# Hosting notes — OMEGA object exploration 02

Additional consequences of the six labeled baseline marks. Not a source paper.
Not a replacement of Paper VII v1.6. Canonical seed remains one arcsecond.
The 36-degree Gauss–Lobatto member is an explicitly declared family extension.

## Hosted corrected files (this archive)

| File | Bytes | SHA-256 |
|---|---|---|
| OMEGA_Object_Exploration_02.py | 15581 | 4c1b3cfa46262e21d19ece458d4dcb8fccd617d15ca4579a2f013108396c13a6 |
| OMEGA_Object_Exploration_02.md | 20104 | 12f3106a7980ce56e328c3ae29392f306c1c321e4c7c92decbce38fa00560513 |

The checker completed 21 check groups: the original 19 mathematical groups
and two groups verifying malformed-input rejection. Normal and optimized
Python runs both passed. The decoder rejects inconsistent or empty coordinate
vectors, incorrect record counts, and requested recovery budgets outside the
proved bounds. The accompanying note restores the damaged mathematical notation.

## Named author replacement hashes (not received)

The instruction named these replacement files, but the embedding document
that was to reconstruct them was not in the upload. Hosted bytes therefore
do **not** match:

| Named file | Named bytes | Named SHA-256 |
|---|---|---|
| OMEGA_Object_Exploration_02.py | 15034 | 6c35365d9265bd91bf2f79cfe4a1de56ba28bda76d4c59303ae2e245de9715b5 |
| OMEGA_Object_Exploration_02.md | 19434 | e50f3443454bc628f1b543732d5e337ebc477ee56f25fc83df784c6e4af4ea82 |

## This-archive replay

Python 3.10.21 / SymPy 1.14.0 / mpmath 1.3.0:

```bash
python3 OMEGA_Object_Exploration_02.py --output this_archive_exploration_results.json
python3 -O OMEGA_Object_Exploration_02.py --output this_archive_exploration_results.optimized.json
```

Both exit 0. COMPLETED 21 check groups. Results JSON `script_sha256` equals
the hosted checker. Logs are the actual stdout of those two runs.

Not a proof-assistant certificate, not peer review, not a camera-noise model.
Does not enlarge Paper VII or Paper VIII. Frozen G₆ unchanged.