079643636e-09,
            "right_normalized_residual": 1.0586080944610151e-09,
            "bracket_width_N_local": 1.3393752488282513e-05
          },
          {
            "left_index": 25,
            "right_index": 26,
            "fraction": 0.10861769095028793,
            "N_local": 0.00033629865336303816,
            "N_physical": -56.52295065860906,
            "H_Mpl": 4.2969108856930467e-07,
            "required_standard_density_Mpl4": 1.632294715167814e-26,
            "vacuum_frequency_margin_Mpl2": 6.297071861276627e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9545550439856322e-22,
            "right_raychaudhuri_residual_Mpl2": -1.6040258019018917e-21,
            "left_normalized_residual": 1.0586080944610151e-09,
            "right_normalized_residual": -8.687577003418813e-09,
            "bracket_width_N_local": 1.3393752303225248e-05
          },
          {
            "left_index": 33,
            "right_index": 34,
            "fraction": 0.13926962174921662,
            "N_local": 0.00044385921029726295,
            "N_physical": -56.56376027875831,
            "H_Mpl": 4.2969103521283754e-07,
            "required_standard_density_Mpl4": 1.8390939987308983e-26,
            "vacuum_frequency_margin_Mpl2": 6.296167423070462e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.346817207134511e-22,
            "right_raychaudhuri_residual_Mpl2": 1.4504073731310303e-21,
            "left_normalized_residual": -1.2710618265437261e-09,
            "right_normalized_residual": 7.855564988217522e-09,
            "bracket_width_N_local": 1.3393750630116873e-05
          },
          {
            "left_index": 34,
            "right_index": 35,
            "fraction": 0.5055272399122602,
            "N_local": 0.00046215852401300156,
            "N_physical": -56.57458662423859,
            "H_Mpl": 4.296910249770431e-07,
            "required_standard_density_Mpl4": 2.571830012847015e-26,
            "vacuum_frequency_margin_Mpl2": 6.296003522202786e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.4504073731310303e-21,
            "right_raychaudhuri_residual_Mpl2": -1.418690983236006e-21,
            "left_normalized_residual": 7.855564988217522e-09,
            "right_normalized_residual": -7.683785823388853e-09,
            "bracket_width_N_local": 1.3393750395837372e-05
          },
          {
            "left_index": 37,
            "right_index": 38,
            "fraction": 0.276125812241024,
            "N_local": 0.0004992672288069428,
            "N_physical": -56.93762018185274,
            "H_Mpl": 4.2969100314236153e-07,
            "required_standard_density_Mpl4": 7.981736123679241e-26,
            "vacuum_frequency_margin_Mpl2": 6.295662530834801e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.891542920940026e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5444901046846047e-21,
            "left_normalized_residual": -3.1909244394413767e-09,
            "right_normalized_residual": 8.365128584891796e-09,
            "bracket_width_N_local": 1.3393749656707803e-05
          },
          {
            "left_index": 38,
            "right_index": 39,
            "fraction": 0.6120500481314499,
            "N_local": 0.0005171602634243091,
            "N_physical": -56.99253316050132,
            "H_Mpl": 4.296909920560628e-07,
            "required_standard_density_Mpl4": 1.060345683575618e-25,
            "vacuum_frequency_margin_Mpl2": 6.295493822077319e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5444901046846047e-21,
            "right_raychaudhuri_residual_Mpl2": -9.7898017262333e-22,
            "left_normalized_residual": 8.365128584891796e-09,
            "right_normalized_residual": -5.3022646903302215e-09,
            "bracket_width_N_local": 1.3393749397776797e-05
          },
          {
            "left_index": 51,
            "right_index": 52,
            "fraction": 0.5175800610958081,
            "N_local": 0.0006900136735670953,
            "N_physical": -56.74792551302662,
            "H_Mpl": 4.296908650774178e-07,
            "required_standard_density_Mpl4": 3.6734690159206753e-26,
            "vacuum_frequency_margin_Mpl2": 6.293722225096286e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2188684917175272e-21,
            "right_raychaudhuri_residual_Mpl2": -1.1360686152818574e-21,
            "left_normalized_residual": 6.601529931363605e-09,
            "right_normalized_residual": -6.153076736594218e-09,
            "bracket_width_N_local": 1.3393745416623716e-05
          },
          {
            "left_index": 52,
            "right_index": 53,
            "fraction": 0.605724418068719,
            "N_local": 0.0007045880018459338,
            "N_physical": -56.913771421324846,
            "H_Mpl": 4.2969085267255115e-07,
            "required_standard_density_Mpl4": 8.090900160206902e-26,
            "vacuum_frequency_margin_Mpl2": 6.2935610924018695e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1360686152818574e-21,
            "right_raychaudhuri_residual_Mpl2": 7.394849886228333e-22,
            "left_normalized_residual": -6.153076736594218e-09,
            "right_normalized_residual": 4.005134956587216e-09,
            "bracket_width_N_local": 1.3393745061689535e-05
          },
          {
            "left_index": 55,
            "right_index": 56,
            "fraction": 0.4213549325273889,
            "N_local": 0.0007422998375837658,
            "N_physical": -57.01509376633059,
            "H_Mpl": 4.296908192883742e-07,
            "required_standard_density_Mpl4": 1.1423856538356398e-25,
            "vacuum_frequency_margin_Mpl2": 6.293135635828252e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.1468762964365425e-22,
            "right_raychaudhuri_residual_Mpl2": -5.694888867109958e-22,
            "left_normalized_residual": 2.245995700188187e-09,
            "right_normalized_residual": -3.084417214585183e-09,
            "bracket_width_N_local": 1.3393743953274851e-05
          },
          {
            "left_index": 56,
            "right_index": 57,
            "fraction": 0.7437032561652872,
            "N_local": 0.0007600110321617558,
            "N_physical": -56.87962543128211,
            "H_Mpl": 4.296908029617291e-07,
            "required_standard_density_Mpl4": 6.232692584897697e-26,
            "vacuum_frequency_margin_Mpl2": 6.292931638020909e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.694888867109958e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9625858311644235e-22,
            "left_normalized_residual": -3.084417214585183e-09,
            "right_normalized_residual": 1.062959087504521e-09,
            "bracket_width_N_local": 1.3393743568903388e-05
          },
          {
            "left_index": 57,
            "right_index": 58,
            "fraction": 0.4514139162492868,
            "N_local": 0.0007694899270869379,
            "N_physical": -56.931258044471065,
            "H_Mpl": 4.29690794036849e-07,
            "required_standard_density_Mpl4": 7.927004785751863e-26,
            "vacuum_frequency_margin_Mpl2": 6.292821284196655e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9625858311644235e-22,
            "right_raychaudhuri_residual_Mpl2": -2.385055569595171e-22,
            "left_normalized_residual": 1.062959087504521e-09,
            "right_normalized_residual": -1.2917736394072443e-09,
            "bracket_width_N_local": 1.3393743176885482e-05
          },
          {
            "left_index": 60,
            "right_index": 61,
            "fraction": 0.6625219412326159,
            "N_local": 0.0008124986812692087,
            "N_physical": -56.66582825554061,
            "H_Mpl": 4.296907519909621e-07,
            "required_standard_density_Mpl4": 2.789200352206314e-26,
            "vacuum_frequency_margin_Mpl2": 6.292311073409497e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.0632697424233701e-21,
            "right_raychaudhuri_residual_Mpl2": 5.416125659952262e-22,
            "left_normalized_residual": -5.758792413808427e-09,
            "right_normalized_residual": 2.933436744509508e-09,
            "bracket_width_N_local": 1.339374195376004e-05
          },
          {
            "left_index": 62,
            "right_index": 63,
            "fraction": 0.282887480288517,
            "N_local": 0.0008342014385042497,
            "N_physical": -56.06006583522319,
            "H_Mpl": 4.296907297633613e-07,
            "required_standard_density_Mpl4": 3.498514943209665e-27,
            "vacuum_frequency_margin_Mpl2": 6.2920475754838106e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.5494491289160525e-22,
            "right_raychaudhuri_residual_Mpl2": -8.99776266460683e-22,
            "left_normalized_residual": 1.9224231150545972e-09,
            "right_normalized_residual": -4.8732936938489635e-09,
            "bracket_width_N_local": 1.3393741098036778e-05
          },
          {
            "left_index": 70,
            "right_index": 71,
            "fraction": 0.04710941972609012,
            "N_local": 0.0009381934040119483,
            "N_physical": -56.54262850157841,
            "H_Mpl": 4.296906134320268e-07,
            "required_standard_density_Mpl4": 1.76773790228934e-26,
            "vacuum_frequency_margin_Mpl2": 6.290728775896796e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 5.891613163087179e-23,
            "right_raychaudhuri_residual_Mpl2": -1.1917070340423595e-21,
            "left_normalized_residual": 3.190968293803336e-10,
            "right_normalized_residual": -6.454428596130675e-09,
            "bracket_width_N_local": 1.3393737338068313e-05
          },
          {
            "left_index": 71,
            "right_index": 72,
            "fraction": 0.5614562475093277,
            "N_local": 0.0009584761673761439,
            "N_physical": -56.93453205914418,
            "H_Mpl": 4.296905887516195e-07,
            "required_standard_density_Mpl4": 7.768046559313933e-26,
            "vacuum_frequency_margin_Mpl2": 6.290460530019069e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1917070340423595e-21,
            "right_raychaudhuri_residual_Mpl2": 9.308217281343606e-22,
            "left_normalized_residual": -6.454428596130675e-09,
            "right_normalized_residual": 5.041442795197326e-09,
            "bracket_width_N_local": 1.339373682891006e-05
          },
          {
            "left_index": 73,
            "right_index": 74,
            "fraction": 0.43488983919890944,
            "N_local": 0.0009835684428969498,
            "N_physical": -56.38918734935713,
            "H_Mpl": 4.2969055733935855e-07,
            "required_standard_density_Mpl4": 2.3141510282155108e-26,
            "vacuum_frequency_margin_Mpl2": 6.29012397148223e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.1947031242105148e-21,
            "right_raychaudhuri_residual_Mpl2": -1.5524365339871163e-21,
            "left_normalized_residual": 6.4706567820210675e-09,
            "right_normalized_residual": -8.408184913345116e-09,
            "bracket_width_N_local": 1.3393735783597243e-05
          },
          {
            "left_index": 76,
            "right_index": 77,
            "fraction": 0.91236185460444,
            "N_local": 0.001030144781154639,
            "N_physical": -56.921180542154566,
            "H_Mpl": 4.2969049631689576e-07,
            "required_standard_density_Mpl4": 7.842884506615522e-26,
            "vacuum_frequency_margin_Mpl2": 6.289485020099031e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3406179565126475e-21,
            "right_raychaudhuri_residual_Mpl2": 1.287748614212858e-22,
            "left_normalized_residual": -7.260950941504702e-09,
            "right_normalized_residual": 6.974604695244548e-10,
            "bracket_width_N_local": 1.3393734146858972e-05
          },
          {
            "left_index": 89,
            "right_index": 90,
            "fraction": 0.9686482065517606,
            "N_local": 0.0012050171549081996,
            "N_physical": -56.78219536782073,
            "H_Mpl": 4.296902338905297e-07,
            "required_standard_density_Mpl4": 4.2529441996659365e-26,
            "vacuum_frequency_margin_Mpl2": 6.28691910938257e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3204042757906989e-21,
            "right_raychaudhuri_residual_Mpl2": 4.273692125041883e-23,
            "left_normalized_residual": -7.151479742731011e-09,
            "right_normalized_residual": 2.3146869752845777e-10,
            "bracket_width_N_local": 1.3393726058015575e-05
          },
          {
            "left_index": 92,
            "right_index": 93,
            "fraction": 0.024266763939932597,
            "N_local": 0.001232549544608639,
            "N_physical": -56.81644093784453,
            "H_Mpl": 4.2969018758530873e-07,
            "required_standard_density_Mpl4": 4.83256551767023e-26,
            "vacuum_frequency_margin_Mpl2": 6.2864911731655225e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.0154929710785815e-23,
            "right_raychaudhuri_residual_Mpl2": -1.6145745517388676e-21,
            "left_normalized_residual": 2.1748434273569588e-10,
            "right_normalized_residual": -8.744747540497185e-09,
            "bracket_width_N_local": 1.3393723951315778e-05
          },
          {
            "left_index": 93,
            "right_index": 94,
            "fraction": 0.48486660190487285,
            "N_local": 0.0012521124152910003,
            "N_physical": -56.965158704231285,
            "H_Mpl": 4.296901537786455e-07,
            "required_standard_density_Mpl4": 9.840604486651191e-26,
            "vacuum_frequency_margin_Mpl2": 6.286182970939913e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.6145745517388676e-21,
            "right_raychaudhuri_residual_Mpl2": 1.7153610334215944e-21,
            "left_normalized_residual": -8.744747540497185e-09,
            "right_normalized_residual": 9.290621355241775e-09,
            "bracket_width_N_local": 1.3393723228069879e-05
          },
          {
            "left_index": 94,
            "right_index": 95,
            "fraction": 0.454910496853212,
            "N_local": 0.001265104914405143,
            "N_physical": -56.97669642428039,
            "H_Mpl": 4.2969013094839296e-07,
            "required_standard_density_Mpl4": 1.0317320502127516e-25,
            "vacuum_frequency_margin_Mpl2": 6.28597658128694e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7153610334215944e-21,
            "right_raychaudhuri_residual_Mpl2": -2.055404964038116e-21,
            "left_normalized_residual": 9.290621355241775e-09,
            "right_normalized_residual": -1.1132345313114721e-08,
            "bracket_width_N_local": 1.3393722494135915e-05
          },
          {
            "left_index": 95,
            "right_index": 96,
            "fraction": 0.7538598907913923,
            "N_local": 0.0012825026815600534,
            "N_physical": -56.85850392116257,
            "H_Mpl": 4.2969009987711344e-07,
            "required_standard_density_Mpl4": 5.722389417124539e-26,
            "vacuum_frequency_margin_Mpl2": 6.28569798764857e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.055404964038116e-21,
            "right_raychaudhuri_residual_Mpl2": 6.711029575869207e-22,
            "left_normalized_residual": -1.1132345313114721e-08,
            "right_normalized_residual": 3.6347828443052786e-09,
            "bracket_width_N_local": 1.3393721749403948e-05
          },
          {
            "left_index": 96,
            "right_index": 97,
            "fraction": 0.7092905677632287,
            "N_local": 0.0012952994536622972,
            "N_physical": -56.95242367566228,
            "H_Mpl": 4.296900766342156e-07,
            "required_standard_density_Mpl4": 8.520632796632194e-26,
            "vacuum_frequency_margin_Mpl2": 6.2854913595927184e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.711029575869207e-22,
            "right_raychaudhuri_residual_Mpl2": -2.750578798583961e-22,
            "left_normalized_residual": 3.6347828443052786e-09,
            "right_normalized_residual": -1.4897502167506632e-09,
            "bracket_width_N_local": 1.3393720993773364e-05
          },
          {
            "left_index": 98,
            "right_index": 99,
            "fraction": 0.4569342704070551,
            "N_local": 0.0013187069043397405,
            "N_physical": -56.779304261087084,
            "H_Mpl": 4.296900332814902e-07,
            "required_standard_density_Mpl4": 5.374159800523803e-26,
            "vacuum_frequency_margin_Mpl2": 6.2851097590434225e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.944639009937234e-22,
            "right_raychaudhuri_residual_Mpl2": 1.1819189299719113e-21,
            "left_normalized_residual": -5.386149939199723e-09,
            "right_normalized_residual": 6.401432280282112e-09,
            "bracket_width_N_local": 1.3393719449427549e-05
          },
          {
            "left_index": 101,
            "right_index": 102,
            "fraction": 0.49814063759881017,
            "N_local": 0.001359439965636071,
            "N_physical": -56.630773667387984,
            "H_Mpl": 4.296899552381088e-07,
            "required_standard_density_Mpl4": 2.464734060767976e-26,
            "vacuum_frequency_margin_Mpl2": 6.284434542120683e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.0692650882119744e-21,
            "right_raychaudhuri_residual_Mpl2": -1.0772473773563003e-21,
            "left_normalized_residual": 5.791285268304049e-09,
            "right_normalized_residual": -5.834519144752921e-09,
            "bracket_width_N_local": 1.3393717048993748e-05
          },
          {
            "left_index": 114,
            "right_index": 115,
            "fraction": 0.8582959847412699,
            "N_local": 0.0015383820286779492,
            "N_physical": -57.009277022770746,
            "H_Mpl": 4.296895721020778e-07,
            "required_standard_density_Mpl4": 1.0449470661455906e-25,
            "vacuum_frequency_margin_Mpl2": 6.28129964498867e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2661681907546316e-21,
            "right_raychaudhuri_residual_Mpl2": -2.090434067181368e-22,
            "left_normalized_residual": 6.857751070114867e-09,
            "right_normalized_residual": -1.1322096572886528e-09,
            "bracket_width_N_local": 1.3393705454777492e-05
          },
          {
            "left_index": 116,
            "right_index": 117,
            "fraction": 0.4342157958746595,
            "N_local": 0.0015594894326235306,
            "N_physical": -57.17032448690594,
            "H_Mpl": 4.2968952243838237e-07,
            "required_standard_density_Mpl4": 1.992341831731475e-25,
            "vacuum_frequency_margin_Mpl2": 6.2809116368252744e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -7.284934051100014e-22,
            "right_raychaudhuri_residual_Mpl2": 9.492286216591213e-22,
            "left_normalized_residual": -3.945627380409077e-09,
            "right_normalized_residual": 5.1411625260420396e-09,
            "bracket_width_N_local": 1.3393703494664864e-05
          },
          {
            "left_index": 117,
            "right_index": 118,
            "fraction": 0.9878717784597792,
            "N_local": 0.001580298639200672,
            "N_physical": -57.153844914050346,
            "H_Mpl": 4.296894725891193e-07,
            "required_standard_density_Mpl4": 1.8632386064259786e-25,
            "vacuum_frequency_margin_Mpl2": 6.280525642719541e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.492286216591213e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1653794821175694e-23,
            "left_normalized_residual": 5.1411625260420396e-09,
            "right_normalized_residual": -6.311868483692348e-11,
            "bracket_width_N_local": 1.339370249623978e-05
          },
          {
            "left_index": 119,
            "right_index": 120,
            "fraction": 0.8428270315282054,
            "N_local": 0.0016051433552787522,
            "N_physical": -57.15416151963356,
            "H_Mpl": 4.296894117258706e-07,
            "required_standard_density_Mpl4": 1.8668441228553679e-25,
            "vacuum_frequency_margin_Mpl2": 6.280059620948187e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.306276127103913e-22,
            "right_raychaudhuri_residual_Mpl2": 9.895306382327749e-23,
            "left_normalized_residual": -2.8739584532859524e-09,
            "right_normalized_residual": 5.359446647116602e-10,
            "bracket_width_N_local": 1.3393700462002202e-05
          },
          {
            "left_index": 120,
            "right_index": 121,
            "fraction": 0.09179379695141979,
            "N_local": 0.0016084779414647203,
            "N_physical": -57.14391533459248,
            "H_Mpl": 4.2968940346388504e-07,
            "required_standard_density_Mpl4": 1.7954099118725103e-25,
            "vacuum_frequency_margin_Mpl2": 6.279996720083441e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.895306382327749e-23,
            "right_raychaudhuri_residual_Mpl2": -9.790398628191036e-22,
            "left_normalized_residual": 5.359446647116602e-10,
            "right_normalized_residual": -5.302627856293225e-09,
            "bracket_width_N_local": 1.3393699425939256e-05
          },
          {
            "left_index": 121,
            "right_index": 122,
            "fraction": 0.5318839029684527,
            "N_local": 0.0016277660749331173,
            "N_physical": -56.9792741256401,
            "H_Mpl": 4.296893550841149e-07,
            "required_standard_density_Mpl4": 1.0000465370171191e-25,
            "vacuum_frequency_margin_Mpl2": 6.2796306676541076e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.790398628191036e-22,
            "right_raychaudhuri_residual_Mpl2": 8.61662323043387e-22,
            "left_normalized_residual": -5.302627856293225e-09,
            "right_normalized_residual": 4.666894097359877e-09,
            "bracket_width_N_local": 1.3393698377093784e-05
          }
        ]
      },
      {
        "prefix_intervals": 256,
        "stride": 2,
        "nodes": 129,
        "mode_nodes": 32,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 89,
        "simultaneous_sign_change_brackets": 46,
        "positive_frequency_brackets": 46,
        "selected_earliest_admissible": {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878424918659659,
          "N_local": 7.752094603022733e-05,
          "N_physical": -56.69916548479827,
          "H_Mpl": 4.296911741311537e-07,
          "required_standard_density_Mpl4": 3.0226135855542e-26,
          "vacuum_frequency_margin_Mpl2": 6.298838760821422e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720254262479897e-22,
          "right_raychaudhuri_residual_Mpl2": 1.2711136964889178e-22,
          "left_normalized_residual": -2.5565395845435113e-09,
          "right_normalized_residual": 6.884486187484683e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684762566172333e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 4.2e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 5,
            "right_index": 6,
            "fraction": 0.7878424918659659,
            "N_local": 7.752094603022733e-05,
            "N_physical": -56.69916548479827,
            "H_Mpl": 4.296911741311537e-07,
            "required_standard_density_Mpl4": 3.0226135855542e-26,
            "vacuum_frequency_margin_Mpl2": 6.298838760821422e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -4.720254262479897e-22,
            "right_raychaudhuri_residual_Mpl2": 1.2711136964889178e-22,
            "left_normalized_residual": -2.5565395845435113e-09,
            "right_normalized_residual": 6.884486187484683e-10,
            "bracket_width_N_local": 1.339375507064178e-05
          },
          {
            "left_index": 6,
            "right_index": 7,
            "fraction": 0.364227541594887,
            "N_local": 8.524090617772684e-05,
            "N_physical": -56.74698683115346,
            "H_Mpl": 4.296911723471609e-07,
            "required_standard_density_Mpl4": 3.7775176645002666e-26,
            "vacuum_frequency_margin_Mpl2": 6.298794363555188e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2711136964889178e-22,
            "right_raychaudhuri_residual_Mpl2": -2.2187753188308436e-22,
            "left_normalized_residual": 6.884486187484683e-10,
            "right_normalized_residual": -1.201712191533928e-09,
            "bracket_width_N_local": 1.3393754974687068e-05
          },
          {
            "left_index": 7,
            "right_index": 8,
            "fraction": 0.21241428628194792,
            "N_local": 9.660131158762097e-05,
            "N_physical": -56.700927088948404,
            "H_Mpl": 4.2969116965550983e-07,
            "required_standard_density_Mpl4": 4.093023348840733e-26,
            "vacuum_frequency_margin_Mpl2": 6.298728217568932e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.2187753188308436e-22,
