OMEGA Synthesis 1.0 — focused claim check

The review cites OMEGA_Synthesis(3).pdf with SHA-256 01f0d19cdb140951c80ea59ed4b1e82928c9b2bfedab27e42d946fb78a6498a1Copy. That file was not attached to this deposit. The hash is recorded as claimed and has not been verified here. The original synthesis runner package was also not supplied.

Python 3.11.2 on 2026-09-17T19:30:11Z. Three modes, three exit codes 0, identical stdout. The checker uses require(), so -O and -OO do not disable the tests.

python3.11 omega_synthesis_claim_check.py
python3.11 -O omega_synthesis_claim_check.py
python3.11 -OO omega_synthesis_claim_check.py

Result: independent Farey boundary first disagreement $42189065$; Sacks real-parameter counterexample $m=1,\;k=5/2$; streaming-domain counterexample $s=1/2,\;r=0,\;b=255\Rightarrow q=510$; 72 integer streaming examples. ALL FOCUSED CLAIM CHECKS PASS.

omega_synthesis_claim_check.py stdout ENVIRONMENT.json · REVIEW.md · README.md

Checker 4891 bytes, SHA-256 9397c5300b9eaf125958bf21c6a7064f369d14e388313d458cd21b1d825fb41dCopy.

Stdout 434 bytes, SHA-256 a6e768c3be44016a5778817d6bf018c50f91252d578775ae9a2d78b2b0b77f0eCopy.

Sacks finite-error identity: require integer samples $m\in\mathbb Z_{\ge 1},\;k\in\mathbb Z,\;k>\varphi^m$. The identity is false for arbitrary real $k>\varphi^m$. Exact counterexample $m=1,\;k=5/2$. This does not invalidate the integer-sampled asymptote.

Streaming byte quotients: require $s\in\mathbb Z_{\ge 1},\; r_i\in\{0,\ldots,s-1\},\; b_i\in\{0,\ldots,255\}$. The printed implication from $r_i<s$ alone is insufficient. Named implementation scales remain integers.

Iteration superscripts ${}^{,n}$ are typographical; replace by composition ${}^{\circ n}$. Not a change of result.

Neighbors $846547/2490212$ and $13495616/39698853$ are unimodular. Any rational strictly between them has denominator at least $42189065$. The mediant $14342163/42189065$ is the witness. This does not call a supplied floor_sum routine.

Same first-disagreement integer already stated on the dynamics page. Claim record. Not a proof that the maps agree on all nonnegative integers.

Not peer review. Not independent third-party reproduction of the eight source works. Not a Lean kernel certificate. Not a cubature package. Not authenticity of an original decoder core. Frozen G₆ bytes are unchanged.