# Apeiron — Start Here (latest persistent checkpoint)

## Publication resume point — R1–R3 closed

This section supersedes the older publication checkpoint near the end of this file. The numerical resume below remains authoritative and unchanged.

The autonomous publication-blocker package completed on 30 August 2026 without starting a solver, executing the physical map, changing a gate, or recomputing any accepted result.

Current publication status:

- former documentary blocker R-01 is closed by /Apeiron/PUBLICATION/APEIRON_CANONICAL_MODEL_SPECIFICATION_LATEST.md; it defines the homogeneous v7.13 model operationally, including units, state, parameters, equations, quantum closure and discrete map, but does not claim a unique fundamental covariant action
- former blocker R-02 is closed by /Apeiron/PUBLICATION/APEIRON_V7_13_GATE_SPECIFICATION_LATEST.json; exact thresholds, operators, stored values, classification logic and frozen solver budget are included
- former blocker R-03 is closed by /Apeiron/PUBLICATION/APEIRON_REPRODUCIBILITY_MANIFEST_LATEST.json, README_REPRODUCIBILITY.md, verify_apeiron_publication_package.py and the individually included technical sources
- the read-only verifier reports APEIRON_PUBLICATION_PACKAGE_VERIFY_PASS both in the working package and after extraction from the ZIP; it verifies hashes, identities, array forms, stored gate comparisons and Float64 crossing rules only
- /Apeiron/PUBLICATION/APEIRON_PUBLICATION_REPRODUCIBILITY_PACKAGE_LATEST.zip has SHA-256 801f19dc26808184ccf4dfa33dd5429831c42fdba0b2048d16fd7c50b6ae0ac2; archive test and extracted verifier passed
- the venue-neutral master manuscript now contains exact operational equations, the exact v7.13 gate table, results, limits, reproducibility levels and AP1–AP3 as prospective work only
- the updated milestone dossier has 27 A4 pages, SHA-256 75b7d1c5688776cfadf1193dea578beca76e1d190f850b8d2b5a14f0f1526c3f, and passed full-page rendering and visual inspection
- the approved 15-file public download package is deployed at https://apeiron-publication-files.info523741.chatgpt.site; this public file distribution is not a journal publication, peer review, DOI registration or empirical confirmation

Publication scope:

- the controlled technical core is ready for preprint packaging after editorial and administrative completion
- journal submission is not yet complete because authorship, affiliation, declarations, repository/DOI and license, venue format, figures and final language edit remain open
- independent numerical reproduction, continuum convergence, a fundamental covariant completion, perturbations, physical tau mapping and empirical testing remain open scientific work
- no empirical proof, exact physical-boundary claim, fabricated AP1–AP3 output, independent-reproduction claim or proven-action claim is permitted

Authoritative publication Latest files for the next chat:

1. /Apeiron/PUBLICATION/APEIRON_PUBLICATION_CLAIMS_REGISTER_LATEST.md
2. /Apeiron/PUBLICATION/APEIRON_MANUSCRIPT_LATEST.md
3. /Apeiron/PUBLICATION/APEIRON_PUBLICATION_GAP_REPORT_LATEST.md
4. /Apeiron/PUBLICATION/APEIRON_PUBLICATION_META_LATEST.json
5. /Apeiron/PUBLICATION/APEIRON_CANONICAL_MODEL_SPECIFICATION_LATEST.md
6. /Apeiron/PUBLICATION/APEIRON_V7_13_GATE_SPECIFICATION_LATEST.json
7. /Apeiron/PUBLICATION/APEIRON_REPRODUCIBILITY_MANIFEST_LATEST.json
8. /Apeiron/PUBLICATION/README_REPRODUCIBILITY.md
9. /Apeiron/PUBLICATION/verify_apeiron_publication_package.py
10. /Apeiron/PUBLICATION/APEIRON_PUBLICATION_REPRODUCIBILITY_PACKAGE_LATEST.zip
11. /Apeiron/PUBLICATION/APEIRON_PUBLICATION_MASTER_DOSSIER_LATEST.pdf
12. /Apeiron/PUBLICATION/build_publication_dossier.py
13. Appendix A, unchanged and prospective

Next permitted work: editorial/figure preparation, permanent archive and license preparation, authorship/declaration completion after authorization, or venue selection and formatting. Do not reopen v7.13 or start AP1 physics merely to prepare the first narrowly scoped numerical-foundations publication.

## Authoritative resume point

Resume **after the v7.13 Stage 0 terminal HARD PASS and Float64 crossing-schedule completion** at:

- target `tau = 0.47878124999999994` (protocol midpoint `0.47878124999999994315658113919198513031005859375`)
- Newton control index `1`
- GMRES cycle `0`
- stored checkpoint phase `gmres`; the terminal result and crossing-resolution result already exist and must not be recomputed
- current residual infinity norm `4.6838977141305804e-11`
- v7.13 Stage 0 was initialized exactly once from the hash-verified immutable v7.12 Stage 0 HARD PASS at `tau = 0.4787812499999999`; its initial residual was already below the fixed-point tolerance, so no Newton/GMRES step ran
- v7.13 direct active-tau terminal diagnostics passed every gate with zero Newton steps: fixed point `4.6838977141305804e-11`, Friedmann `3.818888298257304e-12`, continuity `3.7214611922998273e-06`, Raychaudhuri `1.4051164250399966e-05`, quantum source `3.883856960984437e-08`, and Wronskian `7.432742701266731e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.13 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_13.json`, `STAGE00_HARD_PASS_SOLUTION_v7_13.npz`, and `RECOVERY_GATE_REGISTER_v7_13_STAGE00.json`
- the v7.13 HARD PASS at binary `0.47878124999999994` and immutable v6.74 NONPASS at binary `0.47878125` are adjacent Float64 values; the next exact midpoint rounds to the NONPASS endpoint, so further Float64 bisection is forbidden. This terminal scientific decision is persisted in `CROSSING_RESOLUTION_RESULT_v7_13.json`
- v7.12 Stage 0 was initialized exactly once from the hash-verified immutable v7.11 Stage 0 HARD PASS at `tau = 0.47878124999999977`; its initial residual was already below the fixed-point tolerance, so no Newton/GMRES step ran
- v7.12 direct active-tau terminal diagnostics passed every gate with zero Newton steps: fixed point `4.18367562815547e-11`, Friedmann `3.3208452524442056e-12`, continuity `3.721460588570432e-06`, Raychaudhuri `1.4051164266686057e-05`, quantum source `3.883845028610797e-08`, and Wronskian `1.2750649886676766e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.12 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_12.json`, `STAGE00_HARD_PASS_SOLUTION_v7_12.npz`, and `RECOVERY_GATE_REGISTER_v7_12_STAGE00.json`; this HARD PASS is the sole permissible seed for the next recursive midpoint
- v7.11 Stage 0 was initialized exactly once from the hash-verified immutable v7.10 Stage 0 HARD PASS at `tau = 0.47878124999999955`; its initial residual was already below the fixed-point tolerance, so no Newton/GMRES step ran
- v7.11 direct active-tau terminal diagnostics passed every gate with zero Newton steps: fixed point `3.501554601825774e-11`, Friedmann `2.9716693728424165e-12`, continuity `3.721459938579102e-06`, Raychaudhuri `1.4051164331998535e-05`, quantum source `3.883858066956591e-08`, and Wronskian `1.0164213568898683e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.11 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_11.json`, `STAGE00_HARD_PASS_SOLUTION_v7_11.npz`, and `RECOVERY_GATE_REGISTER_v7_11_STAGE00.json`; this HARD PASS is the sole permissible seed for the next recursive midpoint
- v7.10 Stage 0 was initialized exactly once from the hash-verified immutable v7.09 Stage 0 HARD PASS at `tau = 0.4787812499999991`; its initial residual was already below the fixed-point tolerance, so no Newton/GMRES step ran
- v7.10 direct active-tau terminal diagnostics passed every gate with zero Newton steps: fixed point `2.091837814077735e-11`, Friedmann `1.6088728410144733e-12`, continuity `3.7214584526375066e-06`, Raychaudhuri `1.4051164393098164e-05`, quantum source `3.883857407369949e-08`, and Wronskian `9.28488794822626e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.10 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_10.json`, `STAGE00_HARD_PASS_SOLUTION_v7_10.npz`, and `RECOVERY_GATE_REGISTER_v7_10_STAGE00.json`; this HARD PASS is the sole permissible seed for the next recursive midpoint
- v7.09 Stage 0 was initialized exactly once from the hash-verified immutable v7.08 Stage 0 HARD PASS at `tau = 0.47878124999999816`
- v7.09 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.011530491528653344`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.0020235469431213e-12`
- v7.09 direct active-tau terminal diagnostics passed every gate after one accepted Newton step: fixed point `2.0020235469431213e-12`, Friedmann `2.176023019588497e-12`, continuity `3.7214562440635782e-06`, Raychaudhuri `1.4051164218785234e-05`, quantum source `3.883860032927197e-08`, and Wronskian `5.859065720765187e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.09 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_09.json`, `STAGE00_HARD_PASS_SOLUTION_v7_09.npz`, and `RECOVERY_GATE_REGISTER_v7_09_STAGE00.json`; this HARD PASS is the sole permissible seed for the next recursive midpoint
- v7.08 Stage 0 was initialized exactly once from the hash-verified immutable v7.07 Stage 0 HARD PASS at `tau = 0.4787812499999964`
- v7.08 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.004542774799671643`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.4569682106375694e-12`
- v7.08 direct active-tau terminal diagnostics passed every gate after one accepted Newton step: fixed point `5.4569682106375694e-12`, Friedmann `4.3519093174568835e-13`, continuity `3.7214563592440328e-06`, Raychaudhuri `1.4051135781115589e-05`, quantum source `3.883738630046617e-08`, and Wronskian `7.634588479259966e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.08 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_08.json`, `STAGE00_HARD_PASS_SOLUTION_v7_08.npz`, and `RECOVERY_GATE_REGISTER_v7_08_STAGE00.json`; this HARD PASS is the sole permissible seed for the next recursive midpoint
- v7.07 Stage 0 was initialized exactly once from the hash-verified immutable v7.06 Stage 0 HARD PASS at `tau = 0.4787812499999927`
- v7.07 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.007308842391732212`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.888534022029489e-12`
- v7.07 direct active-tau terminal diagnostics passed every gate after one accepted Newton step: fixed point `4.888534022029489e-12`, Friedmann `3.522652208017227e-12`, continuity `3.721454219396561e-06`, Raychaudhuri `1.4050945402975356e-05`, quantum source `3.8838933280929564e-08`, and Wronskian `1.1830285241449384e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.07 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_07.json`, `STAGE00_HARD_PASS_SOLUTION_v7_07.npz`, and `RECOVERY_GATE_REGISTER_v7_07_STAGE00.json`; this HARD PASS is the sole permissible seed for the next recursive midpoint
- v7.06 Stage 0 was initialized exactly once from the hash-verified immutable v7.05 Stage 0 HARD PASS at `tau = 0.47878124999998545`
- v7.06 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.005412395622404191`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.319211489520967e-11`
- v7.06 direct active-tau terminal diagnostics passed every gate after one accepted Newton step: fixed point `2.319211489520967e-11`, Friedmann `6.773501636519926e-12`, continuity `3.7214552173406584e-06`, Raychaudhuri `1.4050920668227264e-05`, quantum source `3.883927739050584e-08`, and Wronskian `1.2268380485721663e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.06 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_06.json`, `STAGE00_HARD_PASS_SOLUTION_v7_06.npz`, and `RECOVERY_GATE_REGISTER_v7_06_STAGE00.json`; this HARD PASS is the sole permissible v7.07 seed
- v7.05 Stage 0 was initialized exactly once from the hash-verified immutable v7.04 Stage 0 HARD PASS at `tau = 0.4787812499999709`
- v7.05 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.00659595499286915`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.432898327242583e-11`
- v7.05 direct active-tau terminal diagnostics passed every gate after one accepted Newton step: fixed point `2.432898327242583e-11`, Friedmann `9.977597933494458e-12`, continuity `3.721462324934833e-06`, Raychaudhuri `1.405087041866808e-05`, quantum source `3.883947598638886e-08`, and Wronskian `9.871985641386923e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.05 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_05.json`, `STAGE00_HARD_PASS_SOLUTION_v7_05.npz`, and `RECOVERY_GATE_REGISTER_v7_05_STAGE00.json`; this HARD PASS is the sole permissible v7.06 seed
- v7.04 Stage 0 was initialized exactly once from the hash-verified immutable v7.03 Stage 0 HARD PASS at `tau = 0.4787812499999418`
- v7.04 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006281727970487329`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.8629279502645488e-11`
- v7.04 direct active-tau terminal diagnostics passed every gate after one accepted Newton step: fixed point `2.8629279502645488e-11`, Friedmann `2.762197455837518e-11`, continuity `3.7214607452341314e-06`, Raychaudhuri `1.4050492098689825e-05`, quantum source `3.8839176051820726e-08`, and Wronskian `8.501559545595356e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.04 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_04.json`, `STAGE00_HARD_PASS_SOLUTION_v7_04.npz`, and `RECOVERY_GATE_REGISTER_v7_04_STAGE00.json`; this HARD PASS is the sole permissible v7.05 seed