            "right_raychaudhuri_residual_Mpl2": 8.226733585809187e-22,
            "left_normalized_residual": -1.201712191533928e-09,
            "right_normalized_residual": 4.455686032339831e-09,
            "bracket_width_N_local": 1.339375487477941e-05
          },
          {
            "left_index": 8,
            "right_index": 9,
            "fraction": 0.6065846247724822,
            "N_local": 0.00011527448729200055,
            "N_physical": -56.223771979160226,
            "H_Mpl": 4.2969116501791043e-07,
            "required_standard_density_Mpl4": 4.5139303881558215e-27,
            "vacuum_frequency_margin_Mpl2": 6.298616934763413e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 8.226733585809187e-22,
            "right_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
            "left_normalized_residual": 4.455686032339831e-09,
            "right_normalized_residual": -2.8898447940549242e-09,
            "bracket_width_N_local": 1.3393754770835335e-05
          },
          {
            "left_index": 9,
            "right_index": 10,
            "fraction": 0.2574202995656594,
            "N_local": 0.00012399162068847292,
            "N_physical": -56.32060338324056,
            "H_Mpl": 4.296911627704443e-07,
            "required_standard_density_Mpl4": 8.69484844629573e-27,
            "vacuum_frequency_margin_Mpl2": 6.298564016845657e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
            "left_normalized_residual": -2.8898447940549242e-09,
            "right_normalized_residual": 8.336328255348749e-09,
            "bracket_width_N_local": 1.3393754662768595e-05
          },
          {
            "left_index": 10,
            "right_index": 11,
            "fraction": 0.941339829513841,
            "N_local": 0.0001465456256387538,
            "N_physical": -56.851734465963354,
            "H_Mpl": 4.296911566910209e-07,
            "required_standard_density_Mpl4": 5.690277511795504e-26,
            "vacuum_frequency_margin_Mpl2": 6.298424066949671e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
            "right_raychaudhuri_residual_Mpl2": -9.591455845314117e-23,
            "left_normalized_residual": 8.336328255348749e-09,
            "right_normalized_residual": -5.194834317105734e-10,
            "bracket_width_N_local": 1.3393754550492778e-05
          },
          {
            "left_index": 14,
            "right_index": 15,
            "fraction": 0.11548722809982548,
            "N_local": 0.0001890593760284551,
            "N_physical": -56.960027140984835,
            "H_Mpl": 4.296911441259768e-07,
            "required_standard_density_Mpl4": 8.827708968758236e-26,
            "vacuum_frequency_margin_Mpl2": 6.298148090170559e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.551391888088821e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1882057971386725e-21,
            "left_normalized_residual": 8.402503639035793e-10,
            "right_normalized_residual": -6.435449230029863e-09,
            "bracket_width_N_local": 1.3393754057482415e-05
          },
          {
            "left_index": 17,
            "right_index": 18,
            "fraction": 0.08744034409863553,
            "N_local": 0.00022886498468911742,
            "N_physical": -56.78923199741035,
            "H_Mpl": 4.296911310119384e-07,
            "required_standard_density_Mpl4": 4.5680376275880174e-26,
            "vacuum_frequency_margin_Mpl2": 6.297875603092633e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.106235820604966e-23,
            "right_raychaudhuri_residual_Mpl2": 6.372692738969685e-22,
            "left_normalized_residual": -3.307202535217781e-10,
            "right_normalized_residual": 3.4515185235886736e-09,
            "bracket_width_N_local": 1.339375363908614e-05
          },
          {
            "left_index": 22,
            "right_index": 23,
            "fraction": 0.3109410648407037,
            "N_local": 0.00029882726468669887,
            "N_physical": -56.70810398465158,
            "H_Mpl": 4.2969110456494574e-07,
            "required_standard_density_Mpl4": 3.7581962067033493e-26,
            "vacuum_frequency_margin_Mpl2": 6.297363409476353e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.9985661419662003e-22,
            "right_raychaudhuri_residual_Mpl2": 6.644953100184646e-22,
            "left_normalized_residual": -1.6240556373194738e-09,
            "right_normalized_residual": 3.598978080981499e-09,
            "bracket_width_N_local": 1.3393752842742138e-05
          },
          {
            "left_index": 23,
            "right_index": 24,
            "fraction": 0.5647066610452707,
            "N_local": 0.0003156198911063822,
            "N_physical": -56.695311835554385,
            "H_Mpl": 4.296910975511769e-07,
            "required_standard_density_Mpl4": 4.013615947237264e-26,
            "vacuum_frequency_margin_Mpl2": 6.297234186259953e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.644953100184646e-22,
            "right_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "left_normalized_residual": 3.598978080981499e-09,
            "right_normalized_residual": -2.774203555973799e-09,
            "bracket_width_N_local": 1.3393752668113652e-05
          },
          {
            "left_index": 24,
            "right_index": 25,
            "fraction": 0.7238164271918855,
            "N_local": 0.0003311447204991803,
            "N_physical": -56.67592240321177,
            "H_Mpl": 4.2969109083978294e-07,
            "required_standard_density_Mpl4": 3.1800670545861125e-26,
            "vacuum_frequency_margin_Mpl2": 6.2971126129239e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
            "left_normalized_residual": -2.774203555973799e-09,
            "right_normalized_residual": 1.058541146449756e-09,
            "bracket_width_N_local": 1.3393752488282513e-05
          },
          {
            "left_index": 25,
            "right_index": 26,
            "fraction": 0.10861082179822887,
            "N_local": 0.00033629856135931695,
            "N_physical": -56.6223775919006,
            "H_Mpl": 4.2969108856934607e-07,
            "required_standard_density_Mpl4": 2.3340453548590064e-26,
            "vacuum_frequency_margin_Mpl2": 6.297071862011722e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
            "right_raychaudhuri_residual_Mpl2": -1.6040381628345865e-21,
            "left_normalized_residual": 1.058541146449756e-09,
            "right_normalized_residual": -8.687643951565464e-09,
            "bracket_width_N_local": 1.3393752303225248e-05
          },
          {
            "left_index": 30,
            "right_index": 31,
            "fraction": 0.8427289428470681,
            "N_local": 0.0004130999163473352,
            "N_physical": -56.65091947782211,
            "H_Mpl": 4.2969105162177203e-07,
            "required_standard_density_Mpl4": 3.344055211061206e-26,
            "vacuum_frequency_margin_Mpl2": 6.296436238914824e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.223594087232129e-21,
            "right_raychaudhuri_residual_Mpl2": 4.1496971920361313e-22,
            "left_normalized_residual": -1.2043227205322555e-08,
            "right_normalized_residual": 2.2475211642255185e-09,
            "bracket_width_N_local": 1.3393751298504256e-05
          },
          {
            "left_index": 32,
            "right_index": 33,
            "fraction": 0.8794008720663888,
            "N_local": 0.0004403785930398991,
            "N_physical": -56.60458671439098,
            "H_Mpl": 4.296910371192947e-07,
            "required_standard_density_Mpl4": 2.4223187493460128e-26,
            "vacuum_frequency_margin_Mpl2": 6.296198262521841e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7113735512347915e-21,
            "right_raychaudhuri_residual_Mpl2": -2.346940563779451e-22,
            "left_normalized_residual": 9.268985722633025e-09,
            "right_normalized_residual": -1.2711286378496756e-09,
            "bracket_width_N_local": 1.3393750858574967e-05
          },
          {
            "left_index": 33,
            "right_index": 34,
            "fraction": 0.13927694223128434,
            "N_local": 0.0004438593083459743,
            "N_physical": -56.650839420451234,
            "H_Mpl": 4.296910352127832e-07,
            "required_standard_density_Mpl4": 2.540855497514184e-26,
            "vacuum_frequency_margin_Mpl2": 6.296167422196462e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.346940563779451e-22,
            "right_raychaudhuri_residual_Mpl2": 1.4503950374665363e-21,
            "left_normalized_residual": -1.2711286378496756e-09,
            "right_normalized_residual": 7.855498176909263e-09,
            "bracket_width_N_local": 1.3393750630116873e-05
          },
          {
            "left_index": 34,
            "right_index": 35,
            "fraction": 0.5055229389350889,
            "N_local": 0.00046215846640678684,
            "N_physical": -56.67410985006656,
            "H_Mpl": 4.296910249770759e-07,
            "required_standard_density_Mpl4": 3.271033035804424e-26,
            "vacuum_frequency_margin_Mpl2": 6.296003522722937e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.4503950374665363e-21,
            "right_raychaudhuri_residual_Mpl2": -1.418703327331451e-21,
            "left_normalized_residual": 7.855498176909263e-09,
            "right_normalized_residual": -7.683852680362432e-09,
            "bracket_width_N_local": 1.3393750395837372e-05
          },
          {
            "left_index": 37,
            "right_index": 38,
            "fraction": 0.2761315966010662,
            "N_local": 0.000499267306281213,
            "N_physical": -56.959310334916786,
            "H_Mpl": 4.296910031423141e-07,
            "required_standard_density_Mpl4": 8.679834326107116e-26,
            "vacuum_frequency_margin_Mpl2": 6.2956625301084145e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.891666361894475e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5444777690201107e-21,
            "left_normalized_residual": -3.1909912964198733e-09,
            "right_normalized_residual": 8.365061773573706e-09,
            "bracket_width_N_local": 1.3393749656707803e-05
          },
          {
            "left_index": 38,
            "right_index": 39,
            "fraction": 0.612045159746284,
            "N_local": 0.0005171601979505031,
            "N_physical": -57.01135999033991,
            "H_Mpl": 4.296909920561039e-07,
            "required_standard_density_Mpl4": 1.1305188709035638e-25,
            "vacuum_frequency_margin_Mpl2": 6.2954938226987506e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5444777690201107e-21,
            "right_raychaudhuri_residual_Mpl2": -9.789925083371279e-22,
            "left_normalized_residual": 8.365061773573706e-09,
            "right_normalized_residual": -5.302331501917962e-09,
            "bracket_width_N_local": 1.3393749397776797e-05
          },
          {
            "left_index": 43,
            "right_index": 44,
            "fraction": 0.3686707604562576,
            "N_local": 0.0005808692459908588,
            "N_physical": -56.387682085002396,
            "H_Mpl": 4.2969094952328095e-07,
            "required_standard_density_Mpl4": 1.3813187764105545e-26,
            "vacuum_frequency_margin_Mpl2": 6.294870827937973e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -8.89864103757697e-22,
            "right_raychaudhuri_residual_Mpl2": 1.523845360633848e-21,
            "left_normalized_residual": -4.8196030257789005e-09,
            "right_normalized_residual": 8.253316438136793e-09,
            "bracket_width_N_local": 1.3393748003819256e-05
          },
          {
            "left_index": 51,
            "right_index": 52,
            "fraction": 0.5175748335911357,
            "N_local": 0.0006900136035512285,
            "N_physical": -56.79163219032492,
            "H_Mpl": 4.296908650774767e-07,
            "required_standard_density_Mpl4": 4.375239539654301e-26,
            "vacuum_frequency_margin_Mpl2": 6.29372222586588e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2188561812472784e-21,
            "right_raychaudhuri_residual_Mpl2": -1.1360809257028024e-21,
            "left_normalized_residual": 6.601463256461129e-09,
            "right_normalized_residual": -6.153143411233157e-09,
            "bracket_width_N_local": 1.3393745416623716e-05
          },
          {
            "left_index": 52,
            "right_index": 53,
            "fraction": 0.605730992564168,
            "N_local": 0.0007045880899030498,
            "N_physical": -56.940285309469274,
            "H_Mpl": 4.2969085267247555e-07,
            "required_standard_density_Mpl4": 8.789660470243546e-26,
            "vacuum_frequency_margin_Mpl2": 6.293561091423813e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1360809257028024e-21,
            "right_raychaudhuri_residual_Mpl2": 7.394726445273884e-22,
            "left_normalized_residual": -6.153143411233157e-09,
            "right_normalized_residual": 4.005068099559779e-09,
            "bracket_width_N_local": 1.3393745061689535e-05
          },
          {
            "left_index": 55,
            "right_index": 56,
            "fraction": 0.42134240572916865,
            "N_local": 0.0007422996698030379,
            "N_physical": -57.0319696630844,
            "H_Mpl": 4.2969081928852715e-07,
            "required_standard_density_Mpl4": 1.212359794649853e-25,
            "vacuum_frequency_margin_Mpl2": 6.293135637749869e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.1467529397916027e-22,
            "right_raychaudhuri_residual_Mpl2": -5.695012055628918e-22,
            "left_normalized_residual": 2.2459288888163688e-09,
            "right_normalized_residual": -3.084483934901836e-09,
            "bracket_width_N_local": 1.3393743953274851e-05
          },
          {
            "left_index": 56,
            "right_index": 57,
            "fraction": 0.7437193680383242,
            "N_local": 0.0007600112479600516,
            "N_physical": -56.906204788718306,
            "H_Mpl": 4.296908029615285e-07,
            "required_standard_density_Mpl4": 6.92940012729539e-26,
            "vacuum_frequency_margin_Mpl2": 6.292931635524449e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.695012055628918e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9624623902099746e-22,
            "left_normalized_residual": -3.084483934901836e-09,
            "right_normalized_residual": 1.0628922304620323e-09,
            "bracket_width_N_local": 1.3393743568903388e-05
          },
          {
            "left_index": 57,
            "right_index": 58,
            "fraction": 0.4513855323769797,
            "N_local": 0.0007694895469206419,
            "N_physical": -56.953776274475594,
            "H_Mpl": 4.2969079403720947e-07,
            "required_standard_density_Mpl4": 8.625884705128972e-26,
            "vacuum_frequency_margin_Mpl2": 6.292821288638451e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9624623902099746e-22,
            "right_raychaudhuri_residual_Mpl2": -2.3851789262401107e-22,
            "left_normalized_residual": 1.0628922304620323e-09,
            "right_normalized_residual": -1.2918404507906814e-09,
            "bracket_width_N_local": 1.3393743176885482e-05
          },
          {
            "left_index": 60,
            "right_index": 61,
            "fraction": 0.6625296432429001,
            "N_local": 0.000812498784427947,
            "N_physical": -56.72625954007646,
            "H_Mpl": 4.296907519908584e-07,
            "required_standard_density_Mpl4": 3.4859068048274376e-26,
            "vacuum_frequency_margin_Mpl2": 6.292311072168518e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.063282086518815e-21,
            "right_raychaudhuri_residual_Mpl2": 5.416001966562323e-22,
            "left_normalized_residual": -5.7588592708630074e-09,
            "right_normalized_residual": 2.9333697507287355e-09,
            "bracket_width_N_local": 1.339374195376004e-05
          },
          {
            "left_index": 62,
            "right_index": 63,
            "fraction": 0.282877642170178,
            "N_local": 0.0008342013067350398,
            "N_physical": -56.42285530462563,
            "H_Mpl": 4.2969072976349896e-07,
            "required_standard_density_Mpl4": 1.0465661091050631e-26,
            "vacuum_frequency_margin_Mpl2": 6.2920475770993555e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.5493256879616036e-22,
            "right_raychaudhuri_residual_Mpl2": -8.997886105561278e-22,
            "left_normalized_residual": 1.9223562579915553e-09,
            "right_normalized_residual": -4.873360550916359e-09,
            "bracket_width_N_local": 1.3393741098036778e-05
          },
          {
            "left_index": 70,
            "right_index": 71,
            "fraction": 0.04709958878928581,
            "N_local": 0.0009381932723389629,
            "N_physical": -56.63453273864103,
            "H_Mpl": 4.2969061343218594e-07,
            "required_standard_density_Mpl4": 2.4644042680442236e-26,
            "vacuum_frequency_margin_Mpl2": 6.2907287776325865e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 5.890383802252483e-23,
            "right_raychaudhuri_residual_Mpl2": -1.1917193528942554e-21,
            "left_normalized_residual": 3.190302457242691e-10,
            "right_normalized_residual": -6.454495316513854e-09,
            "bracket_width_N_local": 1.3393737338068313e-05
          },
          {
            "left_index": 71,
            "right_index": 72,
            "fraction": 0.5614620491484568,
            "N_local": 0.0009584762450817715,
            "N_physical": -56.95618282524688,
            "H_Mpl": 4.296905887515239e-07,
            "required_standard_density_Mpl4": 8.467609498921751e-26,
            "vacuum_frequency_margin_Mpl2": 6.290460528985753e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1917193528942554e-21,
            "right_raychaudhuri_residual_Mpl2": 9.308094176641118e-22,
            "left_normalized_residual": -6.454495316513854e-09,
            "right_normalized_residual": 5.0413761202050414e-09,
            "bracket_width_N_local": 1.339373682891006e-05
          },
          {
            "left_index": 73,
            "right_index": 74,
            "fraction": 0.43488536319612847,
            "N_local": 0.0009835683829465512,
            "N_physical": -56.62021284899617,
            "H_Mpl": 4.296905573394349e-07,
            "required_standard_density_Mpl4": 3.015939058335241e-26,
            "vacuum_frequency_margin_Mpl2": 6.290123972293256e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.194690838983815e-21,
            "right_raychaudhuri_residual_Mpl2": -1.552448844457365e-21,
            "left_normalized_residual": 6.470590243745698e-09,
            "right_normalized_residual": -8.408251588347898e-09,
            "bracket_width_N_local": 1.3393735783597243e-05
          },
          {
            "left_index": 74,
            "right_index": 75,
            "fraction": 0.5675919898223198,
            "N_local": 0.0009987395559194969,
            "N_physical": -55.83230641437151,
            "H_Mpl": 4.2969053784927485e-07,
            "required_standard_density_Mpl4": 3.6616541393146535e-27,
            "vacuum_frequency_margin_Mpl2": 6.289917856374626e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.552448844457365e-21,
            "right_raychaudhuri_residual_Mpl2": 1.1827004745866668e-21,
            "left_normalized_residual": -8.408251588347898e-09,
            "right_normalized_residual": 6.405650004333988e-09,
            "bracket_width_N_local": 1.3393735247269316e-05
          },
          {
            "left_index": 75,
            "right_index": 76,
            "fraction": 0.4687060887445453,
            "N_local": 0.0010108088393323388,
            "N_physical": -55.99501566188924,
            "H_Mpl": 4.2969052207227326e-07,
            "required_standard_density_Mpl4": 1.1604046981658976e-26,
            "vacuum_frequency_margin_Mpl2": 6.289752465735163e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.1827004745866668e-21,
            "right_raychaudhuri_residual_Mpl2": -1.3406302501209945e-21,
            "left_normalized_residual": 6.405650004333988e-09,
            "right_normalized_residual": -7.2610175251922226e-09,
            "bracket_width_N_local": 1.3393734701716781e-05
          },
          {
            "left_index": 76,
            "right_index": 77,
            "fraction": 0.9123702210590713,
            "N_local": 0.001030144893212708,
            "N_physical": -56.94661378608445,
            "H_Mpl": 4.2969049631674557e-07,
            "required_standard_density_Mpl4": 8.539662252328082e-26,
            "vacuum_frequency_margin_Mpl2": 6.2894850185443455e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3406302501209945e-21,
            "right_raychaudhuri_residual_Mpl2": 1.2876256781293883e-22,
            "left_normalized_residual": -7.2610175251922226e-09,
            "right_normalized_residual": 6.973938858313707e-10,
            "bracket_width_N_local": 1.3393734146858972e-05
          },
          {
            "left_index": 89,
            "right_index": 90,
            "fraction": 0.9686572251393976,
            "N_local": 0.001205017275700692,
            "N_physical": -56.82064789568561,
            "H_Mpl": 4.29690233890331e-07,
            "required_standard_density_Mpl4": 4.949628320252492e-26,
            "vacuum_frequency_margin_Mpl2": 6.286919107525875e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3204165693990459e-21,
            "right_raychaudhuri_residual_Mpl2": 4.2724627642071864e-23,
            "left_normalized_residual": -7.151546326498324e-09,
            "right_normalized_residual": 2.314021137543173e-10,
            "bracket_width_N_local": 1.3393726058015575e-05
          },
          {
            "left_index": 92,
            "right_index": 93,
            "fraction": 0.02425933456341832,
            "N_local": 0.001232549445101621,
            "N_physical": -56.85012173248973,
            "H_Mpl": 4.2969018758547984e-07,
            "required_standard_density_Mpl4": 5.5292827920971e-26,
            "vacuum_frequency_margin_Mpl2": 6.286491174729399e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.014263610243885e-23,
            "right_raychaudhuri_residual_Mpl2": -1.6145868453472146e-21,
            "left_normalized_residual": 2.1741775894759197e-10,
            "right_normalized_residual": -8.744814124292427e-09,
            "bracket_width_N_local": 1.3393723951315778e-05
          },
          {
            "left_index": 93,
            "right_index": 94,
            "fraction": 0.48487029375056556,
            "N_local": 0.0012521124647385596,
            "N_physical": -56.986346626703586,
            "H_Mpl": 4.2969015377855923e-07,
            "required_standard_density_Mpl4": 1.0537359893024091e-25,
            "vacuum_frequency_margin_Mpl2": 6.2861829701570925e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.6145868453472146e-21,
            "right_raychaudhuri_residual_Mpl2": 1.7153487398132474e-21,
            "left_normalized_residual": -8.744814124292427e-09,
            "right_normalized_residual": 9.29055477143929e-09,
            "bracket_width_N_local": 1.3393723228069879e-05
          },
          {
            "left_index": 94,
            "right_index": 95,
            "fraction": 0.45490723762273116,
            "N_local": 0.0012651048707519143,
            "N_physical": -56.997242899211244,
            "H_Mpl": 4.2969013094847025e-07,
            "required_standard_density_Mpl4": 1.1016369177292761e-25,
            "vacuum_frequency_margin_Mpl2": 6.2859765819830525e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7153487398132474e-21,
            "right_raychaudhuri_residual_Mpl2": -2.055417249264816e-21,
            "left_normalized_residual": 9.29055477143929e-09,
            "right_normalized_residual": -1.1132411851528448e-08,
            "bracket_width_N_local": 1.3393722494135915e-05
          },
          {
            "left_index": 95,
            "right_index": 96,
            "fraction": 0.7538643989555636,
            "N_local": 0.0012825027419411498,
            "N_physical": -56.88732829318941,
            "H_Mpl": 4.2969009987700496e-07,
            "required_standard_density_Mpl4": 6.420356590971367e-26,
            "vacuum_frequency_margin_Mpl2": 6.285697986678761e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.055417249264816e-21,
            "right_raychaudhuri_residual_Mpl2": 6.710906639785737e-22,
            "left_normalized_residual": -1.1132411851528448e-08,
            "right_normalized_residual": 3.6347162604879835e-09,
            "bracket_width_N_local": 1.3393721749403948e-05
          },
          {
            "left_index": 96,
