{
  "schema": "apeiron-ap1-r2c-p42-bounded-method-diagnostic-v1.3",
  "updated_utc": "2026-09-02T11:12:41Z",
  "classification": "P42_NONPASS_DIAGNOSTIC_IMPROVED_SCALARS_ONLY",
  "source": "validated_41_PASS_only",
  "target_nodes": 42,
  "frozen_thresholds": {
    "dae_max_abs_scaled_residual": 0.0001,
    "max_abs_friedmann_residual": 0.000001,
    "ward_normalized": 0.000002,
    "validation_source_relative_change": 0.0001,
    "validation_wronskian_relative_error": 1e-11
  },
  "method": {
    "lift": "endpoint_preserving_degree_2_3_bspline_extrapolation",
    "lift_beta": 2.5,
    "rho_chi_partial_projection_alpha": 0.0000125,
    "first_frozen_lobatto_sigma_alpha": 0.000003,
    "first_frozen_lobatto_sigma_dot_alpha": 0.000002,
    "first_frozen_lobatto_theta_dot_alpha": 0.000006,
    "second_recomputed_lobatto_sigma_dot_alpha": 0.000001,
    "second_recomputed_lobatto_theta_dot_alpha": 0.000003,
    "pointwise_isoenergy_velocity_projection_alpha": -0.36,
    "pointwise_classical_rho_preservation_max_abs_error": 1.2924697071141057e-26,
    "algebraic_chi2_projection": "full_residual_verified",
    "equations_changed": false,
    "physics_changed": false,
    "gates_changed": false
  },
  "excluded_families": {
    "same_degree_two_parent_p_secant": {
      "candidate_count": 68,
      "best_dae_max_abs_scaled_residual": 0.001247501392604248,
      "best_degree": 3,
      "best_beta": 0.25
    },
    "single_block_endpoint_bspline_bank": {
      "candidate_count": 18,
      "best_dae_max_abs_scaled_residual": 0.0003152055646809344,
      "best_block": "theta_dot",
      "best_alternative": "degree_1_2_beta_3"
    },
    "five_coordinate_linearized_minimax": {
      "predicted_dae_max_abs_scaled_residual": 0.00030552295200521573,
      "verified_dae_max_abs_scaled_residual": 0.00032723965203140267,
      "accepted": false
    },
    "scaled_scalar_and_nodal_trust_regions": {
      "best_verified_dae_max_abs_scaled_residual": 0.00027862712793367666,
      "source_gate_preserved": false,
      "accepted": false
    },
    "coupled_25_coordinate_last_five_node_trust_region": {
      "predicted_dae_max_abs_scaled_residual": 0.0001888551604588983,
      "verified_dae_max_abs_scaled_residual": 0.0004368954971625951,
      "accepted": false
    },
    "valid_parent_sparse_lifts": {
      "p41_to_p43_best_dae_max_abs_scaled_residual": 0.0009600454020132984,
      "p40_to_p42_best_dae_max_abs_scaled_residual": 0.0013618897140084622,
      "accepted": false
    },
    "tight_p41_newton": {
      "initial_dae_max_abs_scaled_residual": 0.0000992744411235424,
      "best_outer_residual": 0.4414,
      "accepted": false
    },
    "alternative_p41_pass_branch": {
      "beta": 2.19,
      "p41_dae_max_abs_scaled_residual": 0.0000934715143197178,
      "p41_validation_source_relative_change": 0.00008576447626343765,
      "p42_best_dae_max_abs_scaled_residual": 0.0003294637443704861,
      "authoritative_parent_changed": false
    },
    "deeper_alternative_p41_pass_branch": {
      "beta": 2.2,
      "background_alpha": -0.000008,
      "rho_alpha": 0.0000425,
      "p41_dae_max_abs_scaled_residual": 0.00009246057492761888,
      "p41_ward_normalized": 9.780233224098215e-8,
      "p41_validation_source_relative_change": 0.00008490743793048986,
      "p41_full_gate_pass": true,
      "p42_best_dae_max_abs_scaled_residual": 0.0006212973026682732,
      "selected_as_authoritative_parent": false
    },
    "lower_beta_rho_cross_grid": {
      "candidate_count": 20,
      "beta_range": [1.5, 2.4],
      "best_gate_compatible_dae_max_abs_scaled_residual": 0.0002748560244876399,
      "accepted": false
    },
    "smooth_eight_coordinate_minimax": {
      "input_dae_max_abs_scaled_residual": 0.00025836112519572583,
      "best_verified_dae_max_abs_scaled_residual": 0.0002583611240500435,
      "material_improvement": false,
      "accepted": false
    },
    "stronger_defect_and_rho_rebalance": {
      "source_closure_cliff_above_sigma_alpha": 0.000003,
      "accepted": false
    },
    "chebyshev_and_shape_preserving_lifts": {
      "best_gate_compatible_chebyshev_dae": 0.00030389985793761705,
      "best_shape_preserving_dae": 0.00044642501910956324,
      "best_hermite_blend_dae": 0.00027037442635212183,
      "accepted": false
    },
    "inner_background_trust_region": {
      "isolated_background_norm": 1.1649864815440585e-8,
      "smallest_full_step_fraction": 1e-8,
      "smallest_fraction_full_dae": 0.00028532729630845535,
      "accepted": false
    },
    "precision_scan": {
      "digits": [60, 80, 100],
      "invariant_dae_max_abs_scaled_residual": 0.00025836112519572583,
      "wronskian_at_100_digits": 8.6e-90,
      "accepted": false
    },
    "pointwise_isoenergy_velocity_family": {
      "alpha_scan_bounds": [-1.25, 1.25],
      "best_alpha": -0.36,
      "best_dae_max_abs_scaled_residual": 0.00025087964893039544,
      "max_abs_classical_rho_preservation_error": 1.2924697071141057e-26,
      "validation_source_relative_change": 2.0584621803624213e-5,
      "accepted": false,
      "reason": "reproducible_residual_reduction_but_DAE_gate_remains_failed"
    },
    "stacked_isoenergy_velocity_least_squares": {
      "direction_equivalent_to_pointwise_projection_at_tested_scale": true,
      "best_positive_alpha_dae_max_abs_scaled_residual": 0.00026095858423446874,
      "accepted": false
    }
  },
  "repeated_full_diagnostics": {
    "repeats": 3,
    "dae_max_abs_scaled_residual": 0.00025087964893039544,
    "max_abs_friedmann_residual": 1.5127661435732624e-16,
    "ward_normalized": 2.1794407870617619e-7,
    "validation_source_relative_change": 2.0584621803624213e-5,
    "validation_wronskian_relative_error": 6.8e-50,
    "junction_block": 2.327570421458129e-5,
    "finite": true,
    "positive_H": true,
    "min_H": 8.312595082091879e-8,
    "min_PX": 1.8132335484729594,
    "min_K": 3.016188545394498,
    "gate_pass": {
      "dae_residual": false,
      "max_abs_friedmann_residual": true,
      "ward_normalized": true,
      "validation_source_relative_change": true,
      "validation_wronskian_relative_error": true,
      "structural": true
    }
  },
  "prior_p42_dae_max_abs_scaled_residual": 0.00044107284402342004,
  "diagnostic_reduction_factor": 0.5687941398565772,
  "reduction_factor_vs_previous_diagnostic": 0.9710425619966523,
  "accepted_as_checkpoint": false,
  "trial_vector_stored_or_used_as_seed": false,
  "highest_validated_p_level": 41,
  "production_curves_released": false,
  "next_action": "continue_conservative_DAE_p_method_extension_from_stored_41_PASS_only"
}