- v7.03 Stage 0 was initialized exactly once from the hash-verified immutable v7.02 Stage 0 HARD PASS at `tau = 0.4787812499998836`
- v7.03 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.007309389406097633`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.865731594363211e-11`
- v7.03 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.007243940952362966`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.865352482534945e-12`
- v7.03 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `3.865352482534945e-12`, Friedmann `7.679260245081505e-13`, continuity `3.721456922080662e-06`, Raychaudhuri `1.4051140955505016e-05`, quantum source `3.883895021054803e-08`, and Wronskian `1.0176551127282461e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.03 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_03.json`, `STAGE00_HARD_PASS_SOLUTION_v7_03.npz`, and `RECOVERY_GATE_REGISTER_v7_03_STAGE00.json`; this HARD PASS is the sole permissible v7.04 seed
- v7.02 Stage 0 was initialized exactly once from the hash-verified immutable v7.01 Stage 0 HARD PASS at `tau = 0.4787812499997672`
- v7.02 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006349237762695554`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2384868131043447e-10`
- v7.02 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.011766736602372327`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2056050602282653e-12`
- v7.02 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `1.2056050602282653e-12`, Friedmann `1.2597482320576879e-12`, continuity `3.72145542659282e-06`, Raychaudhuri `1.4051159031135628e-05`, quantum source `3.88390643099558e-08`, and Wronskian `9.661919553598415e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.02 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_02.json`, `STAGE00_HARD_PASS_SOLUTION_v7_02.npz`, and `RECOVERY_GATE_REGISTER_v7_02_STAGE00.json`; this HARD PASS is the sole permissible v7.03 seed
- v7.01 Stage 0 was initialized exactly once from the hash-verified immutable v7.00 Stage 0 HARD PASS at `tau = 0.47878124999953436`
- v7.01 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006443822448634129`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.49936529805872e-10`
- v7.01 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008099613230924584`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `7.73070496506989e-12`
- v7.01 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `7.73070496506989e-12`, Friedmann `1.760371900337255e-12`, continuity `3.721456662990254e-06`, Raychaudhuri `1.4051072335260098e-05`, quantum source `3.8839000445731065e-08`, and Wronskian `7.339062990034499e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.01 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_01.json`, `STAGE00_HARD_PASS_SOLUTION_v7_01.npz`, and `RECOVERY_GATE_REGISTER_v7_01_STAGE00.json`; this HARD PASS is the sole permissible v7.02 seed
- v7.00 Stage 0 was initialized exactly once from the hash-verified immutable v6.99 Stage 0 HARD PASS at `tau = 0.4787812499990687`
- v7.00 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006922412148812311`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.352308457551302e-10`
- v7.00 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.011625596550106317`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.5234036254696548e-11`
- v7.00 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `1.5234036254696548e-11`, Friedmann `4.18562722215076e-12`, continuity `3.7214562447303838e-06`, Raychaudhuri `1.40512369732196e-05`, quantum source `3.883819602526571e-08`, and Wronskian `7.964843338581322e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v7.00 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v7_00.json`, `STAGE00_HARD_PASS_SOLUTION_v7_00.npz`, and `RECOVERY_GATE_REGISTER_v7_00_STAGE00.json`; this HARD PASS is the sole permissible v7.01 seed
- v6.99 Stage 0 was initialized exactly once from the hash-verified immutable v6.98 Stage 0 HARD PASS at `tau = 0.47878124999813737`
- v6.99 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.00657109152857626`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `9.903091402474473e-10`
- v6.99 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.0067652567160564865`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.287195598529081e-12`
- v6.99 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `4.287195598529081e-12`, Friedmann `4.361263361805522e-12`, continuity `3.721455937458941e-06`, Raychaudhuri `1.4051069178587197e-05`, quantum source `3.8838735192636044e-08`, and Wronskian `1.328191768346738e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.99 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_99.json`, `STAGE00_HARD_PASS_SOLUTION_v6_99.npz`, and `RECOVERY_GATE_REGISTER_v6_99_STAGE00.json`; this HARD PASS is the sole permissible v7.00 seed
- v6.98 Stage 0 was initialized exactly once from the hash-verified immutable v6.97 Stage 0 HARD PASS at `tau = 0.4787812499962747`
- v6.98 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006691627193814383`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.0423983615458496e-09`
- v6.98 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008118851870016316`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `8.228251413555654e-12`
- v6.98 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `8.228251413555654e-12`, Friedmann `9.053450253582584e-12`, continuity `3.721458376906399e-06`, Raychaudhuri `1.4051035999799665e-05`, quantum source `3.8837616268871534e-08`, and Wronskian `8.187879538333435e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.98 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_98.json`, `STAGE00_HARD_PASS_SOLUTION_v6_98.npz`, and `RECOVERY_GATE_REGISTER_v6_98_STAGE00.json`; this HARD PASS is the sole permissible v6.99 seed
- v6.97 Stage 0 was initialized exactly once from the hash-verified immutable v6.96 Stage 0 HARD PASS at `tau = 0.4787812499925494`
- v6.97 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006612957851419884`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.017506202713683e-09`
- v6.97 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.00838508131924668`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.319211489520967e-11`
- v6.97 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `2.319211489520967e-11`, Friedmann `1.8010198373901834e-11`, continuity `3.721460611328456e-06`, Raychaudhuri `1.405118230925061e-05`, quantum source `3.883825276746492e-08`, and Wronskian `8.824998194126472e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.97 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_97.json`, `STAGE00_HARD_PASS_SOLUTION_v6_97.npz`, and `RECOVERY_GATE_REGISTER_v6_97_STAGE00.json`; this HARD PASS is the sole permissible v6.98 seed
- v6.96 Stage 0 was initialized exactly once from the hash-verified immutable v6.95 Stage 0 HARD PASS at `tau = 0.47878124998509886`
- v6.96 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006672695279030368`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `8.12718367604326e-09`
- v6.96 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008979989693885297`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.478008159252255e-11`
- v6.96 direct active-tau terminal diagnostics passed every gate after two accepted Newton steps: fixed point `3.478008159252255e-11`, Friedmann `3.633317046943472e-11`, continuity `3.721464041701953e-06`, Raychaudhuri `1.4051451817582476e-05`, quantum source `3.883829088478705e-08`, and Wronskian `7.101401350588423e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.96 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_96.json`, `STAGE00_HARD_PASS_SOLUTION_v6_96.npz`, and `RECOVERY_GATE_REGISTER_v6_96_STAGE00.json`; this HARD PASS is the sole permissible v6.97 seed
- v6.95 Stage 0 was initialized exactly once from the hash-verified immutable v6.94 Stage 0 HARD PASS at `tau = 0.47878124997019766`
- v6.95 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006637326616475699`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.6165380561927734e-08`
- v6.95 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009500359241119522`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.735226265597305e-11`
- v6.95 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.018413800043566856`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.0535769185723325e-12`
- v6.95 direct active-tau terminal diagnostics passed every gate after three accepted Newton steps: fixed point `4.0535769185723325e-12`, Friedmann `2.9732587628383277e-12`, continuity `3.7214601404893205e-06`, Raychaudhuri `1.4051276149109535e-05`, quantum source `3.88375859755055e-08`, and Wronskian `6.94731553427079e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.95 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_95.json`, `STAGE00_HARD_PASS_SOLUTION_v6_95.npz`, and `RECOVERY_GATE_REGISTER_v6_95_STAGE00.json`; this HARD PASS is the sole permissible v6.96 seed