            "right_index": 97,
            "fraction": 0.7092775746146429,
            "N_local": 0.0012952992796356902,
            "N_physical": -56.97299512272377,
            "H_Mpl": 4.296900766345328e-07,
            "required_standard_density_Mpl4": 9.217306044030259e-26,
            "vacuum_frequency_margin_Mpl2": 6.285491362407865e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.710906639785737e-22,
            "right_raychaudhuri_residual_Mpl2": -2.7507017346674304e-22,
            "left_normalized_residual": 3.6347162604879835e-09,
            "right_normalized_residual": -1.4898168005755257e-09,
            "bracket_width_N_local": 1.3393720993773364e-05
          },
          {
            "left_index": 98,
            "right_index": 99,
            "fraction": 0.45693992223341096,
            "N_local": 0.0013187069800387168,
            "N_physical": -56.82730406612569,
            "H_Mpl": 4.296900332813482e-07,
            "required_standard_density_Mpl4": 6.073586491251042e-26,
            "vacuum_frequency_margin_Mpl2": 6.285109757801457e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.944761861218157e-22,
            "right_raychaudhuri_residual_Mpl2": 1.1819066111200154e-21,
            "left_normalized_residual": -5.3862164771020654e-09,
            "right_normalized_residual": 6.4013655597193205e-09,
            "bracket_width_N_local": 1.3393719449427549e-05
          },
          {
            "left_index": 101,
            "right_index": 102,
            "fraction": 0.4981349122963239,
            "N_local": 0.0013594398889529894,
            "N_physical": -56.70040417163514,
            "H_Mpl": 4.296899552382589e-07,
            "required_standard_density_Mpl4": 3.1639811126884363e-26,
            "vacuum_frequency_margin_Mpl2": 6.284434543405257e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.0692527946036274e-21,
            "right_raychaudhuri_residual_Mpl2": -1.0772596625830001e-21,
            "left_normalized_residual": 5.7912186844478115e-09,
            "right_normalized_residual": -5.834585683221136e-09,
            "bracket_width_N_local": 1.3393717048993748e-05
          },
          {
            "left_index": 114,
            "right_index": 115,
            "fraction": 0.8582876683988421,
            "N_local": 0.0015383819172913081,
            "N_physical": -57.025414175192424,
            "H_Mpl": 4.2968957210233605e-07,
            "required_standard_density_Mpl4": 1.1146193993795313e-25,
            "vacuum_frequency_margin_Mpl2": 6.281299647021066e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2661559223898336e-21,
            "right_raychaudhuri_residual_Mpl2": -2.090556750829348e-22,
            "left_normalized_residual": 6.8576846228668344e-09,
            "right_normalized_residual": -1.1322761045462894e-09,
            "bracket_width_N_local": 1.3393705454777492e-05
          },
          {
            "left_index": 116,
            "right_index": 117,
            "fraction": 0.4342231149215186,
            "N_local": 0.001559489530652674,
            "N_physical": -57.1789371427103,
            "H_Mpl": 4.296895224381494e-07,
            "required_standard_density_Mpl4": 2.0620154552218532e-25,
            "vacuum_frequency_margin_Mpl2": 6.280911635014074e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -7.285056734747994e-22,
            "right_raychaudhuri_residual_Mpl2": 9.492163280507743e-22,
            "left_normalized_residual": -3.945693827676438e-09,
            "right_normalized_residual": 5.1410959420420406e-09,
            "bracket_width_N_local": 1.3393703494664864e-05
          },
          {
            "left_index": 117,
            "right_index": 118,
            "fraction": 0.9878589843778645,
            "N_local": 0.0015802984678405451,
            "N_physical": -57.16302461261505,
            "H_Mpl": 4.2968947258953167e-07,
            "required_standard_density_Mpl4": 1.9329139036137397e-25,
            "vacuum_frequency_margin_Mpl2": 6.280525645905304e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.492163280507743e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1666088429522658e-23,
            "left_normalized_residual": 5.1410959420420406e-09,
            "right_normalized_residual": -6.318526884691058e-11,
            "bracket_width_N_local": 1.339370249623978e-05
          },
          {
            "left_index": 119,
            "right_index": 120,
            "fraction": 0.8428465471001942,
            "N_local": 0.0016051436166644778,
            "N_physical": -57.16339033749111,
            "H_Mpl": 4.296894117252259e-07,
            "required_standard_density_Mpl4": 1.9369378485244054e-25,
            "vacuum_frequency_margin_Mpl2": 6.280059616028694e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.306399063187383e-22,
            "right_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "left_normalized_residual": -2.8740250373060523e-09,
            "right_normalized_residual": 5.358781255435093e-10,
            "bracket_width_N_local": 1.3393700462002202e-05
          },
          {
            "left_index": 120,
            "right_index": 121,
            "fraction": 0.09178239976574161,
            "N_local": 0.001608477788814241,
            "N_physical": -57.15354798384819,
            "H_Mpl": 4.296894034642662e-07,
            "required_standard_density_Mpl4": 1.8655455109898024e-25,
            "vacuum_frequency_margin_Mpl2": 6.279996722973984e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "right_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
            "left_normalized_residual": 5.358781255435093e-10,
            "right_normalized_residual": -5.302694440333927e-09,
            "bracket_width_N_local": 1.3393699425939256e-05
          },
          {
            "left_index": 121,
            "right_index": 122,
            "fraction": 0.5318905744341766,
            "N_local": 0.001627766164288717,
            "N_physical": -56.99863458940055,
            "H_Mpl": 4.2968935508388905e-07,
            "required_standard_density_Mpl4": 1.0697136247727802e-25,
            "vacuum_frequency_margin_Mpl2": 6.279630665951833e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
            "right_raychaudhuri_residual_Mpl2": 8.61650054678589e-22,
            "left_normalized_residual": -5.302694440333927e-09,
            "right_normalized_residual": 4.66682765003158e-09,
            "bracket_width_N_local": 1.3393698377093784e-05
          }
        ]
      },
      {
        "prefix_intervals": 256,
        "stride": 2,
        "nodes": 129,
        "mode_nodes": 48,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 89,
        "simultaneous_sign_change_brackets": 46,
        "positive_frequency_brackets": 46,
        "selected_earliest_admissible": {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878425229289858,
          "N_local": 7.752094644627781e-05,
          "N_physical": -56.699492844607995,
          "H_Mpl": 4.296911741311536e-07,
          "required_standard_density_Mpl4": 3.0265911756443045e-26,
          "vacuum_frequency_margin_Mpl2": 6.29883876081906e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
          "right_raychaudhuri_residual_Mpl2": 1.2711135282396778e-22,
          "left_normalized_residual": -2.5565397212652397e-09,
          "right_normalized_residual": 6.884485276229008e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684877842062498e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 3.6e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 5,
            "right_index": 6,
            "fraction": 0.7878425229289858,
            "N_local": 7.752094644627781e-05,
            "N_physical": -56.699492844607995,
            "H_Mpl": 4.296911741311536e-07,
            "required_standard_density_Mpl4": 3.0265911756443045e-26,
            "vacuum_frequency_margin_Mpl2": 6.29883876081906e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
            "right_raychaudhuri_residual_Mpl2": 1.2711135282396778e-22,
            "left_normalized_residual": -2.5565397212652397e-09,
            "right_normalized_residual": 6.884485276229008e-10,
            "bracket_width_N_local": 1.339375507064178e-05
          },
          {
            "left_index": 6,
            "right_index": 7,
            "fraction": 0.3642275197173483,
            "N_local": 8.524090588470445e-05,
            "N_physical": -56.747341568978065,
            "H_Mpl": 4.2969117234716095e-07,
            "required_standard_density_Mpl4": 3.782566329700232e-26,
            "vacuum_frequency_margin_Mpl2": 6.298794363556885e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2711135282396778e-22,
            "right_raychaudhuri_residual_Mpl2": -2.2187752347678534e-22,
            "left_normalized_residual": 6.884485276229008e-10,
            "right_normalized_residual": -1.201712146004523e-09,
            "bracket_width_N_local": 1.3393754974687068e-05
          },
          {
            "left_index": 7,
            "right_index": 8,
            "fraction": 0.21241428507703713,
            "N_local": 9.66013115714827e-05,
            "N_physical": -56.70112292945049,
            "H_Mpl": 4.2969116965550983e-07,
            "required_standard_density_Mpl4": 4.09699964611411e-26,
            "vacuum_frequency_margin_Mpl2": 6.298728217569028e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.2187752347678534e-22,
            "right_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
            "left_normalized_residual": -1.201712146004523e-09,
            "right_normalized_residual": 4.455685895618096e-09,
            "bracket_width_N_local": 1.339375487477941e-05
          },
          {
            "left_index": 8,
            "right_index": 9,
            "fraction": 0.6065846212206618,
            "N_local": 0.00011527448724442834,
            "N_physical": -56.22547452563042,
            "H_Mpl": 4.296911650179105e-07,
            "required_standard_density_Mpl4": 4.544555085714001e-27,
            "vacuum_frequency_margin_Mpl2": 6.298616934763699e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
            "right_raychaudhuri_residual_Mpl2": -5.335650290560938e-22,
            "left_normalized_residual": 4.455685895618096e-09,
            "right_normalized_residual": -2.889844748392e-09,
            "bracket_width_N_local": 1.3393754770835335e-05
          },
          {
            "left_index": 9,
            "right_index": 10,
            "fraction": 0.25742029550117956,
            "N_local": 0.0001239916206340343,
            "N_physical": -56.32284307582264,
            "H_Mpl": 4.296911627704443e-07,
            "required_standard_density_Mpl4": 8.745335477549417e-27,
            "vacuum_frequency_margin_Mpl2": 6.298564016845991e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.335650290560938e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5391737502125706e-21,
            "left_normalized_residual": -2.889844748392e-09,
            "right_normalized_residual": 8.336328300878156e-09,
            "bracket_width_N_local": 1.3393754662768595e-05
          },
          {
            "left_index": 10,
            "right_index": 11,
            "fraction": 0.9413398152824122,
            "N_local": 0.00014654562544814153,
            "N_physical": -56.85176988349896,
            "H_Mpl": 4.2969115669102096e-07,
            "required_standard_density_Mpl4": 5.690573615580371e-26,
            "vacuum_frequency_margin_Mpl2": 6.298424066950863e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5391737502125706e-21,
            "right_raychaudhuri_residual_Mpl2": -9.591458369669014e-23,
            "left_normalized_residual": 8.336328300878156e-09,
            "right_normalized_residual": -5.194835684323147e-10,
            "bracket_width_N_local": 1.3393754550492778e-05
          },
          {
            "left_index": 14,
            "right_index": 15,
            "fraction": 0.11548723435968136,
            "N_local": 0.0001890593761122981,
            "N_physical": -56.96018065282632,
            "H_Mpl": 4.296911441259767e-07,
            "required_standard_density_Mpl4": 8.832757645283166e-26,
            "vacuum_frequency_margin_Mpl2": 6.298148090169995e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5513919721518112e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1882057887077216e-21,
            "left_normalized_residual": 8.402504094329899e-10,
            "right_normalized_residual": -6.4354491843669336e-09,
            "bracket_width_N_local": 1.3393754057482415e-05
          },
          {
            "left_index": 17,
            "right_index": 18,
            "fraction": 0.08744038024700374,
            "N_local": 0.00022886498517327977,
            "N_physical": -56.789232006461916,
            "H_Mpl": 4.296911310119382e-07,
            "required_standard_density_Mpl4": 4.568037874804944e-26,
            "vacuum_frequency_margin_Mpl2": 6.2978756030892115e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.106238344959863e-23,
            "right_raychaudhuri_residual_Mpl2": 6.372692486534195e-22,
            "left_normalized_residual": -3.307203902435353e-10,
            "right_normalized_residual": 3.4515183868669134e-09,
            "bracket_width_N_local": 1.339375363908614e-05
          },
          {
            "left_index": 22,
            "right_index": 23,
            "fraction": 0.3109410883069142,
            "N_local": 0.0002988272650009995,
            "N_physical": -56.70844680981584,
            "H_Mpl": 4.296911045649456e-07,
            "required_standard_density_Mpl4": 3.759765968933461e-26,
            "vacuum_frequency_margin_Mpl2": 6.29736340947395e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.99856639440169e-22,
            "right_raychaudhuri_residual_Mpl2": 6.644952931812146e-22,
            "left_normalized_residual": -1.624055774041247e-09,
            "right_normalized_residual": 3.598977989789142e-09,
            "bracket_width_N_local": 1.3393752842742138e-05
          },
          {
            "left_index": 23,
            "right_index": 24,
            "fraction": 0.5647066548167605,
            "N_local": 0.0003156198910229591,
            "N_physical": -56.69579177351017,
            "H_Mpl": 4.29691097551177e-07,
            "required_standard_density_Mpl4": 4.015813585341848e-26,
            "vacuum_frequency_margin_Mpl2": 6.2972341862606e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.644952931812146e-22,
            "right_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "left_normalized_residual": 3.598977989789142e-09,
            "right_normalized_residual": -2.774203555973799e-09,
            "bracket_width_N_local": 1.3393752668113652e-05
          },
          {
            "left_index": 24,
            "right_index": 25,
            "fraction": 0.7238164185936237,
            "N_local": 0.0003311447203840173,
            "N_physical": -56.67637467543066,
            "H_Mpl": 4.29691090839783e-07,
            "required_standard_density_Mpl4": 3.1837214298215623e-26,
            "vacuum_frequency_margin_Mpl2": 6.2971126129248075e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "right_raychaudhuri_residual_Mpl2": 1.954431518968193e-22,
            "left_normalized_residual": -2.774203555973799e-09,
            "right_normalized_residual": 1.0585411919791782e-09,
            "bracket_width_N_local": 1.3393752488282513e-05
          },
          {
            "left_index": 25,
            "right_index": 26,
            "fraction": 0.10861082596236435,
            "N_local": 0.0003362985614150903,
            "N_physical": -56.622934568867905,
            "H_Mpl": 4.29691088569346e-07,
            "required_standard_density_Mpl4": 2.3385457322489655e-26,
            "vacuum_frequency_margin_Mpl2": 6.297071862011276e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.954431518968193e-22,
            "right_raychaudhuri_residual_Mpl2": -1.6040381628345865e-21,
            "left_normalized_residual": 1.0585411919791782e-09,
            "right_normalized_residual": -8.687643951565464e-09,
            "bracket_width_N_local": 1.3393752303225248e-05
          },
          {
            "left_index": 30,
            "right_index": 31,
            "fraction": 0.8427289482168314,
            "N_local": 0.00041309991641925645,
            "N_physical": -56.651190135538535,
            "H_Mpl": 4.29691051621772e-07,
            "required_standard_density_Mpl4": 3.348309924875711e-26,
            "vacuum_frequency_margin_Mpl2": 6.296436238914208e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.223594087232129e-21,
            "right_raychaudhuri_residual_Mpl2": 4.149697023910151e-22,
            "left_normalized_residual": -1.2043227205322555e-08,
            "right_normalized_residual": 2.2475210731666576e-09,
            "bracket_width_N_local": 1.3393751298504256e-05
          },
          {
            "left_index": 32,
            "right_index": 33,
            "fraction": 0.8794008743118584,
            "N_local": 0.0004403785930699743,
            "N_physical": -56.604995134273686,
            "H_Mpl": 4.296910371192947e-07,
            "required_standard_density_Mpl4": 2.4267585946053196e-26,
            "vacuum_frequency_margin_Mpl2": 6.2961982625215765e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7113735259912426e-21,
            "right_raychaudhuri_residual_Mpl2": -2.3469404794699416e-22,
            "left_normalized_residual": 9.268985585911212e-09,
            "right_normalized_residual": -1.2711285921867248e-09,
            "bracket_width_N_local": 1.3393750858574967e-05
          },
          {
            "left_index": 33,
            "right_index": 34,
            "fraction": 0.13927693931446128,
            "N_local": 0.0004438593083069071,
            "N_physical": -56.651359071670235,
            "H_Mpl": 4.2969103521278323e-07,
            "required_standard_density_Mpl4": 2.5459042109583684e-26,
            "vacuum_frequency_margin_Mpl2": 6.2961674221968104e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.3469404794699416e-22,
            "right_raychaudhuri_residual_Mpl2": 1.4503950206539382e-21,
            "left_normalized_residual": -1.2711285921867248e-09,
            "right_normalized_residual": 7.855498085850394e-09,
            "bracket_width_N_local": 1.3393750630116873e-05
          },
          {
            "left_index": 34,
            "right_index": 35,
            "fraction": 0.5055229375230059,
            "N_local": 0.0004621584663878738,
            "N_physical": -56.67466211644937,
            "H_Mpl": 4.296910249770759e-07,
            "required_standard_density_Mpl4": 3.276081740548983e-26,
            "vacuum_frequency_margin_Mpl2": 6.296003522723108e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.4503950206539382e-21,
            "right_raychaudhuri_residual_Mpl2": -1.4187033189005e-21,
            "left_normalized_residual": 7.855498085850394e-09,
            "right_normalized_residual": -7.683852634699478e-09,
            "bracket_width_N_local": 1.3393750395837372e-05
          },
          {
            "left_index": 37,
            "right_index": 38,
            "fraction": 0.2761315926560149,
            "N_local": 0.000499267306228374,
            "N_physical": -56.95946019606728,
            "H_Mpl": 4.296910031423141e-07,
            "required_standard_density_Mpl4": 8.684883048059696e-26,
            "vacuum_frequency_margin_Mpl2": 6.29566253010891e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.891666277584966e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5444777774017578e-21,
            "left_normalized_residual": -3.190991250756916e-09,
            "right_normalized_residual": 8.365061818969631e-09,
            "bracket_width_N_local": 1.3393749656707803e-05
          },
          {
            "left_index": 38,
            "right_index": 39,
            "fraction": 0.6120451569571216,
            "N_local": 0.0005171601979131458,
            "N_physical": -57.01148959056543,
            "H_Mpl": 4.2969099205610395e-07,
            "required_standard_density_Mpl4": 1.131023739669781e-25,
            "vacuum_frequency_margin_Mpl2": 6.295493822699105e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5444777774017578e-21,
            "right_raychaudhuri_residual_Mpl2": -9.789925251497259e-22,
            "left_normalized_residual": 8.365061818969631e-09,
            "right_normalized_residual": -5.302331592976849e-09,
            "bracket_width_N_local": 1.3393749397776797e-05
          },
          {
            "left_index": 43,
            "right_index": 44,
            "fraction": 0.36867076485375644,
            "N_local": 0.0005808692460497577,
            "N_physical": -56.38806595362483,
            "H_Mpl": 4.296909495232809e-07,
            "required_standard_density_Mpl4": 1.3845061662489435e-26,
            "vacuum_frequency_margin_Mpl2": 6.29487082793738e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -8.89864120570295e-22,
            "right_raychaudhuri_residual_Mpl2": 1.523845360633848e-21,
            "left_normalized_residual": -4.819603116837803e-09,
            "right_normalized_residual": 8.253316438136793e-09,
            "bracket_width_N_local": 1.3393748003819256e-05
          },
          {
            "left_index": 51,
            "right_index": 52,
            "fraction": 0.5175748353182742,
            "N_local": 0.0006900136035743613,
            "N_physical": -56.791771715076074,
            "H_Mpl": 4.2969086507747667e-07,
            "required_standard_density_Mpl4": 4.3776751643532655e-26,
            "vacuum_frequency_margin_Mpl2": 6.293722225865625e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2188561896782293e-21,
            "right_raychaudhuri_residual_Mpl2": -1.1360809257028024e-21,
            "left_normalized_residual": 6.601463302124115e-09,
            "right_normalized_residual": -6.153143411233157e-09,
            "bracket_width_N_local": 1.3393745416623716e-05
          },
          {
            "left_index": 52,
            "right_index": 53,
            "fraction": 0.6057309898412981,
            "N_local": 0.0007045880898665803,
            "N_physical": -56.94035089368814,
            "H_Mpl": 4.2969085267247555e-07,
            "required_standard_density_Mpl4": 8.792718610437579e-26,
            "vacuum_frequency_margin_Mpl2": 6.293561091424217e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1360809257028024e-21,
            "right_raychaudhuri_residual_Mpl2": 7.394726529583393e-22,
            "left_normalized_residual": -6.153143411233157e-09,
            "right_normalized_residual": 4.005068145222769e-09,
            "bracket_width_N_local": 1.3393745061689535e-05
          },
          {
            "left_index": 55,
            "right_index": 56,
            "fraction": 0.42134239853141464,
            "N_local": 0.000742299669706633,
            "N_physical": -57.03203966644007,
            "H_Mpl": 4.2969081928852725e-07,
            "required_standard_density_Mpl4": 1.2125725238328269e-25,
            "vacuum_frequency_margin_Mpl2": 6.293135637750973e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.1467529397916027e-22,
            "right_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
            "left_normalized_residual": 2.2459288888163688e-09,
            "right_normalized_residual": -3.084484025960798e-09,
            "bracket_width_N_local": 1.3393743953274851e-05
          },
          {
            "left_index": 56,
            "right_index": 57,
            "fraction": 0.7437193655246365,
            "N_local": 0.000760011247926384,
            "N_physical": -56.906387415728744,
            "H_Mpl": 4.2969080296152854e-07,
            "required_standard_density_Mpl4": 6.934448839336835e-26,
            "vacuum_frequency_margin_Mpl2": 6.292931635524838e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
            "left_normalized_residual": -3.084484025960798e-09,
            "right_normalized_residual": 1.0628922758579984e-09,
            "bracket_width_N_local": 1.3393743568903388e-05
          },
          {
            "left_index": 57,
            "right_index": 58,
            "fraction": 0.4513855429535026,
            "N_local": 0.000769489547062301,
            "N_physical": -56.953879584273736,
            "H_Mpl": 4.2969079403720936e-07,
            "required_standard_density_Mpl4": 8.628654545432148e-26,
            "vacuum_frequency_margin_Mpl2": 6.2928212886367955e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
            "right_raychaudhuri_residual_Mpl2": -2.3851789262401107e-22,
            "left_normalized_residual": 1.0628922758579984e-09,
            "right_normalized_residual": -1.2918404507906814e-09,
            "bracket_width_N_local": 1.3393743176885482e-05
          },
          {
            "left_index": 60,
            "right_index": 61,
            "fraction": 0.6625296379999533,
