# Hosting notes — paper 8 Proof Audit 01

This directory hosts a 19 September 2026 audit of paper 8 Theorems 7.3–7.6
and the angular-energy connection in Theorem 8.6. It is additional work,
not a relabeling of the earlier adversarial review, not institutional peer
review, and not an additional source paper. The published manuscript and
Zenodo ZIP were not edited.

Site label remains **paper 8**. The manuscript heading says Paper VIII.

## Hash-matched originals (bytes preserved)

| File | Bytes | SHA-256 |
|---|---|---|
| OMEGA_Localized_Flow_Complete_Proof.pdf | 306508 | e3985cb5dfb75f1ffe03be5238de1b0a0bab55ead183d45c14043e5117d4bcff |
| OMEGA_Paper_VIII_Proof_Audit_01_Forced_Flow.md | 21406 | 4617fd3f00c66e97ea8ea47365cf5a0c805b5c93228953662323329f8c064656 |
| independent_checks.py | 9339 | 380c32bd6bf54acc3fa055d2200e33e209b2e49dd5aa68cdf76b16f6c49c40da |
| independent_results.json | 3754 | 01b5ece2e3234e6231b9f9ecee08e17fea89f3ba052c6149c74f26b221f10f1a |
| build_proof_pdf.py | 2580 | 3cde0dc5dd0f065ea3e8ceadb4f880fba42bf3893a45f781e51aced888f47d9c |
| README.md | 1717 | b4c56d8ea337858581c4b09672068376790e37b374317724fbef9b4c91aa4c45 |
| source_manifest.json | 1904 | 959a97b2cb84afa0cfe13701ba42e550704f890e030e349208e9eeed4a9a6883 |

Reviewed publication identities in the manifest (already hosted at /papers/8):

- public PDF 9827d625… (286306 bytes)
- public ZIP cbdf7a29… (1323852 bytes)
- manuscript Markdown inside the ZIP c53bc0bd…
- bundled PDF inside the ZIP ec072861…

Those two PDFs differ as files; the audit records identical pdftotext extraction
69681ba2…. This archive does not infer a mathematical discrepancy from the
different PDF hashes.

## Missing from the attachment (not hosted, not reconstructed)

| File | Claimed bytes | Claimed SHA-256 |
|---|---|---|
| OMEGA_Localized_Flow_Complete_Proof.tex | 17578 | 1abad3efbfc472950b7a6f8acdb51d01c9b3eafa97e7b16a8662d8265236e884 |
| independent_checks.log | 1652 | ea6f622eaa0717b731b76814f5a30fac542e4b4a6a4f2382b06dfa5960038fe2 |

The LaTeX source was not supplied, so the PDF was not rebuilt here.
The supplied original execution log was not supplied; the this-archive log
below is a separate replay and is not a substitute for those bytes.

## This-archive replay (distinct from the supplied 3.12.14 run)

Python 3.10.21 / SymPy 1.14.0. Command:

```bash
python3 independent_checks.py --output this_archive_independent_results.json
python3 -O independent_checks.py --output /tmp/paper8-audit01-opt.json
```

Both exit 0. 29 check groups PASS, including all 56 monomials through degree
five and the degree-six obstruction −1/105. Script SHA-256 380c32bd… matches
the supplied file. No author companion modules were imported.

This is not a proof-assistant certificate, not journal peer review, and not
independent third-party reproduction of the whole paper. Smooth support and
global ODE arguments remain analytic, as the audit states. Finite checks do
not prove the general-dimension index argument.

Not a Navier–Stokes blowup or unforced global-regularity theorem.
Does not enlarge Paper VI. Frozen G₆ unchanged.