- v6.94 Stage 0 was initialized exactly once from the hash-verified immutable v6.93 Stage 0 HARD PASS at `tau = 0.47878124994039534`
- v6.94 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.0066487789644100554`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.234980187893921e-08`
- v6.94 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009030296667299728`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2385746595011682e-10`
- v6.94 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.02006863577437479`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.357483983698842e-12`
- v6.94 direct active-tau terminal diagnostics passed every gate after three accepted Newton steps: fixed point `6.357483983698842e-12`, Friedmann `6.797815315740496e-12`, continuity `3.721455345130917e-06`, Raychaudhuri `1.4051270519495956e-05`, quantum source `3.883951703941865e-08`, and Wronskian `8.987656631897958e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.94 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_94.json`, `STAGE00_HARD_PASS_SOLUTION_v6_94.npz`, and `RECOVERY_GATE_REGISTER_v6_94_STAGE00.json`; this HARD PASS is the sole permissible v6.95 seed
- v6.93 Stage 0 was initialized exactly once from the hash-verified immutable v6.92 Stage 0 HARD PASS at `tau = 0.47878124988079074`
- v6.93 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006644160320725739`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.47441266432569e-08`
- v6.93 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009133521795066525`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.487209327384221e-10`
- v6.93 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.014407555451446022`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `9.436298964438095e-12`
- v6.93 direct active-tau terminal diagnostics passed every gate after three accepted Newton steps: fixed point `9.436298964438095e-12`, Friedmann `9.080054021614354e-12`, continuity `3.7214586933557554e-06`, Raychaudhuri `1.4051504496159937e-05`, quantum source `3.883855791766304e-08`, and Wronskian `8.822871399184057e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.93 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_93.json`, `STAGE00_HARD_PASS_SOLUTION_v6_93.npz`, and `RECOVERY_GATE_REGISTER_v6_93_STAGE00.json`; this HARD PASS is the sole permissible v6.94 seed
- v6.92 Stage 0 was initialized exactly once from the hash-verified immutable v6.91 Stage 0 HARD PASS at `tau = 0.47878124976158143`
- v6.92 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006644376367120813`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2946006658354214e-07`
- v6.92 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008880325576956397`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.890798876999725e-10`
- v6.92 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01967798989468964`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.7352675679992444e-11`
- v6.92 direct active-tau terminal diagnostics passed every gate after three accepted Newton steps: fixed point `2.7352675679992444e-11`, Friedmann `2.3229065815110025e-11`, continuity `3.721453662532422e-06`, Raychaudhuri `1.4051895436526039e-05`, quantum source `3.883838920324055e-08`, and Wronskian `1.1573427867537373e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.92 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_92.json`, `STAGE00_HARD_PASS_SOLUTION_v6_92.npz`, and `RECOVERY_GATE_REGISTER_v6_92_STAGE00.json`; this HARD PASS is the sole permissible v6.93 seed
- v6.91 Stage 0 was initialized exactly once from the hash-verified immutable v6.90 Stage 0 HARD PASS at `tau = 0.47878124952316287`
- v6.91 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006643820577314785`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.5902239836339547e-07`
- v6.91 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008911581582475389`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `9.859268956802225e-10`
- v6.91 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.018847479226299396`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.384684365061787e-11`
- v6.91 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.01524164820243884`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.637978807091713e-12`
- v6.91 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `3.637978807091713e-12`, Friedmann `5.682724360263372e-13`, continuity `3.7214593114587384e-06`, Raychaudhuri `1.4051049112453396e-05`, quantum source `3.883774475762751e-08`, and Wronskian `7.55906303284877e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.91 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_91.json`, `STAGE00_HARD_PASS_SOLUTION_v6_91.npz`, and `RECOVERY_GATE_REGISTER_v6_91_STAGE00.json`; this HARD PASS is the sole permissible v6.92 seed
- v6.90 Stage 0 was initialized exactly once from the hash-verified immutable v6.89 Stage 0 HARD PASS at `tau = 0.4787812490463257`
- v6.90 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006644730985397069`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.178464854149745e-07`
- v6.90 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009199850477031488`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.0415885926272637e-09`
- v6.90 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.019626283550746287`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.0842557407464426e-10`
- v6.90 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.009499819244005154`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.637978807091713e-12`
- v6.90 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `3.637978807091713e-12`, Friedmann `1.323865022035819e-12`, continuity `3.721458284971218e-06`, Raychaudhuri `1.4051111423702375e-05`, quantum source `3.8837536160856246e-08`, and Wronskian `6.963864381199017e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.90 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_90.json`, `STAGE00_HARD_PASS_SOLUTION_v6_90.npz`, and `RECOVERY_GATE_REGISTER_v6_90_STAGE00.json`; this HARD PASS is the sole permissible v6.91 seed
- v6.89 Stage 0 was initialized exactly once from the hash-verified immutable v6.88 Stage 0 HARD PASS at `tau = 0.4787812480926514`
- v6.89 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006645215424511711`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.034512208883398e-06`
- v6.89 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008505706765957403`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.746655166669832e-09`
- v6.89 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.017898251715825625`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.99309554971272e-10`
- v6.89 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.005861394427479832`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `7.958078640513122e-13`
- v6.89 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `7.958078640513122e-13`, Friedmann `6.06976076285002e-13`, continuity `3.72145474015921e-06`, Raychaudhuri `1.4051164721420113e-05`, quantum source `3.883817896329127e-08`, and Wronskian `1.2873295965299628e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.89 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_89.json`, `STAGE00_HARD_PASS_SOLUTION_v6_89.npz`, and `RECOVERY_GATE_REGISTER_v6_89_STAGE00.json`; this HARD PASS is the sole permissible v6.90 seed
- v6.88 Stage 0 was initialized exactly once from the hash-verified immutable v6.87 Stage 0 HARD PASS at `tau = 0.4787812461853027`
- v6.88 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006644435869720332`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.070383343710791e-06`
- v6.88 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009136115621588331`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `8.132251663739432e-09`
- v6.88 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.018246567913691187`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.2500072905404807e-10`
- v6.88 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.01014166975334027`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `9.094947017729282e-12`
- v6.88 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `9.094947017729282e-12`, Friedmann `2.9101445988074283e-12`, continuity `3.7214523201228813e-06`, Raychaudhuri `1.4050861792439791e-05`, quantum source `3.883856560396467e-08`, and Wronskian `9.743392826767634e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.88 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_88.json`, `STAGE00_HARD_PASS_SOLUTION_v6_88.npz`, and `RECOVERY_GATE_REGISTER_v6_88_STAGE00.json`; this HARD PASS is the sole permissible v6.89 seed
- v6.87 Stage 0 was initialized exactly once from the hash-verified immutable v6.86 Stage 0 HARD PASS at `tau = 0.4787812423706055`
- v6.87 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006643334500206108`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.137434619133629e-06`
