# Inspection and execution evidence

Date: 2026-09-24 UTC.

## Live source findings

- `/dynamics` publicly states Q, S, the floor map, the first 399 identity, and
  reverse reconstruction. This contradicts the claim that no underlying
  transformation equation is provided anywhere on the site.
- `/tools/reconstruct` provides the ledger table and an evidence link to the
  floor page. It does not put the complete defining equations beside that
  table in the retrieved HTML. This is the immediate discoverability issue.
- `/start/shape-to-record` shows the same example with h = 1/100.
- `/reproduce` exposes many source downloads, including the Paper VIII source
  package. `/papers/8/omega_reference_checker.py` is directly downloadable.
- The deployed reconstruction bundle contains BigInt constants and computes
  a product, quotient, and remainder. Its reverse code checks bounds and
  divisibility. It is not a function guessed from the example.

These URLs returned HTTP 200 using decompressed content retrieval. A guessed
`/reconstruct` URL returned 404; that is not the linked tool route and is not
reported as a website defect. Search-service retrieval was unavailable, so
the observations above come from direct HTTP retrieval rather than indexed
search results.

## Retrieved source identity

| Local file | Public URL | SHA-256 |
|---|---|---|
| evidence/omega_reference_checker.py | https://omega-naught.grok.me/papers/8/omega_reference_checker.py | dbf0650cf80c9e618684d98292bf7592baadadc51bd2eccf15b950392dcd5c8b |
| evidence/bridge.js | https://omega-naught.grok.me/assets/bridge-B-L3WbJ0.js | 36932658afd9bc3d8ce7e44abb6225b6420ee33907969449648bde587bbb9927 |
| evidence/ledger-tool.js | https://omega-naught.grok.me/assets/ledger-tool-D1EKZ0Pj.js | 270b4301715fce3d219e9eb4f2ddeb9397e8b312224a6b98cbfb13cfbbce3abb |

The ledger-tool bundle was inspected, not executed as an interactive React
application. The bridge module's pure exported step function was executed.
The Python reference module's `make_row` and `check_row` were executed; its
full Paper VIII entry point, unrelated cubature checks, and irrational-floor
certification were not rerun for this focused task.

## Reproduction results

Environment: Python 3.12.14 and Node v24.19.0, standard libraries only.

Commands whose outputs are included:

```bash
python3 floor_kernel.py 399 --verify --site-reference evidence/omega_reference_checker.py
python3 -O floor_kernel.py 399 --verify --site-reference evidence/omega_reference_checker.py
node verify_floor_kernel.mjs --site-bridge evidence/bridge.js
```

The first two outputs are byte-identical. All three runs passed.

| Check | Observed result |
|---|---|
| 399 trajectory | 399,135,45,15,5,1,0 |
| Reverse of the six remainders | 399 |
| Seeds tested | Every integer 0 through 32767 |
| Unpadded transitions tested per implementation | 300871 |
| Largest extinction depth on that domain | 10 |
| Rejection controls per implementation | 14 passed |
| Valid suffix interpreted as its own record | Recovered 135 |
| Larger exact-integer example | 10^80 + 399 round trip passed |
| Downloaded site Python comparison | All 32768 ledgers and reversals matched |
| Downloaded deployed bridge comparison | All 32768 one-step quotient-remainder pairs matched |
| New Python versus JavaScript domain checksum | Identical |

Domain checksum:

```text
804ac6ba40a63a0596bc577d0721e98000c30e2a00e4a9173d3749e8d7adf059
```

Its serialization is defined in the accompanying note. This is not the hash
of an existing frozen site artifact. The 300871 transition count counts each
unpadded seed trajectory, so transitions repeated in different trajectories
are counted again. It is different from fixed-length padded coverage counts.

The rejection controls cover negative, Boolean, and floating-point inputs;
noncanonical decimal text; a nonzero extinction terminal; invalid remainder
bounds and types; zero padding; a remainder changed by one; and mismatch with
an externally expected seed. They are not a general authenticity guarantee.

The written proof establishes the rational-map identities on all nonnegative
integers. These local runs check implementations on the stated finite domain
and examples. No website files were deployed or edited during this task.