            "N_local": 0.0008124987843577243,
            "N_physical": -56.7266455427175,
            "H_Mpl": 4.296907519908585e-07,
            "required_standard_density_Mpl4": 3.4909555251713116e-26,
            "vacuum_frequency_margin_Mpl2": 6.292311072169363e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.0632820781371679e-21,
            "right_raychaudhuri_residual_Mpl2": 5.416002050871833e-22,
            "left_normalized_residual": -5.7588592254670335e-09,
            "right_normalized_residual": 2.9333697963917477e-09,
            "bracket_width_N_local": 1.339374195376004e-05
          },
          {
            "left_index": 62,
            "right_index": 63,
            "fraction": 0.2828776488502654,
            "N_local": 0.0008342013068245111,
            "N_physical": -56.42416066977023,
            "H_Mpl": 4.2969072976349885e-07,
            "required_standard_density_Mpl4": 1.0516148238801056e-26,
            "vacuum_frequency_margin_Mpl2": 6.292047577098258e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.5493257717780747e-22,
            "right_raychaudhuri_residual_Mpl2": -8.997886021744807e-22,
            "left_normalized_residual": 1.922356303387535e-09,
            "right_normalized_residual": -4.873360505520376e-09,
            "bracket_width_N_local": 1.3393741098036778e-05
          },
          {
            "left_index": 70,
            "right_index": 71,
            "fraction": 0.047099575381619345,
            "N_local": 0.0009381932721593841,
            "N_physical": -56.635086844218016,
            "H_Mpl": 4.2969061343218615e-07,
            "required_standard_density_Mpl4": 2.469452902028483e-26,
            "vacuum_frequency_margin_Mpl2": 6.290728777634954e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 5.890382125923059e-23,
            "right_raychaudhuri_residual_Mpl2": -1.1917193697561573e-21,
            "left_normalized_residual": 3.190301549322586e-10,
            "right_normalized_residual": -6.454495407839942e-09,
            "bracket_width_N_local": 1.3393737338068313e-05
          },
          {
            "left_index": 71,
            "right_index": 72,
            "fraction": 0.5614620526323124,
            "N_local": 0.0009584762451284334,
            "N_physical": -56.95625329358598,
            "H_Mpl": 4.2969058875152384e-07,
            "required_standard_density_Mpl4": 8.469823553569635e-26,
            "vacuum_frequency_margin_Mpl2": 6.290460528985132e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1917193697561573e-21,
            "right_raychaudhuri_residual_Mpl2": 9.308094176641118e-22,
            "left_normalized_residual": -6.454495407839942e-09,
            "right_normalized_residual": 5.0413761202050414e-09,
            "bracket_width_N_local": 1.339373682891006e-05
          },
          {
            "left_index": 73,
            "right_index": 74,
            "fraction": 0.4348853540070985,
            "N_local": 0.0009835683828234758,
            "N_physical": -56.62021285300039,
            "H_Mpl": 4.2969055733943505e-07,
            "required_standard_density_Mpl4": 3.015939093992669e-26,
            "vacuum_frequency_margin_Mpl2": 6.2901239722949215e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.194690813740266e-21,
            "right_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
            "left_normalized_residual": 6.47059010702358e-09,
            "right_normalized_residual": -8.408251725070025e-09,
            "bracket_width_N_local": 1.3393735783597243e-05
          },
          {
            "left_index": 74,
            "right_index": 75,
            "fraction": 0.5675919990516327,
            "N_local": 0.0009987395560431117,
            "N_physical": -55.832306405564,
            "H_Mpl": 4.296905378492747e-07,
            "required_standard_density_Mpl4": 3.661654065023267e-27,
            "vacuum_frequency_margin_Mpl2": 6.289917856372939e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
            "right_raychaudhuri_residual_Mpl2": 1.1827004493431179e-21,
            "left_normalized_residual": -8.408251725070025e-09,
            "right_normalized_residual": 6.405649867611848e-09,
            "bracket_width_N_local": 1.3393735247269316e-05
          },
          {
            "left_index": 75,
            "right_index": 76,
            "fraction": 0.46870608029736877,
            "N_local": 0.0010108088392191998,
            "N_physical": -55.99525635353091,
            "H_Mpl": 4.296905220722734e-07,
            "required_standard_density_Mpl4": 1.1627710385567055e-26,
            "vacuum_frequency_margin_Mpl2": 6.28975246573672e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.1827004493431179e-21,
            "right_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
            "left_normalized_residual": 6.405649867611848e-09,
            "right_normalized_residual": -7.261017616518347e-09,
            "bracket_width_N_local": 1.3393734701716781e-05
          },
          {
            "left_index": 76,
            "right_index": 77,
            "fraction": 0.9123702325344928,
            "N_local": 0.0010301448933664069,
            "N_physical": -56.94678496980313,
            "H_Mpl": 4.2969049631674535e-07,
            "required_standard_density_Mpl4": 8.5447110386488e-26,
            "vacuum_frequency_margin_Mpl2": 6.289485018542213e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
            "right_raychaudhuri_residual_Mpl2": 1.2876255095103698e-22,
            "left_normalized_residual": -7.261017616518347e-09,
            "right_normalized_residual": 6.973937945052388e-10,
            "bracket_width_N_local": 1.3393734146858972e-05
          },
          {
            "left_index": 89,
            "right_index": 90,
            "fraction": 0.9686572368565195,
            "N_local": 0.0012050172758576278,
            "N_physical": -56.820905901339486,
            "H_Mpl": 4.2969023389033076e-07,
            "required_standard_density_Mpl4": 4.95467698089527e-26,
            "vacuum_frequency_margin_Mpl2": 6.286919107523463e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3204165609187911e-21,
            "right_raychaudhuri_residual_Mpl2": 4.272461087877763e-23,
            "left_normalized_residual": -7.151546280568172e-09,
            "right_normalized_residual": 2.3140202296214582e-10,
            "bracket_width_N_local": 1.3393726058015575e-05
          },
          {
            "left_index": 92,
            "right_index": 93,
            "fraction": 0.024259324374738003,
            "N_local": 0.0012325494449651566,
            "N_physical": -56.85034996265226,
            "H_Mpl": 4.296901875854801e-07,
            "required_standard_density_Mpl4": 5.534331495476367e-26,
            "vacuum_frequency_margin_Mpl2": 6.286491174731544e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.0142619240537e-23,
            "right_raychaudhuri_residual_Mpl2": -1.6145868621105088e-21,
            "left_normalized_residual": 2.1741766762132975e-10,
            "right_normalized_residual": -8.744814215084628e-09,
            "bracket_width_N_local": 1.3393723951315778e-05
          },
          {
            "left_index": 93,
            "right_index": 94,
            "fraction": 0.48487029878468524,
            "N_local": 0.0012521124648059853,
            "N_physical": -56.98649265831082,
            "H_Mpl": 4.296901537785591e-07,
            "required_standard_density_Mpl4": 1.0542408648435847e-25,
            "vacuum_frequency_margin_Mpl2": 6.286182970156025e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.6145868621105088e-21,
            "right_raychaudhuri_residual_Mpl2": 1.715348723049953e-21,
            "left_normalized_residual": -8.744814215084628e-09,
            "right_normalized_residual": 9.29055468064708e-09,
            "bracket_width_N_local": 1.3393723228069879e-05
          },
          {
            "left_index": 94,
            "right_index": 95,
            "fraction": 0.4549072351994701,
            "N_local": 0.0012651048707194579,
            "N_physical": -56.99728813966236,
            "H_Mpl": 4.296901309484703e-07,
            "required_standard_density_Mpl4": 1.1019121214787307e-25,
            "vacuum_frequency_margin_Mpl2": 6.28597658198357e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.715348723049953e-21,
            "right_raychaudhuri_residual_Mpl2": -2.055417249264816e-21,
            "left_normalized_residual": 9.29055468064708e-09,
            "right_normalized_residual": -1.1132411851528448e-08,
            "bracket_width_N_local": 1.3393722494135915e-05
          },
          {
            "left_index": 95,
            "right_index": 96,
            "fraction": 0.7538644036177865,
            "N_local": 0.0012825027420035945,
            "N_physical": -56.88747331538877,
            "H_Mpl": 4.2969009987700486e-07,
            "required_standard_density_Mpl4": 6.424162636187733e-26,
            "vacuum_frequency_margin_Mpl2": 6.285697986677758e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.055417249264816e-21,
            "right_raychaudhuri_residual_Mpl2": 6.710906471166719e-22,
            "left_normalized_residual": -1.1132411851528448e-08,
            "right_normalized_residual": 3.634716169161681e-09,
            "bracket_width_N_local": 1.3393721749403948e-05
          },
          {
            "left_index": 96,
            "right_index": 97,
            "fraction": 0.7092775757167614,
            "N_local": 0.0012952992796504516,
            "N_physical": -56.973137884697586,
            "H_Mpl": 4.296900766345328e-07,
            "required_standard_density_Mpl4": 9.222354757954903e-26,
            "vacuum_frequency_margin_Mpl2": 6.2854913624076265e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.710906471166719e-22,
            "right_raychaudhuri_residual_Mpl2": -2.7507016508509593e-22,
            "left_normalized_residual": 3.634716169161681e-09,
            "right_normalized_residual": -1.4898167551794054e-09,
            "bracket_width_N_local": 1.3393720993773364e-05
          },
          {
            "left_index": 98,
            "right_index": 99,
            "fraction": 0.4569399267725271,
            "N_local": 0.0013187069800995126,
            "N_physical": -56.827533211533186,
            "H_Mpl": 4.296900332813481e-07,
            "required_standard_density_Mpl4": 6.075893418585004e-26,
            "vacuum_frequency_margin_Mpl2": 6.2851097578004595e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.944762113653646e-22,
            "right_raychaudhuri_residual_Mpl2": 1.1819066195016625e-21,
            "left_normalized_residual": -5.386216613824514e-09,
            "right_normalized_residual": 6.401365605115451e-09,
            "bracket_width_N_local": 1.3393719449427549e-05
          },
          {
            "left_index": 101,
            "right_index": 102,
            "fraction": 0.49813490839779684,
            "N_local": 0.0013594398889007736,
            "N_physical": -56.70056065015728,
            "H_Mpl": 4.29689955238259e-07,
            "required_standard_density_Mpl4": 3.16651489079118e-26,
            "vacuum_frequency_margin_Mpl2": 6.284434543406132e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.0692528029852745e-21,
            "right_raychaudhuri_residual_Mpl2": -1.0772596878265491e-21,
            "left_normalized_residual": 5.7912187298439525e-09,
            "right_normalized_residual": -5.83458581994365e-09,
            "bracket_width_N_local": 1.3393717048993748e-05
          },
          {
            "left_index": 114,
            "right_index": 115,
            "fraction": 0.8582876692134755,
            "N_local": 0.0015383819173022191,
            "N_physical": -57.02543001634501,
            "H_Mpl": 4.29689572102336e-07,
            "required_standard_density_Mpl4": 1.114690945809234e-25,
            "vacuum_frequency_margin_Mpl2": 6.2812996470208665e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2661559308700883e-21,
            "right_raychaudhuri_residual_Mpl2": -2.090556750829348e-22,
            "left_normalized_residual": 6.857684668797127e-09,
            "right_normalized_residual": -1.1322761045462894e-09,
            "bracket_width_N_local": 1.3393705454777492e-05
          },
          {
            "left_index": 116,
            "right_index": 117,
            "fraction": 0.4342231033999393,
            "N_local": 0.0015594895304983575,
            "N_physical": -57.178998479091064,
            "H_Mpl": 4.2968952243814975e-07,
            "required_standard_density_Mpl4": 2.0625203239527125e-25,
            "vacuum_frequency_margin_Mpl2": 6.280911635016925e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -7.285056651917599e-22,
            "right_raychaudhuri_residual_Mpl2": 9.49216361774578e-22,
            "left_normalized_residual": -3.945693782814278e-09,
            "right_normalized_residual": 5.141096124695147e-09,
            "bracket_width_N_local": 1.3393703494664864e-05
          },
          {
            "left_index": 117,
            "right_index": 118,
            "fraction": 0.9878590194745663,
            "N_local": 0.0015802984683106198,
            "N_physical": -57.16308991323408,
            "H_Mpl": 4.296894725895305e-07,
            "required_standard_density_Mpl4": 1.9334187660835745e-25,
            "vacuum_frequency_margin_Mpl2": 6.280525645896565e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.49216361774578e-22,
            "right_raychaudhuri_residual_Mpl2": -1.166605470571896e-23,
            "left_normalized_residual": 5.141096124695147e-09,
            "right_normalized_residual": -6.318508619377742e-11,
            "bracket_width_N_local": 1.339370249623978e-05
          },
          {
            "left_index": 119,
            "right_index": 120,
            "fraction": 0.8428465450326145,
            "N_local": 0.0016051436166367853,
            "N_physical": -57.16339974076531,
            "H_Mpl": 4.29689411725226e-07,
            "required_standard_density_Mpl4": 1.937017191165672e-25,
            "vacuum_frequency_margin_Mpl2": 6.280059616029215e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.306398980356988e-22,
            "right_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "left_normalized_residual": -2.874024992443872e-09,
            "right_normalized_residual": 5.358781255435093e-10,
            "bracket_width_N_local": 1.3393700462002202e-05
          },
          {
            "left_index": 120,
            "right_index": 121,
            "fraction": 0.09178240048776687,
            "N_local": 0.0016084777888239117,
            "N_physical": -57.15355582626668,
            "H_Mpl": 4.2968940346426615e-07,
            "required_standard_density_Mpl4": 1.8655918489512582e-25,
            "vacuum_frequency_margin_Mpl2": 6.2799967229738004e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "right_raychaudhuri_residual_Mpl2": -9.790521479471958e-22,
            "left_normalized_residual": 5.358781255435093e-10,
            "right_normalized_residual": -5.302694394403586e-09,
            "bracket_width_N_local": 1.3393699425939256e-05
          },
          {
            "left_index": 121,
            "right_index": 122,
            "fraction": 0.5318905771214941,
            "N_local": 0.0016277661643247102,
            "N_physical": -56.99876892933285,
            "H_Mpl": 4.2968935508388895e-07,
            "required_standard_density_Mpl4": 1.0702184936948242e-25,
            "vacuum_frequency_margin_Mpl2": 6.279630665951148e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.790521479471958e-22,
            "right_raychaudhuri_residual_Mpl2": 8.616500379152947e-22,
            "left_normalized_residual": -5.302694394403586e-09,
            "right_normalized_residual": 4.666827559239031e-09,
            "bracket_width_N_local": 1.3393698377093784e-05
          }
        ]
      },
      {
        "prefix_intervals": 256,
        "stride": 2,
        "nodes": 129,
        "mode_nodes": 64,
        "decimal_digits": 80,
        "first_stored_index": 0,
        "last_stored_index": 256,
        "last_N_local": 0.001714398048252598,
        "friedmann_density_matches": 89,
        "simultaneous_sign_change_brackets": 46,
        "positive_frequency_brackets": 46,
        "selected_earliest_admissible": {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878425339991634,
          "N_local": 7.752094659454906e-05,
          "N_physical": -56.69916548500461,
          "H_Mpl": 4.296911741311535e-07,
          "required_standard_density_Mpl4": 3.022613588034913e-26,
          "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
          "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
          "left_normalized_residual": -2.5565397212652397e-09,
          "right_normalized_residual": 6.884484820267378e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        "exact_initial_HARD_PASS_junction_probe": {
          "stored_index": 0,
          "N_local": 0.0,
          "N_physical": -56.97244594022879,
          "N_offset_physical_minus_local": -56.97244594022879,
          "H_Mpl": 4.296911897956572e-07,
          "required_standard_density_Mpl4": 9.017902368676568e-26,
          "standard_pressure_Mpl4": 3.0059674562255395e-26,
          "quantum_rho_Mpl4": 2.5653546520792134e-21,
          "quantum_pressure_Mpl4": 5.953926906537879e-21,
          "quantum_chi2_Mpl2": 1.7684877974411396e-15,
          "friedmann_residual_Mpl4": -4.936157918492028e-40,
          "friedmann_normalized": -8.91158373533706e-28,
          "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
          "raychaudhuri_normalized": -3.625504617408686e-08,
          "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
          "positive_vacuum_frequency_margin": true
        },
        "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "initial_normalized_residual": -3.625504617408686e-08,
        "wronskian_relative_error": 3.86e-78,
        "finite": true,
        "root_candidates": [
          {
            "left_index": 5,
            "right_index": 6,
            "fraction": 0.7878425339991634,
            "N_local": 7.752094659454906e-05,
            "N_physical": -56.69916548500461,
            "H_Mpl": 4.296911741311535e-07,
            "required_standard_density_Mpl4": 3.022613588034913e-26,
            "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
            "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
            "left_normalized_residual": -2.5565397212652397e-09,
            "right_normalized_residual": 6.884484820267378e-10,
            "bracket_width_N_local": 1.339375507064178e-05
          },
          {
            "left_index": 6,
            "right_index": 7,
            "fraction": 0.3642274780348604,
            "N_local": 8.524090532641941e-05,
            "N_physical": -56.74707739119948,
            "H_Mpl": 4.2969117234716105e-07,
            "required_standard_density_Mpl4": 3.779356413779906e-26,
            "vacuum_frequency_margin_Mpl2": 6.29879436356012e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
            "right_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
            "left_normalized_residual": 6.884484820267378e-10,
            "right_normalized_residual": -1.2017122827262556e-09,
            "bracket_width_N_local": 1.3393754974687068e-05
          },
          {
            "left_index": 7,
            "right_index": 8,
            "fraction": 0.21241430411053652,
            "N_local": 9.660131182641272e-05,
            "N_physical": -56.70112291800134,
            "H_Mpl": 4.296911696555098e-07,
            "required_standard_density_Mpl4": 4.096999558168485e-26,
            "vacuum_frequency_margin_Mpl2": 6.298728217567521e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
            "right_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
            "left_normalized_residual": -1.2017122827262556e-09,
            "right_normalized_residual": 4.455685895618096e-09,
            "bracket_width_N_local": 1.339375487477941e-05
          },
          {
            "left_index": 8,
            "right_index": 9,
            "fraction": 0.6065846174498755,
            "N_local": 0.00011527448719392336,
            "N_physical": -56.223771979203654,
            "H_Mpl": 4.296911650179105e-07,
            "required_standard_density_Mpl4": 4.513930388941858e-27,
            "vacuum_frequency_margin_Mpl2": 6.298616934764003e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
            "right_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
            "left_normalized_residual": 4.455685895618096e-09,
            "right_normalized_residual": -2.8898447940549242e-09,
            "bracket_width_N_local": 1.3393754770835335e-05
          },
          {
            "left_index": 9,
            "right_index": 10,
            "fraction": 0.2574202995656594,
            "N_local": 0.00012399162068847292,
            "N_physical": -56.32060338324056,
            "H_Mpl": 4.296911627704443e-07,
            "required_standard_density_Mpl4": 8.69484844629573e-27,
            "vacuum_frequency_margin_Mpl2": 6.298564016845657e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
            "left_normalized_residual": -2.8898447940549242e-09,
            "right_normalized_residual": 8.336328255348749e-09,
            "bracket_width_N_local": 1.3393754662768595e-05
          },
          {
            "left_index": 10,
            "right_index": 11,
            "fraction": 0.9413398149808291,
            "N_local": 0.0001465456254441022,
            "N_physical": -56.85173446217978,
            "H_Mpl": 4.2969115669102096e-07,
            "required_standard_density_Mpl4": 5.690277456177136e-26,
            "vacuum_frequency_margin_Mpl2": 6.2984240669508886e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
            "right_raychaudhuri_residual_Mpl2": -9.591458369669014e-23,
            "left_normalized_residual": 8.336328255348749e-09,
            "right_normalized_residual": -5.194835684323147e-10,
            "bracket_width_N_local": 1.3393754550492778e-05
          },
          {
            "left_index": 14,
            "right_index": 15,
            "fraction": 0.11548721003307255,
            "N_local": 0.00018905937578647347,
            "N_physical": -56.96006244393786,
            "H_Mpl": 4.2969114412597683e-07,
            "required_standard_density_Mpl4": 8.828292126183686e-26,
            "vacuum_frequency_margin_Mpl2": 6.298148090172184e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5513916356533313e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1882058139512706e-21,
            "left_normalized_residual": 8.402502271818305e-10,
            "right_normalized_residual": -6.4354493210886855e-09,
            "bracket_width_N_local": 1.3393754057482415e-05
          },
          {
            "left_index": 17,
            "right_index": 18,
            "fraction": 0.08744038024700374,
            "N_local": 0.00022886498517327977,
            "N_physical": -56.789232006461916,
            "H_Mpl": 4.296911310119382e-07,
            "required_standard_density_Mpl4": 4.568037874804944e-26,
            "vacuum_frequency_margin_Mpl2": 6.2978756030892115e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -6.106238344959863e-23,
            "right_raychaudhuri_residual_Mpl2": 6.372692486534195e-22,
            "left_normalized_residual": -3.307203902435353e-10,
            "right_normalized_residual": 3.4515183868669134e-09,
            "bracket_width_N_local": 1.339375363908614e-05
          },
          {
            "left_index": 22,
            "right_index": 23,
            "fraction": 0.3109410910174016,
            "N_local": 0.0002988272650373031,
            "N_physical": -56.70810397507022,
            "H_Mpl": 4.296911045649456e-07,
            "required_standard_density_Mpl4": 3.7581961073256013e-26,
            "vacuum_frequency_margin_Mpl2": 6.297363409473673e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.99856639440169e-22,
            "right_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
            "left_normalized_residual": -1.624055774041247e-09,
            "right_normalized_residual": 3.5989779442597223e-09,
            "bracket_width_N_local": 1.3393752842742138e-05
          },
          {
            "left_index": 23,
            "right_index": 24,
            "fraction": 0.564706651707065,
            "N_local": 0.0003156198909813086,
            "N_physical": -56.69531183159522,
            "H_Mpl": 4.29691097551177e-07,
            "required_standard_density_Mpl4": 4.0136158997550725e-26,
            "vacuum_frequency_margin_Mpl2": 6.297234186260923e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
            "right_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "left_normalized_residual": 3.5989779442597223e-09,
            "right_normalized_residual": -2.774203555973799e-09,
            "bracket_width_N_local": 1.3393752668113652e-05