- v6.87 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008943022175095879`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.5864915589580697e-08`
- v6.87 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.018039838990933896`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `8.360547115726646e-10`
- v6.87 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.00990112278223801`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.547473508864641e-12`
- v6.87 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `4.547473508864641e-12`, Friedmann `4.014935851372072e-12`, continuity `3.72144129660684e-06`, Raychaudhuri `1.4050750759932764e-05`, quantum source `3.883869249980753e-08`, and Wronskian `6.664413533400207e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.87 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_87.json`, `STAGE00_HARD_PASS_SOLUTION_v6_87.npz`, and `RECOVERY_GATE_REGISTER_v6_87_STAGE00.json`; this HARD PASS is the sole permissible v6.88 seed
- v6.86 Stage 0 was initialized exactly once from the hash-verified immutable v6.85 Stage 0 HARD PASS at `tau = 0.4787812347412109`
- v6.86 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.00664117201899369`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `8.266500039322278e-06`
- v6.86 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009726243195175812`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.476939404445378e-08`
- v6.86 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01954371760605104`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.9186577465690746e-09`
- v6.86 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.01104485974379332`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.750777300912887e-11`
- v6.86 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `1.750777300912887e-11`, Friedmann `1.0170273017514237e-11`, continuity `3.721429211927429e-06`, Raychaudhuri `1.405029869940323e-05`, quantum source `3.8837714928757665e-08`, and Wronskian `5.928544913129906e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.86 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_86.json`, `STAGE00_HARD_PASS_SOLUTION_v6_86.npz`, and `RECOVERY_GATE_REGISTER_v6_86_STAGE00.json`; this HARD PASS is the sole permissible v6.87 seed
- v6.85 Stage 0 was initialized exactly once from the hash-verified immutable v6.84 Stage 0 HARD PASS at `tau = 0.47878121948242186`
- v6.85 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006638549773334836`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.6457835824920664e-05`
- v6.85 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009358148707560974`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.697953801315659e-08`
- v6.85 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.018848665805720994`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.581129170981967e-09`
- v6.85 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.010233058875154482`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.6825651982799172e-11`
- v6.85 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `1.6825651982799172e-11`, Friedmann `1.5893216350433675e-11`, continuity `3.7214018010791943e-06`, Raychaudhuri `1.4049741715806548e-05`, quantum source `3.883694876832729e-08`, and Wronskian `7.488578041307467e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.85 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_85.json`, `STAGE00_HARD_PASS_SOLUTION_v6_85.npz`, and `RECOVERY_GATE_REGISTER_v6_85_STAGE00.json`; this HARD PASS is the sole permissible v6.86 seed
- v6.84 Stage 0 was initialized exactly once from the hash-verified immutable v6.83 Stage 0 HARD PASS at `tau = 0.47878118896484373`
- v6.84 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006631790715146955`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.271549402050766e-05`
- v6.84 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008855018142872604`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2640418457776637e-07`
- v6.84 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01758577731482879`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.3841944647480275e-09`
- v6.84 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.010209132618032432`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.7284841053187847e-11`
- v6.84 direct active-tau terminal diagnostics passed every gate after four accepted Newton steps: fixed point `2.7284841053187847e-11`, Friedmann `2.866418714031201e-11`, continuity `3.721339758855109e-06`, Raychaudhuri `1.4048407444359158e-05`, quantum source `3.883360561685185e-08`, and Wronskian `6.4949296118199315e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.84 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_84.json`, `STAGE00_HARD_PASS_SOLUTION_v6_84.npz`, and `RECOVERY_GATE_REGISTER_v6_84_STAGE00.json`; this HARD PASS is the sole permissible v6.85 seed
- v6.83 Stage 0 was initialized exactly once from the hash-verified immutable v6.82 Stage 0 HARD PASS at `tau = 0.4787811279296875`
- v6.83 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006615581639236017`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.452877665658052e-05`
- v6.83 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.008829811598202763`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.5326710201278857e-07`
- v6.83 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01852584814037957`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.3364482992495041e-08`
- v6.83 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.010202431723759635`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.071061626171769e-11`
- v6.83 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.03743602274126907`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.855385620812115e-12`
- v6.83 direct active-tau terminal diagnostics passed every gate after five accepted Newton steps: fixed point `5.855385620812115e-12`, Friedmann `4.9926670520777536e-12`, continuity `3.7212277056126687e-06`, Raychaudhuri `1.4047273084150212e-05`, quantum source `3.882909588713434e-08`, and Wronskian `1.1182578370726951e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.83 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_83.json`, `STAGE00_HARD_PASS_SOLUTION_v6_83.npz`, and `RECOVERY_GATE_REGISTER_v6_83_STAGE00.json`; this HARD PASS is the sole permissible v6.84 seed
- v6.82 Stage 0 was initialized exactly once from the hash-verified immutable v6.81 Stage 0 HARD PASS at `tau = 0.478781005859375`
- v6.82 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.00658905712914702`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.00012565662670110944`
- v6.82 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.009666361593030227`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.730812189935763e-07`
- v6.82 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01913685194236701`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.922105418745602e-08`
- v6.82 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.01126130902484609`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2259054882335363e-10`
- v6.82 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.015493740913733327`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.5793980546781086e-12`
- v6.82 direct active-tau terminal diagnostics passed every gate after five accepted Newton steps: fixed point `5.5793980546781086e-12`, Friedmann `5.561144570684296e-12`, continuity `3.7210004752732496e-06`, Raychaudhuri `1.4042827228517137e-05`, quantum source `3.88188114837436e-08`, and Wronskian `1.0982334396384373e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.82 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_82.json`, `STAGE00_HARD_PASS_SOLUTION_v6_82.npz`, and `RECOVERY_GATE_REGISTER_v6_82_STAGE00.json`; this HARD PASS is the sole permissible v6.83 seed
- v6.81 Stage 0 was initialized exactly once from the hash-verified immutable v6.80 Stage 0 HARD PASS at `tau = 0.47878076171875`
- v6.81 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006534365475685417`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.00023828896315145065`
- v6.81 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.010459904560033746`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.314908489397082e-06`
- v6.81 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.019641951955213496`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.242813348211751e-08`
- v6.81 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.01249106925897222`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.901948820133171e-10`
- v6.81 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.02035006858028853`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.718539199835334e-11`
- v6.81 direct active-tau terminal diagnostics passed every gate after five accepted Newton steps: fixed point `1.718539199835334e-11`, Friedmann `1.4684687492759927e-11`, continuity `3.7205468800638155e-06`, Raychaudhuri `1.4034490410970296e-05`, quantum source `3.880106774352268e-08`, and Wronskian `7.96731593915613e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.81 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_81.json`, `STAGE00_HARD_PASS_SOLUTION_v6_81.npz`, and `RECOVERY_GATE_REGISTER_v6_81_STAGE00.json`; this HARD PASS is the sole permissible v6.82 seed
