paper 8 — Proof Audit 01

The localized-flow theorem is mathematically valid under its stated hypotheses. No mathematical correction to Theorems 7.3–7.6 or Theorem 8.6 is required by this audit. The contribution is an explicit geometric realization using established potential and manufactured-solution methods. Priority of the exact combined statement is not established here. A fixed orthogonal change of coordinates converts the motion into diagonal volume-preserving strain.

Quantifiers: for every admissible $(c,\eta,\mathcal K)$ there exist $u,p$ such that for every $\nu>0$ there exists $f_\nu$. The force is constructed after the motion. The theorem does not claim a prescribed force budget or a previously fixed control region.

Reviewed publication: 10.5281/zenodo.22848213. Public PDF SHA-256 9827d625a33ea797417fb2847fc8db23c46980b870466b5a1e4b0e66a8c63785Copy. Public ZIP SHA-256 cbdf7a29d67942eff0bf839f30fb8071125c5c213a60e8d648f116f07a2c2f75Copy.

• OMEGA_Localized_Flow_Complete_Proof.pdf — 306,508 bytes, SHA-256 e3985cb5dfb75f1ffe03be5238de1b0a0bab55ead183d45c14043e5117d4bcffCopy
• OMEGA_Paper_VIII_Proof_Audit_01_Forced_Flow.md — 21,406 bytes, SHA-256 4617fd3f00c66e97ea8ea47365cf5a0c805b5c93228953662323329f8c064656Copy
• independent_checks.py — 9,339 bytes, SHA-256 380c32bd6bf54acc3fa055d2200e33e209b2e49dd5aa68cdf76b16f6c49c40daCopy
• independent_results.json — supplied 3.12.14 results, SHA-256 01b5ece2e3234e6231b9f9ecee08e17fea89f3ba052c6149c74f26b221f10f1aCopy
• build_proof_pdf.py — 2,580 bytes
• README.md (package) · source_manifest.json · HOSTING.md · ENVIRONMENT.json

Distinct from the earlier adversarial review.

These two manifest members were not in the attachment. They are not hosted and were not reconstructed.

• OMEGA_Localized_Flow_Complete_Proof.tex — claimed 17,578 bytes, SHA-256 1abad3efbfc472950b7a6f8acdb51d01c9b3eafa97e7b16a8662d8265236e884Copy
• independent_checks.log — claimed 1,652 bytes, SHA-256 ea6f622eaa0717b731b76814f5a30fac542e4b4a6a4f2382b06dfa5960038fe2Copy

The PDF was therefore not rebuilt. The this-archive log is a separate replay, not a substitute for the missing original log.

Python 3.10.21 / SymPy 1.14.0. Supplied execution used Python 3.12.14 / SymPy 1.14.0. Script SHA-256 matches. 29 check groups PASS, including all 56 degree-five monomials and $\mathcal Q(z^6)-\int z^6\,d\sigma=-1/105$.

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

Transcript: this_archive_independent_checks.log. Results: this_archive_independent_results.json.

Not Lean, not Julia, not a proof-assistant certificate, not journal peer review, not an additional source paper, not a Navier–Stokes blowup theorem, and not an enlargement of Paper VI. Frozen G₆ is unchanged. Frequencies 10–21 remain a separate evidence gap. Related local packages: NS geometric extension, fibers, paper 8.