          },
          {
            "left_index": 24,
            "right_index": 25,
            "fraction": 0.7238164271918855,
            "N_local": 0.0003311447204991803,
            "N_physical": -56.67592240321177,
            "H_Mpl": 4.2969109083978294e-07,
            "required_standard_density_Mpl4": 3.1800670545861125e-26,
            "vacuum_frequency_margin_Mpl2": 6.2971126129239e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
            "left_normalized_residual": -2.774203555973799e-09,
            "right_normalized_residual": 1.058541146449756e-09,
            "bracket_width_N_local": 1.3393752488282513e-05
          },
          {
            "left_index": 25,
            "right_index": 26,
            "fraction": 0.10861082179822887,
            "N_local": 0.00033629856135931695,
            "N_physical": -56.6223775919006,
            "H_Mpl": 4.2969108856934607e-07,
            "required_standard_density_Mpl4": 2.3340453548590064e-26,
            "vacuum_frequency_margin_Mpl2": 6.297071862011722e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
            "right_raychaudhuri_residual_Mpl2": -1.6040381628345865e-21,
            "left_normalized_residual": 1.058541146449756e-09,
            "right_normalized_residual": -8.687643951565464e-09,
            "bracket_width_N_local": 1.3393752303225248e-05
          },
          {
            "left_index": 30,
            "right_index": 31,
            "fraction": 0.8427289524142231,
            "N_local": 0.00041309991647547526,
            "N_physical": -56.65091948474018,
            "H_Mpl": 4.296910516217719e-07,
            "required_standard_density_Mpl4": 3.344055246552905e-26,
            "vacuum_frequency_margin_Mpl2": 6.296436238913727e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.2235941124756778e-21,
            "right_raychaudhuri_residual_Mpl2": 4.1496969396006417e-22,
            "left_normalized_residual": -1.204322734204436e-08,
            "right_normalized_residual": 2.24752102750371e-09,
            "bracket_width_N_local": 1.3393751298504256e-05
          },
          {
            "left_index": 32,
            "right_index": 33,
            "fraction": 0.8794008590948205,
            "N_local": 0.0004403785928661611,
            "N_physical": -56.60458670710162,
            "H_Mpl": 4.2969103711929483e-07,
            "required_standard_density_Mpl4": 2.422318717846245e-26,
            "vacuum_frequency_margin_Mpl2": 6.29619826252337e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7113735259912426e-21,
            "right_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
            "left_normalized_residual": 9.268985585911212e-09,
            "right_normalized_residual": -1.2711287745714935e-09,
            "bracket_width_N_local": 1.3393750858574967e-05
          },
          {
            "left_index": 33,
            "right_index": 34,
            "fraction": 0.13927695721182692,
            "N_local": 0.00044385930854661996,
            "N_physical": -56.65083941813677,
            "H_Mpl": 4.2969103521278307e-07,
            "required_standard_density_Mpl4": 2.5408554787641562e-26,
            "vacuum_frequency_margin_Mpl2": 6.296167422194674e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
            "right_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
            "left_normalized_residual": -1.2711287745714935e-09,
            "right_normalized_residual": 7.855498040187442e-09,
            "bracket_width_N_local": 1.3393750630116873e-05
          },
          {
            "left_index": 34,
            "right_index": 35,
            "fraction": 0.5055229316221608,
            "N_local": 0.0004621584663088393,
            "N_physical": -56.674236408190716,
            "H_Mpl": 4.2969102497707594e-07,
            "required_standard_density_Mpl4": 3.27358524823297e-26,
            "vacuum_frequency_margin_Mpl2": 6.296003522723821e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
            "right_raychaudhuri_residual_Mpl2": -1.418703344144049e-21,
            "left_normalized_residual": 7.855498040187442e-09,
            "right_normalized_residual": -7.683852771421306e-09,
            "bracket_width_N_local": 1.3393750395837372e-05
          },
          {
            "left_index": 37,
            "right_index": 38,
            "fraction": 0.2761316055719378,
            "N_local": 0.0004992673064013667,
            "N_physical": -56.95940617049714,
            "H_Mpl": 4.29691003142314e-07,
            "required_standard_density_Mpl4": 8.683488899909805e-26,
            "vacuum_frequency_margin_Mpl2": 6.295662530107288e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.891666530020456e-22,
            "right_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
            "left_normalized_residual": -3.1909913874787536e-09,
            "right_normalized_residual": 8.365061636851863e-09,
            "bracket_width_N_local": 1.3393749656707803e-05
          },
          {
            "left_index": 38,
            "right_index": 39,
            "fraction": 0.6120451497427785,
            "N_local": 0.0005171601978165187,
            "N_physical": -57.01135998833373,
            "H_Mpl": 4.29690992056104e-07,
            "required_standard_density_Mpl4": 1.1305188629660545e-25,
            "vacuum_frequency_margin_Mpl2": 6.295493822700022e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
            "right_raychaudhuri_residual_Mpl2": -9.789925335806768e-22,
            "left_normalized_residual": 8.365061636851863e-09,
            "right_normalized_residual": -5.302331638639811e-09,
            "bracket_width_N_local": 1.3393749397776797e-05
          },
          {
            "left_index": 43,
            "right_index": 44,
            "fraction": 0.3686707670589538,
            "N_local": 0.0005808692460792936,
            "N_physical": -56.38768208111163,
            "H_Mpl": 4.296909495232809e-07,
            "required_standard_density_Mpl4": 1.3813187640175078e-26,
            "vacuum_frequency_margin_Mpl2": 6.294870827937082e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -8.89864129001246e-22,
            "right_raychaudhuri_residual_Mpl2": 1.523845360633848e-21,
            "left_normalized_residual": -4.819603162500771e-09,
            "right_normalized_residual": 8.253316438136793e-09,
            "bracket_width_N_local": 1.3393748003819256e-05
          },
          {
            "left_index": 51,
            "right_index": 52,
            "fraction": 0.5175748228717203,
            "N_local": 0.0006900136034076554,
            "N_physical": -56.791632190308796,
            "H_Mpl": 4.296908650774768e-07,
            "required_standard_density_Mpl4": 4.3752395393722416e-26,
            "vacuum_frequency_margin_Mpl2": 6.293722225867458e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2188561560037294e-21,
            "right_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
            "left_normalized_residual": 6.6014631197392056e-09,
            "right_normalized_residual": -6.153143547955088e-09,
            "bracket_width_N_local": 1.3393745416623716e-05
          },
          {
            "left_index": 52,
            "right_index": 53,
            "fraction": 0.6057309951478642,
            "N_local": 0.0007045880899376551,
            "N_physical": -56.94035089498465,
            "H_Mpl": 4.296908526724755e-07,
            "required_standard_density_Mpl4": 8.792718649026132e-26,
            "vacuum_frequency_margin_Mpl2": 6.293561091423428e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
            "right_raychaudhuri_residual_Mpl2": 7.394726529583393e-22,
            "left_normalized_residual": -6.153143547955088e-09,
            "right_normalized_residual": 4.005068145222769e-09,
            "bracket_width_N_local": 1.3393745061689535e-05
          },
          {
            "left_index": 55,
            "right_index": 56,
            "fraction": 0.42134239853141464,
            "N_local": 0.000742299669706633,
            "N_physical": -57.03203966644007,
            "H_Mpl": 4.2969081928852725e-07,
            "required_standard_density_Mpl4": 1.2125725238328269e-25,
            "vacuum_frequency_margin_Mpl2": 6.293135637750973e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.1467529397916027e-22,
            "right_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
            "left_normalized_residual": 2.2459288888163688e-09,
            "right_normalized_residual": -3.084484025960798e-09,
            "bracket_width_N_local": 1.3393743953274851e-05
          },
          {
            "left_index": 56,
            "right_index": 57,
            "fraction": 0.7437193655246365,
            "N_local": 0.000760011247926384,
            "N_physical": -56.906387415728744,
            "H_Mpl": 4.2969080296152854e-07,
            "required_standard_density_Mpl4": 6.934448839336835e-26,
            "vacuum_frequency_margin_Mpl2": 6.292931635524838e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
            "right_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
            "left_normalized_residual": -3.084484025960798e-09,
            "right_normalized_residual": 1.0628922758579984e-09,
            "bracket_width_N_local": 1.3393743568903388e-05
          },
          {
            "left_index": 57,
            "right_index": 58,
            "fraction": 0.4513855429535026,
            "N_local": 0.000769489547062301,
            "N_physical": -56.953879584273736,
            "H_Mpl": 4.2969079403720936e-07,
            "required_standard_density_Mpl4": 8.628654545432148e-26,
            "vacuum_frequency_margin_Mpl2": 6.2928212886367955e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
            "right_raychaudhuri_residual_Mpl2": -2.3851789262401107e-22,
            "left_normalized_residual": 1.0628922758579984e-09,
            "right_normalized_residual": -1.2918404507906814e-09,
            "bracket_width_N_local": 1.3393743176885482e-05
          },
          {
            "left_index": 60,
            "right_index": 61,
            "fraction": 0.6625296414804297,
            "N_local": 0.0008124987844043409,
            "N_physical": -56.72634788093764,
            "H_Mpl": 4.2969075199085846e-07,
            "required_standard_density_Mpl4": 3.487610598278128e-26,
            "vacuum_frequency_margin_Mpl2": 6.292311072168803e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.0632820781371679e-21,
            "right_raychaudhuri_residual_Mpl2": 5.416001966562323e-22,
            "left_normalized_residual": -5.7588592254670335e-09,
            "right_normalized_residual": 2.9333697507287355e-09,
            "bracket_width_N_local": 1.339374195376004e-05
          },
          {
            "left_index": 62,
            "right_index": 63,
            "fraction": 0.2828776488502654,
            "N_local": 0.0008342013068245111,
            "N_physical": -56.42416066977023,
            "H_Mpl": 4.2969072976349885e-07,
            "required_standard_density_Mpl4": 1.0516148238801056e-26,
            "vacuum_frequency_margin_Mpl2": 6.292047577098258e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 3.5493257717780747e-22,
            "right_raychaudhuri_residual_Mpl2": -8.997886021744807e-22,
            "left_normalized_residual": 1.922356303387535e-09,
            "right_normalized_residual": -4.873360505520376e-09,
            "bracket_width_N_local": 1.3393741098036778e-05
          },
          {
            "left_index": 70,
            "right_index": 71,
            "fraction": 0.047099575065959104,
            "N_local": 0.0009381932721551563,
            "N_physical": -56.635079275733936,
            "H_Mpl": 4.296906134321862e-07,
            "required_standard_density_Mpl4": 2.4692151081577868e-26,
            "vacuum_frequency_margin_Mpl2": 6.290728777635009e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 5.890382125923059e-23,
            "right_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
            "left_normalized_residual": 3.190301549322586e-10,
            "right_normalized_residual": -6.454495453235951e-09,
            "bracket_width_N_local": 1.3393737338068313e-05
          },
          {
            "left_index": 71,
            "right_index": 72,
            "fraction": 0.5614620610416048,
            "N_local": 0.0009584762452410652,
            "N_physical": -56.95618282563535,
            "H_Mpl": 4.296905887515237e-07,
            "required_standard_density_Mpl4": 8.467609511956364e-26,
            "vacuum_frequency_margin_Mpl2": 6.290460528983634e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
            "right_raychaudhuri_residual_Mpl2": 9.308093924205628e-22,
            "left_normalized_residual": -6.454495453235951e-09,
            "right_normalized_residual": 5.041375983482935e-09,
            "bracket_width_N_local": 1.339373682891006e-05
          },
          {
            "left_index": 73,
            "right_index": 74,
            "fraction": 0.4348853540070985,
            "N_local": 0.0009835683828234758,
            "N_physical": -56.62021285300039,
            "H_Mpl": 4.2969055733943505e-07,
            "required_standard_density_Mpl4": 3.015939093992669e-26,
            "vacuum_frequency_margin_Mpl2": 6.2901239722949215e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.194690813740266e-21,
            "right_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
            "left_normalized_residual": 6.47059010702358e-09,
            "right_normalized_residual": -8.408251725070025e-09,
            "bracket_width_N_local": 1.3393735783597243e-05
          },
          {
            "left_index": 74,
            "right_index": 75,
            "fraction": 0.5675920042901169,
            "N_local": 0.0009987395561132746,
            "N_physical": -55.832306400564924,
            "H_Mpl": 4.296905378492746e-07,
            "required_standard_density_Mpl4": 3.66165402285607e-27,
            "vacuum_frequency_margin_Mpl2": 6.289917856371982e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
            "right_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
            "left_normalized_residual": -8.408251725070025e-09,
            "right_normalized_residual": 6.405649730889708e-09,
            "bracket_width_N_local": 1.3393735247269316e-05
          },
          {
            "left_index": 75,
            "right_index": 76,
            "fraction": 0.46870607498227307,
            "N_local": 0.0010108088391480106,
            "N_physical": -55.995256347003696,
            "H_Mpl": 4.296905220722735e-07,
            "required_standard_density_Mpl4": 1.1627710255761945e-26,
            "vacuum_frequency_margin_Mpl2": 6.289752465737699e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
            "right_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
            "left_normalized_residual": 6.405649730889708e-09,
            "right_normalized_residual": -7.261017616518347e-09,
            "bracket_width_N_local": 1.3393734701716781e-05
          },
          {
            "left_index": 76,
            "right_index": 77,
            "fraction": 0.9123702377387957,
            "N_local": 0.001030144893436112,
            "N_physical": -56.94665879344938,
            "H_Mpl": 4.296904963167453e-07,
            "required_standard_density_Mpl4": 8.540104780800767e-26,
            "vacuum_frequency_margin_Mpl2": 6.289485018541246e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
            "right_raychaudhuri_residual_Mpl2": 1.2876254256938986e-22,
            "left_normalized_residual": -7.261017616518347e-09,
            "right_normalized_residual": 6.973937491092083e-10,
            "bracket_width_N_local": 1.3393734146858972e-05
          },
          {
            "left_index": 89,
            "right_index": 90,
            "fraction": 0.9686572376319323,
            "N_local": 0.0012050172758680136,
            "N_physical": -56.82090151317981,
            "H_Mpl": 4.296902338903307e-07,
            "required_standard_density_Mpl4": 4.95451873713127e-26,
            "vacuum_frequency_margin_Mpl2": 6.286919107523303e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.3204165946425948e-21,
            "right_raychaudhuri_residual_Mpl2": 4.272461087877763e-23,
            "left_normalized_residual": -7.1515464632206394e-09,
            "right_normalized_residual": 2.3140202296214582e-10,
            "bracket_width_N_local": 1.3393726058015575e-05
          },
          {
            "left_index": 92,
            "right_index": 93,
            "fraction": 0.024259324250412394,
            "N_local": 0.0012325494449634913,
            "N_physical": -56.850344980674116,
            "H_Mpl": 4.296901875854801e-07,
            "required_standard_density_Mpl4": 5.534209017110175e-26,
            "vacuum_frequency_margin_Mpl2": 6.28649117473157e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 4.0142619240537e-23,
            "right_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
            "left_normalized_residual": 2.1741766762132975e-10,
            "right_normalized_residual": -8.7448142610148e-09,
            "bracket_width_N_local": 1.3393723951315778e-05
          },
          {
            "left_index": 93,
            "right_index": 94,
            "fraction": 0.4848703013313575,
            "N_local": 0.0012521124648400947,
            "N_physical": -56.9863466284211,
            "H_Mpl": 4.2969015377855907e-07,
            "required_standard_density_Mpl4": 1.053735996171995e-25,
            "vacuum_frequency_margin_Mpl2": 6.286182970155485e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
            "right_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
            "left_normalized_residual": -8.7448142610148e-09,
            "right_normalized_residual": 9.290554634716903e-09,
            "bracket_width_N_local": 1.3393723228069879e-05
          },
          {
            "left_index": 94,
            "right_index": 95,
            "fraction": 0.4549072309281898,
            "N_local": 0.0012651048706622495,
            "N_physical": -56.997242900768406,
            "H_Mpl": 4.296901309484704e-07,
            "required_standard_density_Mpl4": 1.1016369238939384e-25,
            "vacuum_frequency_margin_Mpl2": 6.285976581984483e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
            "right_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
            "left_normalized_residual": 9.290554634716903e-09,
            "right_normalized_residual": -1.113241198825085e-08,
            "bracket_width_N_local": 1.3393722494135915e-05
          },
          {
            "left_index": 95,
            "right_index": 96,
            "fraction": 0.7538644082141279,
            "N_local": 0.0012825027420651565,
            "N_physical": -56.88732829339666,
            "H_Mpl": 4.2969009987700475e-07,
            "required_standard_density_Mpl4": 6.420356596172189e-26,
            "vacuum_frequency_margin_Mpl2": 6.2856979866767695e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
            "right_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
            "left_normalized_residual": -1.113241198825085e-08,
            "right_normalized_residual": 3.634716123765566e-09,
            "bracket_width_N_local": 1.3393721749403948e-05
          },
          {
            "left_index": 96,
            "right_index": 97,
            "fraction": 0.7092775479346664,
            "N_local": 0.001295299279278346,
            "N_physical": -56.97299511970861,
            "H_Mpl": 4.296900766345335e-07,
            "required_standard_density_Mpl4": 9.217305944021855e-26,
            "vacuum_frequency_margin_Mpl2": 6.285491362413646e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
            "right_raychaudhuri_residual_Mpl2": -2.75070198710292e-22,
            "left_normalized_residual": 3.634716123765566e-09,
            "right_normalized_residual": -1.4898169372979586e-09,
            "bracket_width_N_local": 1.3393720993773364e-05
          },
          {
            "left_index": 98,
            "right_index": 99,
            "fraction": 0.4569399285322861,
            "N_local": 0.0013187069801230823,
            "N_physical": -56.82730406410569,
            "H_Mpl": 4.29690033281348e-07,
            "required_standard_density_Mpl4": 6.073586449968256e-26,
            "vacuum_frequency_margin_Mpl2": 6.285109757800073e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.944762113653646e-22,
            "right_raychaudhuri_residual_Mpl2": 1.1819066111200154e-21,
            "left_normalized_residual": -5.386216613824514e-09,
            "right_normalized_residual": 6.4013655597193205e-09,
            "bracket_width_N_local": 1.3393719449427549e-05
          },
          {
            "left_index": 101,
            "right_index": 102,
            "fraction": 0.4981349024957319,
            "N_local": 0.001359439888821723,
            "N_physical": -56.70056065100801,
            "H_Mpl": 4.2968995523825917e-07,
            "required_standard_density_Mpl4": 3.1665149012667346e-26,
            "vacuum_frequency_margin_Mpl2": 6.284434543407456e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.0692527777417256e-21,
            "right_raychaudhuri_residual_Mpl2": -1.0772596878265491e-21,
            "left_normalized_residual": 5.791218593121455e-09,
            "right_normalized_residual": -5.83458581994365e-09,
            "bracket_width_N_local": 1.3393717048993748e-05
          },
          {
            "left_index": 114,
            "right_index": 115,
            "fraction": 0.8582876521016599,
            "N_local": 0.0015383819170730285,
            "N_physical": -57.02543001641031,
            "H_Mpl": 4.296895721023366e-07,
            "required_standard_density_Mpl4": 1.1146909461019985e-25,
            "vacuum_frequency_margin_Mpl2": 6.281299647025049e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 1.2661559056265394e-21,
            "right_raychaudhuri_residual_Mpl2": -2.0905570032648377e-22,
            "left_normalized_residual": 6.857684532074395e-09,
            "right_normalized_residual": -1.1322762412690418e-09,
            "bracket_width_N_local": 1.3393705454777492e-05
          },
          {
            "left_index": 116,
            "right_index": 117,
            "fraction": 0.43422312123954604,
            "N_local": 0.001559489530737296,
            "N_physical": -57.1789623682144,
            "H_Mpl": 4.2968952243814917e-07,
            "required_standard_density_Mpl4": 2.0622346831073145e-25,
            "vacuum_frequency_margin_Mpl2": 6.280911635012511e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -7.285056987183484e-22,
            "right_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
            "left_normalized_residual": -3.9456939643992105e-09,
            "right_normalized_residual": 5.141095987972354e-09,
            "bracket_width_N_local": 1.3393703494664864e-05
          },
          {
            "left_index": 117,
            "right_index": 118,
            "fraction": 0.9878589932033509,
            "N_local": 0.001580298467958751,
            "N_physical": -57.16308991401113,
            "H_Mpl": 4.2968947258953135e-07,
            "required_standard_density_Mpl4": 1.9334187724532636e-25,
            "vacuum_frequency_margin_Mpl2": 6.280525645903106e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
            "right_raychaudhuri_residual_Mpl2": -1.1666079949267927e-23,
            "left_normalized_residual": 5.141095987972354e-09,
            "right_normalized_residual": -6.318522291659054e-11,
            "bracket_width_N_local": 1.339370249623978e-05
          },
          {
            "left_index": 119,
            "right_index": 120,
            "fraction": 0.8428465471001942,
            "N_local": 0.0016051436166644778,
            "N_physical": -57.16339033749111,
            "H_Mpl": 4.296894117252259e-07,
            "required_standard_density_Mpl4": 1.9369378485244054e-25,
            "vacuum_frequency_margin_Mpl2": 6.280059616028694e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -5.306399063187383e-22,
            "right_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "left_normalized_residual": -2.8740250373060523e-09,
            "right_normalized_residual": 5.358781255435093e-10,
            "bracket_width_N_local": 1.3393700462002202e-05
          },
          {
            "left_index": 120,
            "right_index": 121,
            "fraction": 0.09178239976574161,
            "N_local": 0.001608477788814241,
            "N_physical": -57.15354798384819,
            "H_Mpl": 4.296894034642662e-07,
            "required_standard_density_Mpl4": 1.8655455109898024e-25,
            "vacuum_frequency_margin_Mpl2": 6.279996722973984e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
            "right_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