- v6.80 Stage 0 was initialized exactly once from the hash-verified immutable v6.79 Stage 0 HARD PASS at `tau = 0.4787802734375`
- v6.80 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006431592830710142`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.0004265842468678255`
- v6.80 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.01146822532247832`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.302515455869126e-06`
- v6.80 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.019721360510483805`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2802119753185792e-07`
- v6.80 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.013877249720439862`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `7.513012434401389e-10`
- v6.80 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.01948942384110237`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.0693490244159136e-11`
- v6.80 direct active-tau terminal diagnostics passed every gate after five accepted Newton steps: fixed point `4.0693490244159136e-11`, Friedmann `3.406963985225785e-11`, continuity `3.7196314727354285e-06`, Raychaudhuri `1.4017839789442023e-05`, quantum source `3.8763455288985265e-08`, and Wronskian `9.123084826977677e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.80 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_80.json`, `STAGE00_HARD_PASS_SOLUTION_v6_80.npz`, and `RECOVERY_GATE_REGISTER_v6_80_STAGE00.json`; this HARD PASS is the sole permissible v6.81 seed
- v6.79 Stage 0 was initialized exactly once from the hash-verified immutable v6.78 Stage 0 HARD PASS at `tau = 0.478779296875`
- v6.79 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.006248135215783963`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.0006743345646241516`
- v6.79 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.014934772279880612`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.0954030528323444e-05`
- v6.79 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01963460252357184`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.817542656269323e-07`
- v6.79 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.018824343026489443`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `3.103774640078605e-09`
- v6.79 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.01800911147072838`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.2480319555585595e-10`
- v6.79 Newton step 6 completed one GMRES cycle with `info = 0` and final inner residual `0.011381829023531027`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.5425161148385769e-12`
- v6.79 direct active-tau terminal diagnostics passed every gate: fixed point `1.5425161148385769e-12`, Friedmann `1.5060239270860212e-12`, continuity `3.7177985830458383e-06`, Raychaudhuri `1.398739588689951e-05`, quantum source `3.868722734015165e-08`, and Wronskian `7.112424065067874e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.79 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_79.json`, `STAGE00_HARD_PASS_SOLUTION_v6_79.npz`, and `RECOVERY_GATE_REGISTER_v6_79_STAGE00.json`; this HARD PASS is the sole permissible v6.80 seed
- v6.78 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.005953968410969202`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.0011248292230447987`
- v6.78 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.02181829202873664`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.2146663409806107e-05`
- v6.78 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.01591012863785937`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `5.147694520368784e-07`
- v6.78 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.02792508099289574`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.556088601029071e-08`
- v6.78 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.013647715674088345`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `2.657016273666102e-10`
- v6.78 Newton step 6 completed one GMRES cycle with `info = 0` and final inner residual `0.036155414405790204`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `8.185452315956354e-12`
- v6.78 direct active-tau terminal diagnostics passed every gate: fixed point `8.185452315956354e-12`, Friedmann `7.489809514960293e-12`, continuity `3.7141360599352173e-06`, Raychaudhuri `1.3924263653547085e-05`, quantum source `3.8539484134645754e-08`, and Wronskian `7.473888021544781e-09`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.78 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_78.json`, `STAGE00_HARD_PASS_SOLUTION_v6_78.npz`, and `RECOVERY_GATE_REGISTER_v6_78_STAGE00.json`; this HARD PASS is the sole permissible seed for the next crossing midpoint
- v6.77 Newton step 1 completed one GMRES cycle with `info = 0` and final inner residual `0.005560794955552415`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.0035629778685688507`
- v6.77 Newton step 2 completed one GMRES cycle with `info = 0` and final inner residual `0.03090997403778097`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `0.00016290060405764473`
- v6.77 Newton step 3 completed one GMRES cycle with `info = 0` and final inner residual `0.007486304700002975`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `6.818685495263432e-07`
- v6.77 Newton step 4 completed one GMRES cycle with `info = 0` and final inner residual `0.041874424963928854`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.482125277871507e-08`
- v6.77 Newton step 5 completed one GMRES cycle with `info = 0` and final inner residual `0.0037208579849256074`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `1.9933922568160511e-10`
- v6.77 Newton step 6 completed one GMRES cycle with `info = 0` and final inner residual `0.027586298987841346`; the line search accepted `alpha = 1.0` immediately, with no rejected trial, reducing the residual to `4.243147500027078e-12`
- v6.77 direct active-tau terminal diagnostics passed every gate: fixed point `4.243147500027078e-12`, Friedmann `4.7959871610076454e-12`, continuity `3.7068104098998977e-06`, Raychaudhuri `1.3798719347199126e-05`, quantum source `3.82427818665555e-08`, and Wronskian `1.1759910538856194e-08`; rho, H, hyperbolicity, and finite gates passed and no finalization failure occurred
- the immutable v6.77 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_77.json`, `STAGE00_HARD_PASS_SOLUTION_v6_77.npz`, and `RECOVERY_GATE_REGISTER_v6_77_STAGE00.json`; this HARD PASS is the sole permissible seed for the next crossing midpoint
- v6.76 Stage 0 at `tau = 0.4787734375` is an immutable HARD PASS after six accepted Newton steps: fixed point `3.952241311999671e-12`, Friedmann `3.330233477222812e-12`, continuity `3.692124142519601e-06`, Raychaudhuri `1.3551740267133208e-05`, quantum source `3.765999200461156e-08`, and Wronskian `8.91273780809481e-09`; every gate passed and no finalization failure occurred
- the immutable v6.76 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_76.json`, `STAGE00_HARD_PASS_SOLUTION_v6_76.npz`, and `RECOVERY_GATE_REGISTER_v6_76_STAGE00.json`; this HARD PASS is the sole v6.77 seed
- v6.75 Stage 0 at `tau = 0.478765625` is an immutable HARD PASS after six accepted Newton steps: fixed point `1.809727367962921e-11`, Friedmann `1.7649891067590124e-11`, continuity `3.6626663026458305e-06`, Raychaudhuri `1.3073590610980834e-05`, quantum source `3.652709370642984e-08`, and Wronskian `7.249349006721931e-09`; every gate passed and no finalization failure occurred
- the immutable v6.75 result, solution snapshot, and gate register are persisted as `STAGE00_HARD_PASS_RESULT_v6_75.json`, `STAGE00_HARD_PASS_SOLUTION_v6_75.npz`, and `RECOVERY_GATE_REGISTER_v6_75_STAGE00.json`; this HARD PASS is the sole v6.76 seed
- v6.74 Stage 0 at `tau = 0.47878125` is an immutable NONPASS after six accepted Newton steps: fixed point `1.8866305739884126e-10` and Friedmann `1.7440413453847122e-10` failed; every other gate passed and no finalization failure occurred
- the v6.74 Stage-0 NONPASS result, solution snapshot, and gate register are persisted as `STAGE00_NONPASS_RESULT_v6_74.json`, `STAGE00_NONPASS_SOLUTION_v6_74.npz`, and `RECOVERY_GATE_REGISTER_v6_74_STAGE00.json`; none may be used as a seed
- v6.73 Stage 0 at `tau = 0.4788125` is an immutable NONPASS after six accepted Newton steps: fixed point `2.414855121424253e-10` and Friedmann `2.0569575424416466e-10` failed; every other gate passed and no finalization failure occurred
- the v6.73 Stage-0 NONPASS result, solution snapshot, and gate register are persisted as `STAGE00_NONPASS_RESULT_v6_73.json`, `STAGE00_NONPASS_SOLUTION_v6_73.npz`, and `RECOVERY_GATE_REGISTER_v6_73_STAGE00.json`; none may be used as a seed
- v6.72 Stage 0 at `tau = 0.478875` is an immutable NONPASS after six accepted Newton steps; none of its result artifacts may be used as a seed

