# OMEGA–Navier–Stokes geometric transport — Version 3.0

This folder is a **mathematical extension package**, not a source paper.

Version 3.0 is current. Version 1.0 remains under `v1/` as a historical local
host. Frozen G₆, Paper VII, Paper VI cubature certificates, and SRSD are
unchanged.

## Received PDF identity (this archive)

The hosted file is the received 20-page PDF, 2,376,354 bytes.

SHA-256 of **this file**:
`98a3f74742dd3d06626ec03a248e8ce901772c18d836a5e736e1f1e594e6d675`

The revision notes claim
`42802e0077d67c9b35aede91d59cf0ed3318c6135ba337b5206800fdbd4fe4a9`.
That digest does **not** match this file. The PDF also embeds a
`Content Credentials` attachment (24,296 bytes) in addition to the eight
intended supplements. This archive reports the actual bytes, not the claimed
digest.

## Intended supplements (hashes match the notes)

Extracted from the received PDF; byte-identical to the chat copies.

| File | SHA-256 |
|---|---|
| `OMEGA_NS_Geometric_Extension.tex` | `2cadfed871fc74bdf61683b09f0cc9de54aa05ada0df6b7d103f7bd760bd6cf9` |
| `verify_omega_ns.py` | `f054d343f78c96f18d1a4360453dd1761d3fc8de7757edfb56a746996921e531` |
| `audit_omega_sources.py` | `7bb072407b4c2c3ea58c0a8a0ad392d5870fc1d7d339ff20b67679b9ad96f08e` |
| `test_omega_auditor.py` | `9cae8025b0b6637ca5b188b30d84235b3c73a122445f0a7fdd9fcf8df6d5f509` |
| `build_omega_pdf.py` | `a08a93700ee779cb9ac2158cd4c27e4124e1b8c069a62c9b8f26cd71f68e3700` |
| `OMEGA_V3_Verification_Record.txt` | `095d05494a301c1fe21f72df044da569b9a00d01e5edc841bdfe4fe5eed91f01` |
| `sources/LEAN_Proof_Complete_Final(1).docx` | `275da4ea14130d21aa1b797b643ec78192e195780bfd8352bac699a75b73542e` |
| `sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip` | `ef8f1eb75b83f1e5763d280374eb8b73d9ab00b8dcb76b1824aee771869cd27a` |

## This-archive commands

Python 3.11.2, SymPy 1.14.0. Distinct from the author record (Python 3.12.14).

```bash
python3.11 verify_omega_ns.py
python3.11 -O verify_omega_ns.py
python3.11 -OO verify_omega_ns.py
python3.11 audit_omega_sources.py \
  'sources/LEAN_Proof_Complete_Final(1).docx' \
  'sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip'
python3.11 -O audit_omega_sources.py \
  'sources/LEAN_Proof_Complete_Final(1).docx' \
  'sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip'
python3.11 test_omega_auditor.py audit_omega_sources.py \
  'sources/LEAN_Proof_Complete_Final(1).docx' \
  'sources/Julia_OMEGA_NAUGHT_Julia_Proof_v0.1(1).zip'
```

Results (exit 0; verifier and auditor stdout identical under `-O`):

- verifier: 62 exact checks plus retained integer/rational tests
- auditor: original package accepted
- harness: 38 subprocess checks; 36 required rejections

`build_omega_pdf.py` was **not** rerun. No `pdflatex` rebuild. No fresh Lean
or Julia runtime.

## What this does not claim

- not one of the eight source works
- not a joining theorem that Navier–Stokes selected φ+π
- not identification with an external singular vortex or blowup manuscript
- not historical novelty or peer review
- SRSD remains frozen and external