            "left_normalized_residual": 5.358781255435093e-10,
            "right_normalized_residual": -5.302694440333927e-09,
            "bracket_width_N_local": 1.3393699425939256e-05
          },
          {
            "left_index": 121,
            "right_index": 122,
            "fraction": 0.5318905792781098,
            "N_local": 0.0016277661643535953,
            "N_physical": -56.998728930731936,
            "H_Mpl": 4.2968935508388884e-07,
            "required_standard_density_Mpl4": 1.0699821571821313e-25,
            "vacuum_frequency_margin_Mpl2": 6.279630665950597e-09,
            "positive_vacuum_frequency_margin": true,
            "left_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
            "right_raychaudhuri_residual_Mpl2": 8.616500379152947e-22,
            "left_normalized_residual": -5.302694440333927e-09,
            "right_normalized_residual": 4.666827559239031e-09,
            "bracket_width_N_local": 1.3393698377093784e-05
          }
        ]
      }
    ],
    "successive_exact_initial_probe_deltas": [
      {
        "abs_delta_N_physical": 0.020405457167854024,
        "relative_delta_required_standard_density": 0.07837957677753797,
        "abs_delta_quantum_rho_over_H2": 3.8282081621758904e-14,
        "abs_delta_quantum_pressure_over_H2": 1.4656568392330552e-13,
        "abs_delta_quantum_chi2_over_scale": 1.817952939422927e-10,
        "abs_delta_friedmann_normalized": 2.0931859471373094e-27,
        "abs_delta_raychaudhuri_normalized": 6.690251727916795e-14,
        "coarse_nodes": 129,
        "fine_nodes": 129,
        "coarse_stride": 2,
        "fine_stride": 2,
        "coarse_mode_nodes": 24,
        "fine_mode_nodes": 32
      },
      {
        "abs_delta_N_physical": 0.0,
        "relative_delta_required_standard_density": 0.0,
        "abs_delta_quantum_rho_over_H2": 0.0,
        "abs_delta_quantum_pressure_over_H2": 0.0,
        "abs_delta_quantum_chi2_over_scale": 1.7803489445516112e-13,
        "abs_delta_friedmann_normalized": 0.0,
        "abs_delta_raychaudhuri_normalized": 0.0,
        "coarse_nodes": 129,
        "fine_nodes": 129,
        "coarse_stride": 2,
        "fine_stride": 2,
        "coarse_mode_nodes": 32,
        "fine_mode_nodes": 48
      },
      {
        "abs_delta_N_physical": 0.0,
        "relative_delta_required_standard_density": 0.0,
        "abs_delta_quantum_rho_over_H2": 0.0,
        "abs_delta_quantum_pressure_over_H2": 0.0,
        "abs_delta_quantum_chi2_over_scale": 2.0440286389800357e-16,
        "abs_delta_friedmann_normalized": 0.0,
        "abs_delta_raychaudhuri_normalized": 0.0,
        "coarse_nodes": 129,
        "fine_nodes": 129,
        "coarse_stride": 2,
        "fine_stride": 2,
        "coarse_mode_nodes": 48,
        "fine_mode_nodes": 64
      }
    ],
    "root_scan_diagnostic_successive_selection_deltas": [
      {
        "coarse_nodes": 129,
        "fine_nodes": 129,
        "coarse_stride": 2,
        "fine_stride": 2,
        "coarse_mode_nodes": 24,
        "fine_mode_nodes": 32,
        "abs_delta_N_local": 2.7628951589694223e-10,
        "abs_delta_N_physical": 0.06617145859923568,
        "relative_delta_H": 1.4476439314762676e-13,
        "relative_delta_required_standard_density": 0.23252826792844597
      },
      {
        "coarse_nodes": 129,
        "fine_nodes": 129,
        "coarse_stride": 2,
        "fine_stride": 2,
        "coarse_mode_nodes": 32,
        "fine_mode_nodes": 48,
        "abs_delta_N_local": 4.1605048128456196e-13,
        "abs_delta_N_physical": 0.00032735980972375955,
        "relative_delta_H": 2.4640747769808816e-16,
        "relative_delta_required_standard_density": 0.0013142145269281456
      },
      {
        "coarse_nodes": 129,
        "fine_nodes": 129,
        "coarse_stride": 2,
        "fine_stride": 2,
        "coarse_mode_nodes": 48,
        "fine_mode_nodes": 64,
        "abs_delta_N_local": 1.4827124716811774e-13,
        "abs_delta_N_physical": 0.0003273596033821491,
        "relative_delta_H": 1.232037388490441e-16,
        "relative_delta_required_standard_density": 0.001315943137798692
      }
    ]
  },
  "roundoff_pilot": {
    "low_precision_level": {
      "prefix_intervals": 256,
      "stride": 2,
      "nodes": 129,
      "mode_nodes": 64,
      "decimal_digits": 60,
      "first_stored_index": 0,
      "last_stored_index": 256,
      "last_N_local": 0.001714398048252598,
      "friedmann_density_matches": 89,
      "simultaneous_sign_change_brackets": 46,
      "positive_frequency_brackets": 46,
      "selected_earliest_admissible": {
        "left_index": 5,
        "right_index": 6,
        "fraction": 0.7878425339991634,
        "N_local": 7.752094659454906e-05,
        "N_physical": -56.69916548500461,
        "H_Mpl": 4.296911741311535e-07,
        "required_standard_density_Mpl4": 3.022613588034913e-26,
        "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
        "positive_vacuum_frequency_margin": true,
        "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
        "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
        "left_normalized_residual": -2.5565397212652397e-09,
        "right_normalized_residual": 6.884484820267378e-10,
        "bracket_width_N_local": 1.339375507064178e-05
      },
      "exact_initial_HARD_PASS_junction_probe": {
        "stored_index": 0,
        "N_local": 0.0,
        "N_physical": -56.97244594022879,
        "N_offset_physical_minus_local": -56.97244594022879,
        "H_Mpl": 4.296911897956572e-07,
        "required_standard_density_Mpl4": 9.017902368676568e-26,
        "standard_pressure_Mpl4": 3.0059674562255395e-26,
        "quantum_rho_Mpl4": 2.5653546520792134e-21,
        "quantum_pressure_Mpl4": 5.953926906537879e-21,
        "quantum_chi2_Mpl2": 1.7684877974411396e-15,
        "friedmann_residual_Mpl4": -4.936157918492028e-40,
        "friedmann_normalized": -8.91158373533706e-28,
        "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "raychaudhuri_normalized": -3.625504617408686e-08,
        "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
        "positive_vacuum_frequency_margin": true
      },
      "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
      "initial_normalized_residual": -3.625504617408686e-08,
      "wronskian_relative_error": 4.24e-58,
      "finite": true,
      "root_candidates": [
        {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878425339991634,
          "N_local": 7.752094659454906e-05,
          "N_physical": -56.69916548500461,
          "H_Mpl": 4.296911741311535e-07,
          "required_standard_density_Mpl4": 3.022613588034913e-26,
          "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
          "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
          "left_normalized_residual": -2.5565397212652397e-09,
          "right_normalized_residual": 6.884484820267378e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        {
          "left_index": 6,
          "right_index": 7,
          "fraction": 0.3642274780348604,
          "N_local": 8.524090532641941e-05,
          "N_physical": -56.74707739119948,
          "H_Mpl": 4.2969117234716105e-07,
          "required_standard_density_Mpl4": 3.779356413779906e-26,
          "vacuum_frequency_margin_Mpl2": 6.29879436356012e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
          "right_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
          "left_normalized_residual": 6.884484820267378e-10,
          "right_normalized_residual": -1.2017122827262556e-09,
          "bracket_width_N_local": 1.3393754974687068e-05
        },
        {
          "left_index": 7,
          "right_index": 8,
          "fraction": 0.21241430411053652,
          "N_local": 9.660131182641272e-05,
          "N_physical": -56.70112291800134,
          "H_Mpl": 4.296911696555098e-07,
          "required_standard_density_Mpl4": 4.096999558168485e-26,
          "vacuum_frequency_margin_Mpl2": 6.298728217567521e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
          "right_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
          "left_normalized_residual": -1.2017122827262556e-09,
          "right_normalized_residual": 4.455685895618096e-09,
          "bracket_width_N_local": 1.339375487477941e-05
        },
        {
          "left_index": 8,
          "right_index": 9,
          "fraction": 0.6065846174498755,
          "N_local": 0.00011527448719392336,
          "N_physical": -56.223771979203654,
          "H_Mpl": 4.296911650179105e-07,
          "required_standard_density_Mpl4": 4.513930388941858e-27,
          "vacuum_frequency_margin_Mpl2": 6.298616934764003e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
          "right_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
          "left_normalized_residual": 4.455685895618096e-09,
          "right_normalized_residual": -2.8898447940549242e-09,
          "bracket_width_N_local": 1.3393754770835335e-05
        },
        {
          "left_index": 9,
          "right_index": 10,
          "fraction": 0.2574202995656594,
          "N_local": 0.00012399162068847292,
          "N_physical": -56.32060338324056,
          "H_Mpl": 4.296911627704443e-07,
          "required_standard_density_Mpl4": 8.69484844629573e-27,
          "vacuum_frequency_margin_Mpl2": 6.298564016845657e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
          "right_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
          "left_normalized_residual": -2.8898447940549242e-09,
          "right_normalized_residual": 8.336328255348749e-09,
          "bracket_width_N_local": 1.3393754662768595e-05
        },
        {
          "left_index": 10,
          "right_index": 11,
          "fraction": 0.9413398149808291,
          "N_local": 0.0001465456254441022,
          "N_physical": -56.85173446217978,
          "H_Mpl": 4.2969115669102096e-07,
          "required_standard_density_Mpl4": 5.690277456177136e-26,
          "vacuum_frequency_margin_Mpl2": 6.2984240669508886e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
          "right_raychaudhuri_residual_Mpl2": -9.591458369669014e-23,
          "left_normalized_residual": 8.336328255348749e-09,
          "right_normalized_residual": -5.194835684323147e-10,
          "bracket_width_N_local": 1.3393754550492778e-05
        },
        {
          "left_index": 14,
          "right_index": 15,
          "fraction": 0.11548721003307255,
          "N_local": 0.00018905937578647347,
          "N_physical": -56.96006244393786,
          "H_Mpl": 4.2969114412597683e-07,
          "required_standard_density_Mpl4": 8.828292126183686e-26,
          "vacuum_frequency_margin_Mpl2": 6.298148090172184e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.5513916356533313e-22,
          "right_raychaudhuri_residual_Mpl2": -1.1882058139512706e-21,
          "left_normalized_residual": 8.402502271818305e-10,
          "right_normalized_residual": -6.4354493210886855e-09,
          "bracket_width_N_local": 1.3393754057482415e-05
        },
        {
          "left_index": 17,
          "right_index": 18,
          "fraction": 0.08744038024700374,
          "N_local": 0.00022886498517327977,
          "N_physical": -56.789232006461916,
          "H_Mpl": 4.296911310119382e-07,
          "required_standard_density_Mpl4": 4.568037874804944e-26,
          "vacuum_frequency_margin_Mpl2": 6.2978756030892115e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -6.106238344959863e-23,
          "right_raychaudhuri_residual_Mpl2": 6.372692486534195e-22,
          "left_normalized_residual": -3.307203902435353e-10,
          "right_normalized_residual": 3.4515183868669134e-09,
          "bracket_width_N_local": 1.339375363908614e-05
        },
        {
          "left_index": 22,
          "right_index": 23,
          "fraction": 0.3109410910174016,
          "N_local": 0.0002988272650373031,
          "N_physical": -56.70810397507022,
          "H_Mpl": 4.296911045649456e-07,
          "required_standard_density_Mpl4": 3.7581961073256013e-26,
          "vacuum_frequency_margin_Mpl2": 6.297363409473673e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.99856639440169e-22,
          "right_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
          "left_normalized_residual": -1.624055774041247e-09,
          "right_normalized_residual": 3.5989779442597223e-09,
          "bracket_width_N_local": 1.3393752842742138e-05
        },
        {
          "left_index": 23,
          "right_index": 24,
          "fraction": 0.564706651707065,
          "N_local": 0.0003156198909813086,
          "N_physical": -56.69531183159522,
          "H_Mpl": 4.29691097551177e-07,
          "required_standard_density_Mpl4": 4.0136158997550725e-26,
          "vacuum_frequency_margin_Mpl2": 6.297234186260923e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
          "right_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
          "left_normalized_residual": 3.5989779442597223e-09,
          "right_normalized_residual": -2.774203555973799e-09,
          "bracket_width_N_local": 1.3393752668113652e-05
        },
        {
          "left_index": 24,
          "right_index": 25,
          "fraction": 0.7238164271918855,
          "N_local": 0.0003311447204991803,
          "N_physical": -56.67592240321177,
          "H_Mpl": 4.2969109083978294e-07,
          "required_standard_density_Mpl4": 3.1800670545861125e-26,
          "vacuum_frequency_margin_Mpl2": 6.2971126129239e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
          "right_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
          "left_normalized_residual": -2.774203555973799e-09,
          "right_normalized_residual": 1.058541146449756e-09,
          "bracket_width_N_local": 1.3393752488282513e-05
        },
        {
          "left_index": 25,
          "right_index": 26,
          "fraction": 0.10861082179822887,
          "N_local": 0.00033629856135931695,
          "N_physical": -56.6223775919006,
          "H_Mpl": 4.2969108856934607e-07,
          "required_standard_density_Mpl4": 2.3340453548590064e-26,
          "vacuum_frequency_margin_Mpl2": 6.297071862011722e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
          "right_raychaudhuri_residual_Mpl2": -1.6040381628345865e-21,
          "left_normalized_residual": 1.058541146449756e-09,
          "right_normalized_residual": -8.687643951565464e-09,
          "bracket_width_N_local": 1.3393752303225248e-05
        },
        {
          "left_index": 30,
          "right_index": 31,
          "fraction": 0.8427289524142231,
          "N_local": 0.00041309991647547526,
          "N_physical": -56.65091948474018,
          "H_Mpl": 4.296910516217719e-07,
          "required_standard_density_Mpl4": 3.344055246552905e-26,
          "vacuum_frequency_margin_Mpl2": 6.296436238913727e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.2235941124756778e-21,
          "right_raychaudhuri_residual_Mpl2": 4.1496969396006417e-22,
          "left_normalized_residual": -1.204322734204436e-08,
          "right_normalized_residual": 2.24752102750371e-09,
          "bracket_width_N_local": 1.3393751298504256e-05
        },
        {
          "left_index": 32,
          "right_index": 33,
          "fraction": 0.8794008590948205,
          "N_local": 0.0004403785928661611,
          "N_physical": -56.60458670710162,
          "H_Mpl": 4.2969103711929483e-07,
          "required_standard_density_Mpl4": 2.422318717846245e-26,
          "vacuum_frequency_margin_Mpl2": 6.29619826252337e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.7113735259912426e-21,
          "right_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
          "left_normalized_residual": 9.268985585911212e-09,
          "right_normalized_residual": -1.2711287745714935e-09,
          "bracket_width_N_local": 1.3393750858574967e-05
        },
        {
          "left_index": 33,
          "right_index": 34,
          "fraction": 0.13927695721182692,
          "N_local": 0.00044385930854661996,
          "N_physical": -56.65083941813677,
          "H_Mpl": 4.2969103521278307e-07,
          "required_standard_density_Mpl4": 2.5408554787641562e-26,
          "vacuum_frequency_margin_Mpl2": 6.296167422194674e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
          "right_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
          "left_normalized_residual": -1.2711287745714935e-09,
          "right_normalized_residual": 7.855498040187442e-09,
          "bracket_width_N_local": 1.3393750630116873e-05
        },
        {
          "left_index": 34,
          "right_index": 35,
          "fraction": 0.5055229316221608,
          "N_local": 0.0004621584663088393,
          "N_physical": -56.674236408190716,
          "H_Mpl": 4.2969102497707594e-07,
          "required_standard_density_Mpl4": 3.27358524823297e-26,
          "vacuum_frequency_margin_Mpl2": 6.296003522723821e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
          "right_raychaudhuri_residual_Mpl2": -1.418703344144049e-21,
          "left_normalized_residual": 7.855498040187442e-09,
          "right_normalized_residual": -7.683852771421306e-09,
          "bracket_width_N_local": 1.3393750395837372e-05
        },
        {
          "left_index": 37,
          "right_index": 38,
          "fraction": 0.2761316055719378,
          "N_local": 0.0004992673064013667,
          "N_physical": -56.95940617049714,
          "H_Mpl": 4.29691003142314e-07,
          "required_standard_density_Mpl4": 8.683488899909805e-26,
          "vacuum_frequency_margin_Mpl2": 6.295662530107288e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.891666530020456e-22,
          "right_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
          "left_normalized_residual": -3.1909913874787536e-09,
          "right_normalized_residual": 8.365061636851863e-09,
          "bracket_width_N_local": 1.3393749656707803e-05
        },
        {
          "left_index": 38,
          "right_index": 39,
          "fraction": 0.6120451497427785,
          "N_local": 0.0005171601978165187,
          "N_physical": -57.01135998833373,
          "H_Mpl": 4.29690992056104e-07,
          "required_standard_density_Mpl4": 1.1305188629660545e-25,
          "vacuum_frequency_margin_Mpl2": 6.295493822700022e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
          "right_raychaudhuri_residual_Mpl2": -9.789925335806768e-22,
          "left_normalized_residual": 8.365061636851863e-09,
          "right_normalized_residual": -5.302331638639811e-09,
          "bracket_width_N_local": 1.3393749397776797e-05
        },
        {
          "left_index": 43,
          "right_index": 44,
          "fraction": 0.3686707670589538,
          "N_local": 0.0005808692460792936,
          "N_physical": -56.38768208111163,
          "H_Mpl": 4.296909495232809e-07,
          "required_standard_density_Mpl4": 1.3813187640175078e-26,
          "vacuum_frequency_margin_Mpl2": 6.294870827937082e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -8.89864129001246e-22,
          "right_raychaudhuri_residual_Mpl2": 1.523845360633848e-21,
          "left_normalized_residual": -4.819603162500771e-09,
          "right_normalized_residual": 8.253316438136793e-09,
          "bracket_width_N_local": 1.3393748003819256e-05
        },
        {
          "left_index": 51,
          "right_index": 52,
          "fraction": 0.5175748228717203,
          "N_local": 0.0006900136034076554,
          "N_physical": -56.791632190308796,
          "H_Mpl": 4.296908650774768e-07,
          "required_standard_density_Mpl4": 4.3752395393722416e-26,
          "vacuum_frequency_margin_Mpl2": 6.293722225867458e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.2188561560037294e-21,
          "right_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
          "left_normalized_residual": 6.6014631197392056e-09,
          "right_normalized_residual": -6.153143547955088e-09,
          "bracket_width_N_local": 1.3393745416623716e-05
        },
        {
          "left_index": 52,
          "right_index": 53,
          "fraction": 0.6057309951478642,
          "N_local": 0.0007045880899376551,
          "N_physical": -56.94035089498465,
          "H_Mpl": 4.296908526724755e-07,
          "required_standard_density_Mpl4": 8.792718649026132e-26,
          "vacuum_frequency_margin_Mpl2": 6.293561091423428e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
          "right_raychaudhuri_residual_Mpl2": 7.394726529583393e-22,
          "left_normalized_residual": -6.153143547955088e-09,
          "right_normalized_residual": 4.005068145222769e-09,
          "bracket_width_N_local": 1.3393745061689535e-05
        },
        {
          "left_index": 55,
          "right_index": 56,
          "fraction": 0.42134239853141464,
          "N_local": 0.000742299669706633,
          "N_physical": -57.03203966644007,
          "H_Mpl": 4.2969081928852725e-07,
          "required_standard_density_Mpl4": 1.2125725238328269e-25,
          "vacuum_frequency_margin_Mpl2": 6.293135637750973e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 4.1467529397916027e-22,
          "right_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
          "left_normalized_residual": 2.2459288888163688e-09,
          "right_normalized_residual": -3.084484025960798e-09,
          "bracket_width_N_local": 1.3393743953274851e-05
        },
        {
          "left_index": 56,
          "right_index": 57,
          "fraction": 0.7437193655246365,
          "N_local": 0.000760011247926384,
          "N_physical": -56.906387415728744,
          "H_Mpl": 4.2969080296152854e-07,
          "required_standard_density_Mpl4": 6.934448839336835e-26,
          "vacuum_frequency_margin_Mpl2": 6.292931635524838e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
          "right_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
          "left_normalized_residual": -3.084484025960798e-09,
          "right_normalized_residual": 1.0628922758579984e-09,
          "bracket_width_N_local": 1.3393743568903388e-05
        },
        {
          "left_index": 57,
          "right_index": 58,
          "fraction": 0.4513855429535026,
          "N_local": 0.000769489547062301,
          "N_physical": -56.953879584273736,
          "H_Mpl": 4.2969079403720936e-07,
          "required_standard_density_Mpl4": 8.628654545432148e-26,
          "vacuum_frequency_margin_Mpl2": 6.2928212886367955e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
          "right_raychaudhuri_residual_Mpl2": -2.3851789262401107e-22,
          "left_normalized_residual": 1.0628922758579984e-09,
          "right_normalized_residual": -1.2918404507906814e-09,
          "bracket_width_N_local": 1.3393743176885482e-05
        },
        {
          "left_index": 60,
          "right_index": 61,
          "fraction": 0.6625296414804297,
          "N_local": 0.0008124987844043409,
          "N_physical": -56.72634788093764,
          "H_Mpl": 4.2969075199085846e-07,
          "required_standard_density_Mpl4": 3.487610598278128e-26,
          "vacuum_frequency_margin_Mpl2": 6.292311072168803e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.0632820781371679e-21,
          "right_raychaudhuri_residual_Mpl2": 5.416001966562323e-22,
          "left_normalized_residual": -5.7588592254670335e-09,
          "right_normalized_residual": 2.9333697507287355e-09,
          "bracket_width_N_local": 1.339374195376004e-05
        },
        {
          "left_index": 62,
          "right_index": 63,
          "fraction": 0.2828776488502654,
          "N_local": 0.0008342013068245111,
          "N_physical": -56.42416066977023,
          "H_Mpl": 4.2969072976349885e-07,
          "required_standard_density_Mpl4": 1.0516148238801056e-26,
          "vacuum_frequency_margin_Mpl2": 6.292047577098258e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 3.5493257717780747e-22,
          "right_raychaudhuri_residual_Mpl2": -8.997886021744807e-22,
          "left_normalized_residual": 1.922356303387535e-09,
          "right_normalized_residual": -4.873360505520376e-09,
          "bracket_width_N_local": 1.3393741098036778e-05
        },
        {
          "left_index": 70,
          "right_index": 71,
          "fraction": 0.047099575065959104,
          "N_local": 0.0009381932721551563,
          "N_physical": -56.635079275733936,
          "H_Mpl": 4.296906134321862e-07,
          "required_standard_density_Mpl4": 2.4692151081577868e-26,
          "vacuum_frequency_margin_Mpl2": 6.290728777635009e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 5.890382125923059e-23,
          "right_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
          "left_normalized_residual": 3.190301549322586e-10,
          "right_normalized_residual": -6.454495453235951e-09,
          "bracket_width_N_local": 1.3393737338068313e-05
        },
        {