## Fast resume (normal path)

Load only `APEIRON_FAST_RUNTIME_LATEST.zip` plus the latest `CURRENT_STATE_LATEST.npz`, `MASTER_RECOVERY_STATE_LATEST.json`, and `CURRENT_META_LATEST.json`. Read this file and `CURRENT_PROJECT_STATE_LATEST.json`, place the three state files in the capsule's `inputs/` directory, then run `python3 prepare_fast_resume.py`. `FAST_RESUME_COMPLETE` is the authoritative completed state and has no solver command; only a future `FAST_RESUME_READY` state may execute the printed command.

`APEIRON_RESUME_BUNDLE_LATEST.zip` is a historical milestone/fallback archive, not the normal chat-transfer path. Do not scan or rebuild the full history during an ordinary resume. Update the two handoff documents after an accepted Newton step or terminal classification; persist only state, master, and meta after an intermediate GMRES direction.

Do not repeat the v7.13 initialization, initial residual evaluation, terminal diagnostics, HARD PASS classification, or Float64 crossing-resolution decision; no Newton/GMRES step ran.

Do not repeat the v7.12 initialization, initial residual evaluation, terminal diagnostics, or HARD PASS classification; no Newton/GMRES step ran.

Do not repeat the v7.11 initialization, initial residual evaluation, terminal diagnostics, or HARD PASS classification; no Newton/GMRES step ran.

Do not repeat the v7.10 initialization, initial residual evaluation, terminal diagnostics, or HARD PASS classification; no Newton/GMRES step ran.

Do not repeat the v7.09 initialization, initial residual evaluation, Newton step 1 GMRES direction, its `alpha = 1.0` acceptance, terminal diagnostics, or HARD PASS classification.

