**Evidence for Paper VIII Proof Audit 01**

This package accompanies the audit of Theorems 7.3–7.6, their geometric dependencies, and the angular-energy result in Theorem 8.6. The written report contains the proof for all dimensions, endpoint and support arguments, adversarial examples, and literature assessment.

Contents:

- OMEGA_Localized_Flow_Complete_Proof.pdf — complete six-page mathematical proof.
- OMEGA_Localized_Flow_Complete_Proof.tex — editable LaTeX source.
- build_proof_pdf.py — PDF build script using LaTeX and ReportLab.
- OMEGA_Paper_VIII_Proof_Audit_01_Forced_Flow.md — full audit.
- independent_checks.py — independent exact algebra checks; no author modules imported.
- independent_checks.log — complete successful execution log.
- independent_results.json — machine-readable results and scope limits.
- source_manifest.json — hashes of reviewed sources and included evidence files.

To reproduce, use Python 3.12 and SymPy 1.14.0:

```bash
python3 -m pip install sympy==1.14.0
python3 independent_checks.py --output reproduced_results.json
```

The recorded run passed 29 check groups, including all 56 sphere monomials through total degree five and exact counterexamples to stronger claims. Dimensions three and four are symbolic corroborations; the general index proof is in the report. Smooth support and global ODE existence are analytic arguments. This is not proof-assistant verification.

The public standalone PDF and the PDF inside the source ZIP have different file hashes but identical complete text under the same pdftotext extraction. Both identities are recorded. Public source and literature links appear in the report. The published files were not edited.