          "left_index": 71,
          "right_index": 72,
          "fraction": 0.5614620610416048,
          "N_local": 0.0009584762452410652,
          "N_physical": -56.95618282563535,
          "H_Mpl": 4.296905887515237e-07,
          "required_standard_density_Mpl4": 8.467609511956364e-26,
          "vacuum_frequency_margin_Mpl2": 6.290460528983634e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
          "right_raychaudhuri_residual_Mpl2": 9.308093924205628e-22,
          "left_normalized_residual": -6.454495453235951e-09,
          "right_normalized_residual": 5.041375983482935e-09,
          "bracket_width_N_local": 1.339373682891006e-05
        },
        {
          "left_index": 73,
          "right_index": 74,
          "fraction": 0.4348853540070985,
          "N_local": 0.0009835683828234758,
          "N_physical": -56.62021285300039,
          "H_Mpl": 4.2969055733943505e-07,
          "required_standard_density_Mpl4": 3.015939093992669e-26,
          "vacuum_frequency_margin_Mpl2": 6.2901239722949215e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.194690813740266e-21,
          "right_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
          "left_normalized_residual": 6.47059010702358e-09,
          "right_normalized_residual": -8.408251725070025e-09,
          "bracket_width_N_local": 1.3393735783597243e-05
        },
        {
          "left_index": 74,
          "right_index": 75,
          "fraction": 0.5675920042901169,
          "N_local": 0.0009987395561132746,
          "N_physical": -55.832306400564924,
          "H_Mpl": 4.296905378492746e-07,
          "required_standard_density_Mpl4": 3.66165402285607e-27,
          "vacuum_frequency_margin_Mpl2": 6.289917856371982e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
          "right_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
          "left_normalized_residual": -8.408251725070025e-09,
          "right_normalized_residual": 6.405649730889708e-09,
          "bracket_width_N_local": 1.3393735247269316e-05
        },
        {
          "left_index": 75,
          "right_index": 76,
          "fraction": 0.46870607498227307,
          "N_local": 0.0010108088391480106,
          "N_physical": -55.995256347003696,
          "H_Mpl": 4.296905220722735e-07,
          "required_standard_density_Mpl4": 1.1627710255761945e-26,
          "vacuum_frequency_margin_Mpl2": 6.289752465737699e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
          "right_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
          "left_normalized_residual": 6.405649730889708e-09,
          "right_normalized_residual": -7.261017616518347e-09,
          "bracket_width_N_local": 1.3393734701716781e-05
        },
        {
          "left_index": 76,
          "right_index": 77,
          "fraction": 0.9123702377387957,
          "N_local": 0.001030144893436112,
          "N_physical": -56.94665879344938,
          "H_Mpl": 4.296904963167453e-07,
          "required_standard_density_Mpl4": 8.540104780800767e-26,
          "vacuum_frequency_margin_Mpl2": 6.289485018541246e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
          "right_raychaudhuri_residual_Mpl2": 1.2876254256938986e-22,
          "left_normalized_residual": -7.261017616518347e-09,
          "right_normalized_residual": 6.973937491092083e-10,
          "bracket_width_N_local": 1.3393734146858972e-05
        },
        {
          "left_index": 89,
          "right_index": 90,
          "fraction": 0.9686572376319323,
          "N_local": 0.0012050172758680136,
          "N_physical": -56.82090151317981,
          "H_Mpl": 4.296902338903307e-07,
          "required_standard_density_Mpl4": 4.95451873713127e-26,
          "vacuum_frequency_margin_Mpl2": 6.286919107523303e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.3204165946425948e-21,
          "right_raychaudhuri_residual_Mpl2": 4.272461087877763e-23,
          "left_normalized_residual": -7.1515464632206394e-09,
          "right_normalized_residual": 2.3140202296214582e-10,
          "bracket_width_N_local": 1.3393726058015575e-05
        },
        {
          "left_index": 92,
          "right_index": 93,
          "fraction": 0.024259324250412394,
          "N_local": 0.0012325494449634913,
          "N_physical": -56.850344980674116,
          "H_Mpl": 4.296901875854801e-07,
          "required_standard_density_Mpl4": 5.534209017110175e-26,
          "vacuum_frequency_margin_Mpl2": 6.28649117473157e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 4.0142619240537e-23,
          "right_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
          "left_normalized_residual": 2.1741766762132975e-10,
          "right_normalized_residual": -8.7448142610148e-09,
          "bracket_width_N_local": 1.3393723951315778e-05
        },
        {
          "left_index": 93,
          "right_index": 94,
          "fraction": 0.4848703013313575,
          "N_local": 0.0012521124648400947,
          "N_physical": -56.9863466284211,
          "H_Mpl": 4.2969015377855907e-07,
          "required_standard_density_Mpl4": 1.053735996171995e-25,
          "vacuum_frequency_margin_Mpl2": 6.286182970155485e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
          "right_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
          "left_normalized_residual": -8.7448142610148e-09,
          "right_normalized_residual": 9.290554634716903e-09,
          "bracket_width_N_local": 1.3393723228069879e-05
        },
        {
          "left_index": 94,
          "right_index": 95,
          "fraction": 0.4549072309281898,
          "N_local": 0.0012651048706622495,
          "N_physical": -56.997242900768406,
          "H_Mpl": 4.296901309484704e-07,
          "required_standard_density_Mpl4": 1.1016369238939384e-25,
          "vacuum_frequency_margin_Mpl2": 6.285976581984483e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
          "right_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
          "left_normalized_residual": 9.290554634716903e-09,
          "right_normalized_residual": -1.113241198825085e-08,
          "bracket_width_N_local": 1.3393722494135915e-05
        },
        {
          "left_index": 95,
          "right_index": 96,
          "fraction": 0.7538644082141279,
          "N_local": 0.0012825027420651565,
          "N_physical": -56.88732829339666,
          "H_Mpl": 4.2969009987700475e-07,
          "required_standard_density_Mpl4": 6.420356596172189e-26,
          "vacuum_frequency_margin_Mpl2": 6.2856979866767695e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
          "right_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
          "left_normalized_residual": -1.113241198825085e-08,
          "right_normalized_residual": 3.634716123765566e-09,
          "bracket_width_N_local": 1.3393721749403948e-05
        },
        {
          "left_index": 96,
          "right_index": 97,
          "fraction": 0.7092775479346664,
          "N_local": 0.001295299279278346,
          "N_physical": -56.97299511970861,
          "H_Mpl": 4.296900766345335e-07,
          "required_standard_density_Mpl4": 9.217305944021855e-26,
          "vacuum_frequency_margin_Mpl2": 6.285491362413646e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
          "right_raychaudhuri_residual_Mpl2": -2.75070198710292e-22,
          "left_normalized_residual": 3.634716123765566e-09,
          "right_normalized_residual": -1.4898169372979586e-09,
          "bracket_width_N_local": 1.3393720993773364e-05
        },
        {
          "left_index": 98,
          "right_index": 99,
          "fraction": 0.4569399285322861,
          "N_local": 0.0013187069801230823,
          "N_physical": -56.82730406410569,
          "H_Mpl": 4.29690033281348e-07,
          "required_standard_density_Mpl4": 6.073586449968256e-26,
          "vacuum_frequency_margin_Mpl2": 6.285109757800073e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -9.944762113653646e-22,
          "right_raychaudhuri_residual_Mpl2": 1.1819066111200154e-21,
          "left_normalized_residual": -5.386216613824514e-09,
          "right_normalized_residual": 6.4013655597193205e-09,
          "bracket_width_N_local": 1.3393719449427549e-05
        },
        {
          "left_index": 101,
          "right_index": 102,
          "fraction": 0.4981349024957319,
          "N_local": 0.001359439888821723,
          "N_physical": -56.70056065100801,
          "H_Mpl": 4.2968995523825917e-07,
          "required_standard_density_Mpl4": 3.1665149012667346e-26,
          "vacuum_frequency_margin_Mpl2": 6.284434543407456e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.0692527777417256e-21,
          "right_raychaudhuri_residual_Mpl2": -1.0772596878265491e-21,
          "left_normalized_residual": 5.791218593121455e-09,
          "right_normalized_residual": -5.83458581994365e-09,
          "bracket_width_N_local": 1.3393717048993748e-05
        },
        {
          "left_index": 114,
          "right_index": 115,
          "fraction": 0.8582876521016599,
          "N_local": 0.0015383819170730285,
          "N_physical": -57.02543001641031,
          "H_Mpl": 4.296895721023366e-07,
          "required_standard_density_Mpl4": 1.1146909461019985e-25,
          "vacuum_frequency_margin_Mpl2": 6.281299647025049e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.2661559056265394e-21,
          "right_raychaudhuri_residual_Mpl2": -2.0905570032648377e-22,
          "left_normalized_residual": 6.857684532074395e-09,
          "right_normalized_residual": -1.1322762412690418e-09,
          "bracket_width_N_local": 1.3393705454777492e-05
        },
        {
          "left_index": 116,
          "right_index": 117,
          "fraction": 0.43422312123954604,
          "N_local": 0.001559489530737296,
          "N_physical": -57.1789623682144,
          "H_Mpl": 4.2968952243814917e-07,
          "required_standard_density_Mpl4": 2.0622346831073145e-25,
          "vacuum_frequency_margin_Mpl2": 6.280911635012511e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -7.285056987183484e-22,
          "right_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
          "left_normalized_residual": -3.9456939643992105e-09,
          "right_normalized_residual": 5.141095987972354e-09,
          "bracket_width_N_local": 1.3393703494664864e-05
        },
        {
          "left_index": 117,
          "right_index": 118,
          "fraction": 0.9878589932033509,
          "N_local": 0.001580298467958751,
          "N_physical": -57.16308991401113,
          "H_Mpl": 4.2968947258953135e-07,
          "required_standard_density_Mpl4": 1.9334187724532636e-25,
          "vacuum_frequency_margin_Mpl2": 6.280525645903106e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
          "right_raychaudhuri_residual_Mpl2": -1.1666079949267927e-23,
          "left_normalized_residual": 5.141095987972354e-09,
          "right_normalized_residual": -6.318522291659054e-11,
          "bracket_width_N_local": 1.339370249623978e-05
        },
        {
          "left_index": 119,
          "right_index": 120,
          "fraction": 0.8428465471001942,
          "N_local": 0.0016051436166644778,
          "N_physical": -57.16339033749111,
          "H_Mpl": 4.296894117252259e-07,
          "required_standard_density_Mpl4": 1.9369378485244054e-25,
          "vacuum_frequency_margin_Mpl2": 6.280059616028694e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.306399063187383e-22,
          "right_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
          "left_normalized_residual": -2.8740250373060523e-09,
          "right_normalized_residual": 5.358781255435093e-10,
          "bracket_width_N_local": 1.3393700462002202e-05
        },
        {
          "left_index": 120,
          "right_index": 121,
          "fraction": 0.09178239976574161,
          "N_local": 0.001608477788814241,
          "N_physical": -57.15354798384819,
          "H_Mpl": 4.296894034642662e-07,
          "required_standard_density_Mpl4": 1.8655455109898024e-25,
          "vacuum_frequency_margin_Mpl2": 6.279996722973984e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
          "right_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
          "left_normalized_residual": 5.358781255435093e-10,
          "right_normalized_residual": -5.302694440333927e-09,
          "bracket_width_N_local": 1.3393699425939256e-05
        },
        {
          "left_index": 121,
          "right_index": 122,
          "fraction": 0.5318905792781098,
          "N_local": 0.0016277661643535953,
          "N_physical": -56.998728930731936,
          "H_Mpl": 4.2968935508388884e-07,
          "required_standard_density_Mpl4": 1.0699821571821313e-25,
          "vacuum_frequency_margin_Mpl2": 6.279630665950597e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
          "right_raychaudhuri_residual_Mpl2": 8.616500379152947e-22,
          "left_normalized_residual": -5.302694440333927e-09,
          "right_normalized_residual": 4.666827559239031e-09,
          "bracket_width_N_local": 1.3393698377093784e-05
        }
      ]
    },
    "high_precision_level": {
      "prefix_intervals": 256,
      "stride": 2,
      "nodes": 129,
      "mode_nodes": 64,
      "decimal_digits": 80,
      "first_stored_index": 0,
      "last_stored_index": 256,
      "last_N_local": 0.001714398048252598,
      "friedmann_density_matches": 89,
      "simultaneous_sign_change_brackets": 46,
      "positive_frequency_brackets": 46,
      "selected_earliest_admissible": {
        "left_index": 5,
        "right_index": 6,
        "fraction": 0.7878425339991634,
        "N_local": 7.752094659454906e-05,
        "N_physical": -56.69916548500461,
        "H_Mpl": 4.296911741311535e-07,
        "required_standard_density_Mpl4": 3.022613588034913e-26,
        "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
        "positive_vacuum_frequency_margin": true,
        "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
        "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
        "left_normalized_residual": -2.5565397212652397e-09,
        "right_normalized_residual": 6.884484820267378e-10,
        "bracket_width_N_local": 1.339375507064178e-05
      },
      "exact_initial_HARD_PASS_junction_probe": {
        "stored_index": 0,
        "N_local": 0.0,
        "N_physical": -56.97244594022879,
        "N_offset_physical_minus_local": -56.97244594022879,
        "H_Mpl": 4.296911897956572e-07,
        "required_standard_density_Mpl4": 9.017902368676568e-26,
        "standard_pressure_Mpl4": 3.0059674562255395e-26,
        "quantum_rho_Mpl4": 2.5653546520792134e-21,
        "quantum_pressure_Mpl4": 5.953926906537879e-21,
        "quantum_chi2_Mpl2": 1.7684877974411396e-15,
        "friedmann_residual_Mpl4": -4.936157918492028e-40,
        "friedmann_normalized": -8.91158373533706e-28,
        "raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
        "raychaudhuri_normalized": -3.625504617408686e-08,
        "vacuum_frequency_margin_Mpl2": 6.299255678190488e-09,
        "positive_vacuum_frequency_margin": true
      },
      "initial_raychaudhuri_residual_Mpl2": -6.693932996738512e-21,
      "initial_normalized_residual": -3.625504617408686e-08,
      "wronskian_relative_error": 3.86e-78,
      "finite": true,
      "root_candidates": [
        {
          "left_index": 5,
          "right_index": 6,
          "fraction": 0.7878425339991634,
          "N_local": 7.752094659454906e-05,
          "N_physical": -56.69916548500461,
          "H_Mpl": 4.296911741311535e-07,
          "required_standard_density_Mpl4": 3.022613588034913e-26,
          "vacuum_frequency_margin_Mpl2": 6.298838760818218e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -4.720254514915387e-22,
          "right_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
          "left_normalized_residual": -2.5565397212652397e-09,
          "right_normalized_residual": 6.884484820267378e-10,
          "bracket_width_N_local": 1.339375507064178e-05
        },
        {
          "left_index": 6,
          "right_index": 7,
          "fraction": 0.3642274780348604,
          "N_local": 8.524090532641941e-05,
          "N_physical": -56.74707739119948,
          "H_Mpl": 4.2969117234716105e-07,
          "required_standard_density_Mpl4": 3.779356413779906e-26,
          "vacuum_frequency_margin_Mpl2": 6.29879436356012e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.271113444053428e-22,
          "right_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
          "left_normalized_residual": 6.884484820267378e-10,
          "right_normalized_residual": -1.2017122827262556e-09,
          "bracket_width_N_local": 1.3393754974687068e-05
        },
        {
          "left_index": 7,
          "right_index": 8,
          "fraction": 0.21241430411053652,
          "N_local": 9.660131182641272e-05,
          "N_physical": -56.70112291800134,
          "H_Mpl": 4.296911696555098e-07,
          "required_standard_density_Mpl4": 4.096999558168485e-26,
          "vacuum_frequency_margin_Mpl2": 6.298728217567521e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.218775487203343e-22,
          "right_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
          "left_normalized_residual": -1.2017122827262556e-09,
          "right_normalized_residual": 4.455685895618096e-09,
          "bracket_width_N_local": 1.339375487477941e-05
        },
        {
          "left_index": 8,
          "right_index": 9,
          "fraction": 0.6065846174498755,
          "N_local": 0.00011527448719392336,
          "N_physical": -56.223771979203654,
          "H_Mpl": 4.296911650179105e-07,
          "required_standard_density_Mpl4": 4.513930388941858e-27,
          "vacuum_frequency_margin_Mpl2": 6.298616934764003e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 8.226733333373697e-22,
          "right_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
          "left_normalized_residual": 4.455685895618096e-09,
          "right_normalized_residual": -2.8898447940549242e-09,
          "bracket_width_N_local": 1.3393754770835335e-05
        },
        {
          "left_index": 9,
          "right_index": 10,
          "fraction": 0.2574202995656594,
          "N_local": 0.00012399162068847292,
          "N_physical": -56.32060338324056,
          "H_Mpl": 4.296911627704443e-07,
          "required_standard_density_Mpl4": 8.69484844629573e-27,
          "vacuum_frequency_margin_Mpl2": 6.298564016845657e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.3356503748704475e-22,
          "right_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
          "left_normalized_residual": -2.8898447940549242e-09,
          "right_normalized_residual": 8.336328255348749e-09,
          "bracket_width_N_local": 1.3393754662768595e-05
        },
        {
          "left_index": 10,
          "right_index": 11,
          "fraction": 0.9413398149808291,
          "N_local": 0.0001465456254441022,
          "N_physical": -56.85173446217978,
          "H_Mpl": 4.2969115669102096e-07,
          "required_standard_density_Mpl4": 5.690277456177136e-26,
          "vacuum_frequency_margin_Mpl2": 6.2984240669508886e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.5391737418062716e-21,
          "right_raychaudhuri_residual_Mpl2": -9.591458369669014e-23,
          "left_normalized_residual": 8.336328255348749e-09,
          "right_normalized_residual": -5.194835684323147e-10,
          "bracket_width_N_local": 1.3393754550492778e-05
        },
        {
          "left_index": 14,
          "right_index": 15,
          "fraction": 0.11548721003307255,
          "N_local": 0.00018905937578647347,
          "N_physical": -56.96006244393786,
          "H_Mpl": 4.2969114412597683e-07,
          "required_standard_density_Mpl4": 8.828292126183686e-26,
          "vacuum_frequency_margin_Mpl2": 6.298148090172184e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.5513916356533313e-22,
          "right_raychaudhuri_residual_Mpl2": -1.1882058139512706e-21,
          "left_normalized_residual": 8.402502271818305e-10,
          "right_normalized_residual": -6.4354493210886855e-09,
          "bracket_width_N_local": 1.3393754057482415e-05
        },
        {
          "left_index": 17,
          "right_index": 18,
          "fraction": 0.08744038024700374,
          "N_local": 0.00022886498517327977,
          "N_physical": -56.789232006461916,
          "H_Mpl": 4.296911310119382e-07,
          "required_standard_density_Mpl4": 4.568037874804944e-26,
          "vacuum_frequency_margin_Mpl2": 6.2978756030892115e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -6.106238344959863e-23,
          "right_raychaudhuri_residual_Mpl2": 6.372692486534195e-22,
          "left_normalized_residual": -3.307203902435353e-10,
          "right_normalized_residual": 3.4515183868669134e-09,
          "bracket_width_N_local": 1.339375363908614e-05
        },
        {
          "left_index": 22,
          "right_index": 23,
          "fraction": 0.3109410910174016,
          "N_local": 0.0002988272650373031,
          "N_physical": -56.70810397507022,
          "H_Mpl": 4.296911045649456e-07,
          "required_standard_density_Mpl4": 3.7581961073256013e-26,
          "vacuum_frequency_margin_Mpl2": 6.297363409473673e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.99856639440169e-22,
          "right_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
          "left_normalized_residual": -1.624055774041247e-09,
          "right_normalized_residual": 3.5989779442597223e-09,
          "bracket_width_N_local": 1.3393752842742138e-05
        },
        {
          "left_index": 23,
          "right_index": 24,
          "fraction": 0.564706651707065,
          "N_local": 0.0003156198909813086,
          "N_physical": -56.69531183159522,
          "H_Mpl": 4.29691097551177e-07,
          "required_standard_density_Mpl4": 4.0136158997550725e-26,
          "vacuum_frequency_margin_Mpl2": 6.297234186260923e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 6.644952847749156e-22,
          "right_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
          "left_normalized_residual": 3.5989779442597223e-09,
          "right_normalized_residual": -2.774203555973799e-09,
          "bracket_width_N_local": 1.3393752668113652e-05
        },
        {
          "left_index": 24,
          "right_index": 25,
          "fraction": 0.7238164271918855,
          "N_local": 0.0003311447204991803,
          "N_physical": -56.67592240321177,
          "H_Mpl": 4.2969109083978294e-07,
          "required_standard_density_Mpl4": 3.1800670545861125e-26,
          "vacuum_frequency_margin_Mpl2": 6.2971126129239e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.122135122017043e-22,
          "right_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
          "left_normalized_residual": -2.774203555973799e-09,
          "right_normalized_residual": 1.058541146449756e-09,
          "bracket_width_N_local": 1.3393752488282513e-05
        },
        {
          "left_index": 25,
          "right_index": 26,
          "fraction": 0.10861082179822887,
          "N_local": 0.00033629856135931695,
          "N_physical": -56.6223775919006,
          "H_Mpl": 4.2969108856934607e-07,
          "required_standard_density_Mpl4": 2.3340453548590064e-26,
          "vacuum_frequency_margin_Mpl2": 6.297071862011722e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.9544314349052028e-22,
          "right_raychaudhuri_residual_Mpl2": -1.6040381628345865e-21,
          "left_normalized_residual": 1.058541146449756e-09,
          "right_normalized_residual": -8.687643951565464e-09,
          "bracket_width_N_local": 1.3393752303225248e-05
        },
        {
          "left_index": 30,
          "right_index": 31,
          "fraction": 0.8427289524142231,
          "N_local": 0.00041309991647547526,
          "N_physical": -56.65091948474018,
          "H_Mpl": 4.296910516217719e-07,
          "required_standard_density_Mpl4": 3.344055246552905e-26,
          "vacuum_frequency_margin_Mpl2": 6.296436238913727e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.2235941124756778e-21,
          "right_raychaudhuri_residual_Mpl2": 4.1496969396006417e-22,
          "left_normalized_residual": -1.204322734204436e-08,
          "right_normalized_residual": 2.24752102750371e-09,
          "bracket_width_N_local": 1.3393751298504256e-05
        },
        {
          "left_index": 32,
          "right_index": 33,
          "fraction": 0.8794008590948205,
          "N_local": 0.0004403785928661611,
          "N_physical": -56.60458670710162,
          "H_Mpl": 4.2969103711929483e-07,
          "required_standard_density_Mpl4": 2.422318717846245e-26,
          "vacuum_frequency_margin_Mpl2": 6.29619826252337e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.7113735259912426e-21,