Do not repeat the v7.08 initialization, initial residual evaluation, Newton step 1 GMRES direction, its `alpha = 1.0` acceptance, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.07 initialization, initial residual evaluation, Newton step 1 GMRES direction, its `alpha = 1.0` acceptance, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.06 initialization, initial residual evaluation, Newton step 1 GMRES direction, its `alpha = 1.0` acceptance, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.05 initialization, initial residual evaluation, Newton step 1 GMRES direction, its `alpha = 1.0` acceptance, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.04 initialization, accepted Newton step 1, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.03 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.02 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.01 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v7.00 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.99 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.98 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.97 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.96 initialization, accepted Newton steps 1–2, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.95 initialization, accepted Newton steps 1–3, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.94 initialization, accepted Newton steps 1–3, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.93 initialization, accepted Newton steps 1–3, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.92 initialization, accepted Newton steps 1–3, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.91 initialization, accepted Newton steps 1–4, terminal diagnostics, or HARD PASS classification. Do not repeat the v6.90 initialization, accepted Newton steps 1–4, terminal diagnostics, or HARD PASS classification. Do not repeat any v6.89, v6.88, v6.87, v6.86, v6.85, v6.84, or v6.83 initialization, accepted Newton work, terminal diagnostics, or HARD PASS classification.

Do not repeat the v6.83 initialization, initial residual evaluation, or accepted Newton steps 1–4. Do not repeat the v6.82 initialization, initial residual evaluation, accepted Newton steps 1–5, or terminal diagnostics. Do not repeat the v6.81 initialization, initial residual evaluation, accepted Newton steps 1–5, or terminal diagnostics. Do not repeat the v6.80 initialization, initial residual evaluation, accepted Newton steps 1–5, or terminal diagnostics. Do not repeat the v6.79 initialization, initial residual evaluation, accepted Newton steps 1–6, or terminal diagnostics. Do not repeat the v6.78 initialization, Newton/GMRES work, or terminal diagnostics. Do not repeat the v6.77 initialization, Newton/GMRES work, or terminal diagnostics. Do not repeat the v6.76 initialization, Newton/GMRES work, or terminal diagnostics. Do not repeat the v6.75 initialization, Newton/GMRES work, or terminal diagnostics. Do not repeat or use as a seed v6.74, v6.73, or v6.72 Stage 0, any of their accepted Newton/GMRES work or terminal diagnostics; do not repeat v6.71 Stages 0–2, v6.70 Stages 0–2, v6.69 Stage 0, v6.68 Stages 0–2, or any earlier accepted/classified stage.

Scientific decision: the crossing schedule is complete. The latest HARD PASS v7.13 is at exact protocol value `0.47878124999999994315658113919198513031005859375` (binary `0.47878124999999994`), while immutable v6.74 NONPASS is at `0.47878125`; exact bracket width is `5.684341886080801486968994140625e-17` and binary width is one adjacent Float64 step, `5.551115123125783e-17`. The next exact midpoint `0.478781249999999971578290569595992565155029296875` rounds to the NONPASS endpoint. Do not create v7.14 or rerun either endpoint without an explicitly approved change of numerical representation; physics, gates, discretization, tolerances, and solver budget remain frozen.

Physics, gates, discretization, GMRES settings, and the six-Newton budget remain unchanged. Persist each completed GMRES direction, accepted Newton step, and terminal classification. Build a full historical bundle only at schedule completion, checkpoint corruption, or an explicitly requested archival transfer. `publication_ready` remains `false`.

## Publication checkpoint — 2026-08-30

The first autonomous publication block is complete without reopening the numerical line and without starting a solver.

Authoritative publication files:

- `/Apeiron/PUBLICATION/APEIRON_PUBLICATION_CLAIMS_REGISTER_LATEST.md` — German internal claims audit; 31 controlled claims; SHA-256 `e6418a8053e1fc3b540a53db2c8737490784b8aca119c8332da22edf8cc5911a`
- `/Apeiron/PUBLICATION/APEIRON_MANUSCRIPT_LATEST.md` — complete venue-neutral English controlled master draft; SHA-256 `fb84de6b849c3036f1209bbd90c7eb7cdcc45c5dc231941489a0068bafb5f1fa`
- `/Apeiron/PUBLICATION/APEIRON_PUBLICATION_GAP_REPORT_LATEST.md` — German traffic-light gap report; SHA-256 `eec1cf7315aacb019ce92dab7c314941140ddb6964b0ae49f7e2840a770af1a5`
- `/Apeiron/PUBLICATION/APEIRON_PUBLICATION_META_LATEST.json` — publication resume metadata; SHA-256 `7f926c6b8d5b01b2f08ae757c17a5c219fff66f613576cf913f88a364e42fd1e`
- `/Apeiron/PUBLICATION/APEIRON_PUBLICATION_MASTER_DOSSIER_LATEST.pdf` — 22-page A4 milestone dossier; SHA-256 `4d5663ceb81850cd9aec203e7e0b4f861f48ad192321c4a391575de083e96a07`; all pages rendered and visually checked
- `/Apeiron/PUBLICATION/build_publication_dossier.py` — deterministic dossier builder; SHA-256 `77b2ab23852f5c956e66dc607ade9df464c1243bb05114bb897ab43e246c7e0f`

Completed publication work:

- the internal claims freeze is set and external literature is restricted to context and observational constraints
- the master manuscript contains all required sections, a cautious abstract, the exact v7.13/v6.74 values, the Float64 representation limit, AP1–AP3 as prospective work only, and a reproducibility supplement
- a primary-source framework was added for IEEE 754, GMRES, DESI DR2, Pantheon+, eBOSS, DES Y6, Planck, modified-gravity perturbations, filament lensing, GW170817, GWTC-3, and modified GW propagation
- the traffic-light audit is complete
- the terminology audit reviewed all strong terms and found no unqualified empirical or ontological overclaim
- the 22-page milestone dossier PDF was generated, rendered page by page, and passed visual inspection with no clipping, overlap, or missing-glyph marker

Red documentary submission blockers:

1. the canonical action/equations, degrees of freedom, units, signs, and conventions are not available in the controlled latest evidence package
2. the exact immutable v7.13 gate definitions and tolerances are not individually resolvable
3. the hash-referenced v7.13 result/state/crossing files and read-only verification route are not individually resolvable in the controlled publication package

Do not replace any missing v7.13 artifact with an older version, infer tolerances from PASS/NONPASS values, reconstruct equations from history, start AP1 physics, or rerun v7.13. The next autonomous publication task is documentary: resolve R-01 through R-03 from authoritative latest sources only, then integrate them without changing the frozen v7.13 result. AP1–AP3 remain follow-up work and are not prerequisites for reporting the narrowly scoped numerical classification.

For the next publication chat, read only this file, `CURRENT_PROJECT_STATE_LATEST.json`, the four publication source files listed above, and Appendix A. The milestone dossier PDF is optional for visual review and must not replace the source files. Resume at the first unresolved documentary blocker; no history or solver recovery is required.