OMEGA NAUGHT
Relative Representation and Recoverable Information
Research thesis, version 1.0, 15 October 2026.
Hosted here the same day. Not a source paper. Not peer reviewed.

The PDF is the supplied thesis. Its cover says it does not claim independent
peer review, a proof-assistant kernel verification, a physical unification,
or a mathematical proof of the divine. This archive has not reviewed the
written arguments as a proof. Faith and the dream account are provenance
in the thesis, not mathematical evidence.

verify_omega_thesis.py was transcribed from the printed Appendix B listing,
lines 1 through 473. The companion source was not attached. This file is
that transcription. It is not asserted to be the unseen companion bytes.
PDF text extraction rendered apostrophes as U+2019; the hosted file uses
ASCII quotes. Whitespace follows the printed statements, not a hidden
source file.

The thesis says its own Python 3.13.5 normal and python -O JSON outputs
were byte-identical. Those logs, the companion audit log, the mutation
tests, and the manifest were not in this upload. This archive does not
claim those output digests.

This archive ran the transcription on Python 3.10.21, normal and
python3 -O. Both exited 0. Those two logs are byte-identical. They are
not a comparison with the unsupplied 3.13.5 logs.

The program is an exact symbolic-algebra checker with a finite
canonical-ledger audit. Both executions reproduce the declared checks.
Neither establishes physical unification or independent mathematical
review.

The 28 free-variable identities are identities under the program's
construction, including telescoping polynomials for horizons 1 through
23 and the factorization x^5+x+1=(x^2+x+1)(x^3-x^2+1). The finite audit
is separate: seeds 0 through 32767, horizon 23, 753664 prefix identities,
32768 reversals, 32768 first-residue inversions, maximum extinction
step 10, and 4 rejected malformed records. The floor maps agree for
integers 0 <= d < 42189065 by the stated floor-sum certificate. That
threshold was not enumerated state by state. At 42189065 the certified
floors are 14342163 and 14342162. The common prefix sum is
302541195258184.

The auxiliary seed s=1/2 is not the canonical sine. The canonical sine
sin(pi/1296000) is not evaluated. q=339949771344778/10^15 is not
lambda=phi/(phi+pi). C=a*pi is not the retained major-arc length.

The thesis states that this program's JSON grammar produces 62 bytes and
that this differs from the previous bundle's 24-byte grammar. This run
printed payload_bytes 62 and byte_ledgers 62. The encodings are different.
Neither length is a universal property of the measurements.

The thesis uses an upward circle gamma(t)=(sin t, -cos t), with feet at
y=-c and the opening at the bottom. That is not the archive drawing's
frame, and it is not the earlier (c, z_i) exchange.

Table 1 in the thesis lists separate counts. They are not added into one
proof total. A checker field of 25 finite metric pairs is not a row of
that table.

The hosted logs have recorded SHA-256 digests. Matching those digests
checks the logs' byte integrity. The logs document the archive's reported
executions. Rerunning the checker tests whether those results are
reproducible. A matching hash does not itself verify that the recorded
execution occurred or that the checker is mathematically correct.

The thesis says the same limit in its own words: a hash identifies bytes;
it does not certify their mathematical correctness.

No Julia, Rust, or Lean run is claimed. Not an amendment of Paper VII.
Frozen G6 is unchanged.