          "right_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
          "left_normalized_residual": 9.268985585911212e-09,
          "right_normalized_residual": -1.2711287745714935e-09,
          "bracket_width_N_local": 1.3393750858574967e-05
        },
        {
          "left_index": 33,
          "right_index": 34,
          "fraction": 0.13927695721182692,
          "N_local": 0.00044385930854661996,
          "N_physical": -56.65083941813677,
          "H_Mpl": 4.2969103521278307e-07,
          "required_standard_density_Mpl4": 2.5408554787641562e-26,
          "vacuum_frequency_margin_Mpl2": 6.296167422194674e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.3469408162149405e-22,
          "right_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
          "left_normalized_residual": -1.2711287745714935e-09,
          "right_normalized_residual": 7.855498040187442e-09,
          "bracket_width_N_local": 1.3393750630116873e-05
        },
        {
          "left_index": 34,
          "right_index": 35,
          "fraction": 0.5055229316221608,
          "N_local": 0.0004621584663088393,
          "N_physical": -56.674236408190716,
          "H_Mpl": 4.2969102497707594e-07,
          "required_standard_density_Mpl4": 3.27358524823297e-26,
          "vacuum_frequency_margin_Mpl2": 6.296003522723821e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.4503950122229873e-21,
          "right_raychaudhuri_residual_Mpl2": -1.418703344144049e-21,
          "left_normalized_residual": 7.855498040187442e-09,
          "right_normalized_residual": -7.683852771421306e-09,
          "bracket_width_N_local": 1.3393750395837372e-05
        },
        {
          "left_index": 37,
          "right_index": 38,
          "fraction": 0.2761316055719378,
          "N_local": 0.0004992673064013667,
          "N_physical": -56.95940617049714,
          "H_Mpl": 4.29691003142314e-07,
          "required_standard_density_Mpl4": 8.683488899909805e-26,
          "vacuum_frequency_margin_Mpl2": 6.295662530107288e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.891666530020456e-22,
          "right_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
          "left_normalized_residual": -3.1909913874787536e-09,
          "right_normalized_residual": 8.365061636851863e-09,
          "bracket_width_N_local": 1.3393749656707803e-05
        },
        {
          "left_index": 38,
          "right_index": 39,
          "fraction": 0.6120451497427785,
          "N_local": 0.0005171601978165187,
          "N_physical": -57.01135998833373,
          "H_Mpl": 4.29690992056104e-07,
          "required_standard_density_Mpl4": 1.1305188629660545e-25,
          "vacuum_frequency_margin_Mpl2": 6.295493822700022e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.5444777437765618e-21,
          "right_raychaudhuri_residual_Mpl2": -9.789925335806768e-22,
          "left_normalized_residual": 8.365061636851863e-09,
          "right_normalized_residual": -5.302331638639811e-09,
          "bracket_width_N_local": 1.3393749397776797e-05
        },
        {
          "left_index": 43,
          "right_index": 44,
          "fraction": 0.3686707670589538,
          "N_local": 0.0005808692460792936,
          "N_physical": -56.38768208111163,
          "H_Mpl": 4.296909495232809e-07,
          "required_standard_density_Mpl4": 1.3813187640175078e-26,
          "vacuum_frequency_margin_Mpl2": 6.294870827937082e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -8.89864129001246e-22,
          "right_raychaudhuri_residual_Mpl2": 1.523845360633848e-21,
          "left_normalized_residual": -4.819603162500771e-09,
          "right_normalized_residual": 8.253316438136793e-09,
          "bracket_width_N_local": 1.3393748003819256e-05
        },
        {
          "left_index": 51,
          "right_index": 52,
          "fraction": 0.5175748228717203,
          "N_local": 0.0006900136034076554,
          "N_physical": -56.791632190308796,
          "H_Mpl": 4.296908650774768e-07,
          "required_standard_density_Mpl4": 4.3752395393722416e-26,
          "vacuum_frequency_margin_Mpl2": 6.293722225867458e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.2188561560037294e-21,
          "right_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
          "left_normalized_residual": 6.6014631197392056e-09,
          "right_normalized_residual": -6.153143547955088e-09,
          "bracket_width_N_local": 1.3393745416623716e-05
        },
        {
          "left_index": 52,
          "right_index": 53,
          "fraction": 0.6057309951478642,
          "N_local": 0.0007045880899376551,
          "N_physical": -56.94035089498465,
          "H_Mpl": 4.296908526724755e-07,
          "required_standard_density_Mpl4": 8.792718649026132e-26,
          "vacuum_frequency_margin_Mpl2": 6.293561091423428e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.1360809509463514e-21,
          "right_raychaudhuri_residual_Mpl2": 7.394726529583393e-22,
          "left_normalized_residual": -6.153143547955088e-09,
          "right_normalized_residual": 4.005068145222769e-09,
          "bracket_width_N_local": 1.3393745061689535e-05
        },
        {
          "left_index": 55,
          "right_index": 56,
          "fraction": 0.42134239853141464,
          "N_local": 0.000742299669706633,
          "N_physical": -57.03203966644007,
          "H_Mpl": 4.2969081928852725e-07,
          "required_standard_density_Mpl4": 1.2125725238328269e-25,
          "vacuum_frequency_margin_Mpl2": 6.293135637750973e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 4.1467529397916027e-22,
          "right_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
          "left_normalized_residual": 2.2459288888163688e-09,
          "right_normalized_residual": -3.084484025960798e-09,
          "bracket_width_N_local": 1.3393743953274851e-05
        },
        {
          "left_index": 56,
          "right_index": 57,
          "fraction": 0.7437193655246365,
          "N_local": 0.000760011247926384,
          "N_physical": -56.906387415728744,
          "H_Mpl": 4.2969080296152854e-07,
          "required_standard_density_Mpl4": 6.934448839336835e-26,
          "vacuum_frequency_margin_Mpl2": 6.292931635524838e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.695012223754898e-22,
          "right_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
          "left_normalized_residual": -3.084484025960798e-09,
          "right_normalized_residual": 1.0628922758579984e-09,
          "bracket_width_N_local": 1.3393743568903388e-05
        },
        {
          "left_index": 57,
          "right_index": 58,
          "fraction": 0.4513855429535026,
          "N_local": 0.000769489547062301,
          "N_physical": -56.953879584273736,
          "H_Mpl": 4.2969079403720936e-07,
          "required_standard_density_Mpl4": 8.628654545432148e-26,
          "vacuum_frequency_margin_Mpl2": 6.2928212886367955e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.9624624740264457e-22,
          "right_raychaudhuri_residual_Mpl2": -2.3851789262401107e-22,
          "left_normalized_residual": 1.0628922758579984e-09,
          "right_normalized_residual": -1.2918404507906814e-09,
          "bracket_width_N_local": 1.3393743176885482e-05
        },
        {
          "left_index": 60,
          "right_index": 61,
          "fraction": 0.6625296414804297,
          "N_local": 0.0008124987844043409,
          "N_physical": -56.72634788093764,
          "H_Mpl": 4.2969075199085846e-07,
          "required_standard_density_Mpl4": 3.487610598278128e-26,
          "vacuum_frequency_margin_Mpl2": 6.292311072168803e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.0632820781371679e-21,
          "right_raychaudhuri_residual_Mpl2": 5.416001966562323e-22,
          "left_normalized_residual": -5.7588592254670335e-09,
          "right_normalized_residual": 2.9333697507287355e-09,
          "bracket_width_N_local": 1.339374195376004e-05
        },
        {
          "left_index": 62,
          "right_index": 63,
          "fraction": 0.2828776488502654,
          "N_local": 0.0008342013068245111,
          "N_physical": -56.42416066977023,
          "H_Mpl": 4.2969072976349885e-07,
          "required_standard_density_Mpl4": 1.0516148238801056e-26,
          "vacuum_frequency_margin_Mpl2": 6.292047577098258e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 3.5493257717780747e-22,
          "right_raychaudhuri_residual_Mpl2": -8.997886021744807e-22,
          "left_normalized_residual": 1.922356303387535e-09,
          "right_normalized_residual": -4.873360505520376e-09,
          "bracket_width_N_local": 1.3393741098036778e-05
        },
        {
          "left_index": 70,
          "right_index": 71,
          "fraction": 0.047099575065959104,
          "N_local": 0.0009381932721551563,
          "N_physical": -56.635079275733936,
          "H_Mpl": 4.296906134321862e-07,
          "required_standard_density_Mpl4": 2.4692151081577868e-26,
          "vacuum_frequency_margin_Mpl2": 6.290728777635009e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 5.890382125923059e-23,
          "right_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
          "left_normalized_residual": 3.190301549322586e-10,
          "right_normalized_residual": -6.454495453235951e-09,
          "bracket_width_N_local": 1.3393737338068313e-05
        },
        {
          "left_index": 71,
          "right_index": 72,
          "fraction": 0.5614620610416048,
          "N_local": 0.0009584762452410652,
          "N_physical": -56.95618282563535,
          "H_Mpl": 4.296905887515237e-07,
          "required_standard_density_Mpl4": 8.467609511956364e-26,
          "vacuum_frequency_margin_Mpl2": 6.290460528983634e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.1917193781378044e-21,
          "right_raychaudhuri_residual_Mpl2": 9.308093924205628e-22,
          "left_normalized_residual": -6.454495453235951e-09,
          "right_normalized_residual": 5.041375983482935e-09,
          "bracket_width_N_local": 1.339373682891006e-05
        },
        {
          "left_index": 73,
          "right_index": 74,
          "fraction": 0.4348853540070985,
          "N_local": 0.0009835683828234758,
          "N_physical": -56.62021285300039,
          "H_Mpl": 4.2969055733943505e-07,
          "required_standard_density_Mpl4": 3.015939093992669e-26,
          "vacuum_frequency_margin_Mpl2": 6.2901239722949215e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.194690813740266e-21,
          "right_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
          "left_normalized_residual": 6.47059010702358e-09,
          "right_normalized_residual": -8.408251725070025e-09,
          "bracket_width_N_local": 1.3393735783597243e-05
        },
        {
          "left_index": 74,
          "right_index": 75,
          "fraction": 0.5675920042901169,
          "N_local": 0.0009987395561132746,
          "N_physical": -55.832306400564924,
          "H_Mpl": 4.296905378492746e-07,
          "required_standard_density_Mpl4": 3.66165402285607e-27,
          "vacuum_frequency_margin_Mpl2": 6.289917856371982e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.552448869700914e-21,
          "right_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
          "left_normalized_residual": -8.408251725070025e-09,
          "right_normalized_residual": 6.405649730889708e-09,
          "bracket_width_N_local": 1.3393735247269316e-05
        },
        {
          "left_index": 75,
          "right_index": 76,
          "fraction": 0.46870607498227307,
          "N_local": 0.0010108088391480106,
          "N_physical": -55.995256347003696,
          "H_Mpl": 4.296905220722735e-07,
          "required_standard_density_Mpl4": 1.1627710255761945e-26,
          "vacuum_frequency_margin_Mpl2": 6.289752465737699e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.182700424099569e-21,
          "right_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
          "left_normalized_residual": 6.405649730889708e-09,
          "right_normalized_residual": -7.261017616518347e-09,
          "bracket_width_N_local": 1.3393734701716781e-05
        },
        {
          "left_index": 76,
          "right_index": 77,
          "fraction": 0.9123702377387957,
          "N_local": 0.001030144893436112,
          "N_physical": -56.94665879344938,
          "H_Mpl": 4.296904963167453e-07,
          "required_standard_density_Mpl4": 8.540104780800767e-26,
          "vacuum_frequency_margin_Mpl2": 6.289485018541246e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.3406302669828964e-21,
          "right_raychaudhuri_residual_Mpl2": 1.2876254256938986e-22,
          "left_normalized_residual": -7.261017616518347e-09,
          "right_normalized_residual": 6.973937491092083e-10,
          "bracket_width_N_local": 1.3393734146858972e-05
        },
        {
          "left_index": 89,
          "right_index": 90,
          "fraction": 0.9686572376319323,
          "N_local": 0.0012050172758680136,
          "N_physical": -56.82090151317981,
          "H_Mpl": 4.296902338903307e-07,
          "required_standard_density_Mpl4": 4.95451873713127e-26,
          "vacuum_frequency_margin_Mpl2": 6.286919107523303e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.3204165946425948e-21,
          "right_raychaudhuri_residual_Mpl2": 4.272461087877763e-23,
          "left_normalized_residual": -7.1515464632206394e-09,
          "right_normalized_residual": 2.3140202296214582e-10,
          "bracket_width_N_local": 1.3393726058015575e-05
        },
        {
          "left_index": 92,
          "right_index": 93,
          "fraction": 0.024259324250412394,
          "N_local": 0.0012325494449634913,
          "N_physical": -56.850344980674116,
          "H_Mpl": 4.296901875854801e-07,
          "required_standard_density_Mpl4": 5.534209017110175e-26,
          "vacuum_frequency_margin_Mpl2": 6.28649117473157e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 4.0142619240537e-23,
          "right_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
          "left_normalized_residual": 2.1741766762132975e-10,
          "right_normalized_residual": -8.7448142610148e-09,
          "bracket_width_N_local": 1.3393723951315778e-05
        },
        {
          "left_index": 93,
          "right_index": 94,
          "fraction": 0.4848703013313575,
          "N_local": 0.0012521124648400947,
          "N_physical": -56.9863466284211,
          "H_Mpl": 4.2969015377855907e-07,
          "required_standard_density_Mpl4": 1.053735996171995e-25,
          "vacuum_frequency_margin_Mpl2": 6.286182970155485e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -1.6145868705907636e-21,
          "right_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
          "left_normalized_residual": -8.7448142610148e-09,
          "right_normalized_residual": 9.290554634716903e-09,
          "bracket_width_N_local": 1.3393723228069879e-05
        },
        {
          "left_index": 94,
          "right_index": 95,
          "fraction": 0.4549072309281898,
          "N_local": 0.0012651048706622495,
          "N_physical": -56.997242900768406,
          "H_Mpl": 4.296901309484704e-07,
          "required_standard_density_Mpl4": 1.1016369238939384e-25,
          "vacuum_frequency_margin_Mpl2": 6.285976581984483e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.7153487145696985e-21,
          "right_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
          "left_normalized_residual": 9.290554634716903e-09,
          "right_normalized_residual": -1.113241198825085e-08,
          "bracket_width_N_local": 1.3393722494135915e-05
        },
        {
          "left_index": 95,
          "right_index": 96,
          "fraction": 0.7538644082141279,
          "N_local": 0.0012825027420651565,
          "N_physical": -56.88732829339666,
          "H_Mpl": 4.2969009987700475e-07,
          "required_standard_density_Mpl4": 6.420356596172189e-26,
          "vacuum_frequency_margin_Mpl2": 6.2856979866767695e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -2.0554172745083648e-21,
          "right_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
          "left_normalized_residual": -1.113241198825085e-08,
          "right_normalized_residual": 3.634716123765566e-09,
          "bracket_width_N_local": 1.3393721749403948e-05
        },
        {
          "left_index": 96,
          "right_index": 97,
          "fraction": 0.7092775479346664,
          "N_local": 0.001295299279278346,
          "N_physical": -56.97299511970861,
          "H_Mpl": 4.296900766345335e-07,
          "required_standard_density_Mpl4": 9.217305944021855e-26,
          "vacuum_frequency_margin_Mpl2": 6.285491362413646e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 6.710906387350248e-22,
          "right_raychaudhuri_residual_Mpl2": -2.75070198710292e-22,
          "left_normalized_residual": 3.634716123765566e-09,
          "right_normalized_residual": -1.4898169372979586e-09,
          "bracket_width_N_local": 1.3393720993773364e-05
        },
        {
          "left_index": 98,
          "right_index": 99,
          "fraction": 0.4569399285322861,
          "N_local": 0.0013187069801230823,
          "N_physical": -56.82730406410569,
          "H_Mpl": 4.29690033281348e-07,
          "required_standard_density_Mpl4": 6.073586449968256e-26,
          "vacuum_frequency_margin_Mpl2": 6.285109757800073e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -9.944762113653646e-22,
          "right_raychaudhuri_residual_Mpl2": 1.1819066111200154e-21,
          "left_normalized_residual": -5.386216613824514e-09,
          "right_normalized_residual": 6.4013655597193205e-09,
          "bracket_width_N_local": 1.3393719449427549e-05
        },
        {
          "left_index": 101,
          "right_index": 102,
          "fraction": 0.4981349024957319,
          "N_local": 0.001359439888821723,
          "N_physical": -56.70056065100801,
          "H_Mpl": 4.2968995523825917e-07,
          "required_standard_density_Mpl4": 3.1665149012667346e-26,
          "vacuum_frequency_margin_Mpl2": 6.284434543407456e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.0692527777417256e-21,
          "right_raychaudhuri_residual_Mpl2": -1.0772596878265491e-21,
          "left_normalized_residual": 5.791218593121455e-09,
          "right_normalized_residual": -5.83458581994365e-09,
          "bracket_width_N_local": 1.3393717048993748e-05
        },
        {
          "left_index": 114,
          "right_index": 115,
          "fraction": 0.8582876521016599,
          "N_local": 0.0015383819170730285,
          "N_physical": -57.02543001641031,
          "H_Mpl": 4.296895721023366e-07,
          "required_standard_density_Mpl4": 1.1146909461019985e-25,
          "vacuum_frequency_margin_Mpl2": 6.281299647025049e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 1.2661559056265394e-21,
          "right_raychaudhuri_residual_Mpl2": -2.0905570032648377e-22,
          "left_normalized_residual": 6.857684532074395e-09,
          "right_normalized_residual": -1.1322762412690418e-09,
          "bracket_width_N_local": 1.3393705454777492e-05
        },
        {
          "left_index": 116,
          "right_index": 117,
          "fraction": 0.43422312123954604,
          "N_local": 0.001559489530737296,
          "N_physical": -57.1789623682144,
          "H_Mpl": 4.2968952243814917e-07,
          "required_standard_density_Mpl4": 2.0622346831073145e-25,
          "vacuum_frequency_margin_Mpl2": 6.280911635012511e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -7.285056987183484e-22,
          "right_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
          "left_normalized_residual": -3.9456939643992105e-09,
          "right_normalized_residual": 5.141095987972354e-09,
          "bracket_width_N_local": 1.3393703494664864e-05
        },
        {
          "left_index": 117,
          "right_index": 118,
          "fraction": 0.9878589932033509,
          "N_local": 0.001580298467958751,
          "N_physical": -57.16308991401113,
          "H_Mpl": 4.2968947258953135e-07,
          "required_standard_density_Mpl4": 1.9334187724532636e-25,
          "vacuum_frequency_margin_Mpl2": 6.280525645903106e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 9.49216336531029e-22,
          "right_raychaudhuri_residual_Mpl2": -1.1666079949267927e-23,
          "left_normalized_residual": 5.141095987972354e-09,
          "right_normalized_residual": -6.318522291659054e-11,
          "bracket_width_N_local": 1.339370249623978e-05
        },
        {
          "left_index": 119,
          "right_index": 120,
          "fraction": 0.8428465471001942,
          "N_local": 0.0016051436166644778,
          "N_physical": -57.16339033749111,
          "H_Mpl": 4.296894117252259e-07,
          "required_standard_density_Mpl4": 1.9369378485244054e-25,
          "vacuum_frequency_margin_Mpl2": 6.280059616028694e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -5.306399063187383e-22,
          "right_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
          "left_normalized_residual": -2.8740250373060523e-09,
          "right_normalized_residual": 5.358781255435093e-10,
          "bracket_width_N_local": 1.3393700462002202e-05
        },
        {
          "left_index": 120,
          "right_index": 121,
          "fraction": 0.09178239976574161,
          "N_local": 0.001608477788814241,
          "N_physical": -57.15354798384819,
          "H_Mpl": 4.296894034642662e-07,
          "required_standard_density_Mpl4": 1.8655455109898024e-25,
          "vacuum_frequency_margin_Mpl2": 6.279996722973984e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": 9.894077849797003e-23,
          "right_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
          "left_normalized_residual": 5.358781255435093e-10,
          "right_normalized_residual": -5.302694440333927e-09,
          "bracket_width_N_local": 1.3393699425939256e-05
        },
        {
          "left_index": 121,
          "right_index": 122,
          "fraction": 0.5318905792781098,
          "N_local": 0.0016277661643535953,
          "N_physical": -56.998728930731936,
          "H_Mpl": 4.2968935508388884e-07,
          "required_standard_density_Mpl4": 1.0699821571821313e-25,
          "vacuum_frequency_margin_Mpl2": 6.279630665950597e-09,
          "positive_vacuum_frequency_margin": true,
          "left_raychaudhuri_residual_Mpl2": -9.790521564274505e-22,
          "right_raychaudhuri_residual_Mpl2": 8.616500379152947e-22,
          "left_normalized_residual": -5.302694440333927e-09,
          "right_normalized_residual": 4.666827559239031e-09,
          "bracket_width_N_local": 1.3393698377093784e-05
        }
      ]
    },
    "exact_initial_probe_delta": {
      "abs_delta_N_physical": 0.0,
      "relative_delta_required_standard_density": 0.0,
      "abs_delta_quantum_rho_over_H2": 0.0,
      "abs_delta_quantum_pressure_over_H2": 0.0,
      "abs_delta_quantum_chi2_over_scale": 0.0,
      "abs_delta_friedmann_normalized": 0.0,
      "abs_delta_raychaudhuri_normalized": 0.0
    },
    "root_scan_diagnostic_selection_delta": {
      "abs_delta_N_local": 0.0,
      "abs_delta_N_physical": 0.0,
      "relative_delta_H": 0.0,
      "relative_delta_required_standard_density": 0.0
    }
  },
  "held_out": {
    "momentum_nodes": 96,
    "evaluated": false
  },
  "gates": {
    "authority_hashes_exact": true,
    "fixed_prefix_inside_frozen_HARD_PASS_state": true,
    "temporal_grids_exactly_nested": true,
    "all_pilot_levels_finite": true,
    "exact_initial_HARD_PASS_junction_probe_finite_each_level": true,
    "positive_required_standard_density_each_level": true,
    "positive_initial_inherited_frequency_margin_each_level": true,
    "curvature_tail_4_2_1_time_pilot_completed": true,
    "Wronskian_below_existing_1e_11_each_pilot_level": true,
    "independent_roundoff_pair_completed": true,
    "held_out_momentum_level_not_evaluated": true,
    "pilot_candidate_not_released_as_checkpoint_or_seed": true,
    "old_solver_or_physical_map_not_called": true
  },
  "all_structural_pilot_gates_pass": true,
  "matching_tolerances_frozen": false,
  "checkpoint_released": false,
  "seed_released": false,
  "new_AP1_M1_background_started": false,
  "physical_response_kernel_started": false,
  "nonpass_stored_or_used_as_seed": false,
  "equations_changed": false,
  "physics_changed": false,
  "parameters_changed": false,
  "existing_gate_thresholds_changed": false,
  "next_required": "derive and version a junction tolerance manifest from the exact-state, 4/2/1 curvature-tail, momentum, and roundoff pilot budgets; hash-freeze it, then evaluate 96 momentum shells exactly once as held-out validation",
  "claim_boundary": "convergence pilot only; no accepted M1 junction state, background, response kernel, observable, fit or significance"
}
