OMEGA GEOMETRY / OPERATOR BRIDGE -- EXECUTION RECORD
Review date: 2026-10-07
Recorded UTC: 2026-10-07T22:29:58.357476+00:00

EXECUTED: independent Python reference implementation.
NOT EXECUTED: supplied Julia implementation (no runtime found).
NOT BUILT: any Lean formalization.

Normal Python process exit code: 0
Optimized Python process exit code: 0
Groups: 23 PASS in each mode.
Explicit require calls: 7539 in each mode, including input validation.
Logs identical except Optimization mode header: True
Python assert AST nodes: 0 (checked by the program).
Python: 3.13.5; NumPy: 2.3.5; SymPy: 1.14.0.
OPENBLAS_NUM_THREADS=1 was set for these runs.

Actual commands:
  python verify_reference.py
  python -O verify_reference.py

Julia commands supplied for a recipient to run, NOT executed here:
  julia --startup-file=no omega_geometry_operator_bridge.jl
  julia --startup-file=no --check-bounds=yes omega_geometry_operator_bridge.jl
Julia implementation contains 21 test groups, including 4 exact
quadratic-field polynomial groups. No Julia PASS is claimed.

Python source bytes: 15615
Python source SHA-256: f69e15bea4e521343a6de46c20adc77490b327b643adf055ed358ca6b0879885
Julia source bytes: 19070
Julia source SHA-256: 9f81f385077cad025d4830e62f43cb68af224513360374aa9323825da72ee82b

CHECK SCOPE
Exact symbolic identities are checked by SymPy. Numerical checks use
binary64 comparisons and finite samples. The 80-digit values are cross-checks,
not certified enclosures. The analytic proofs in START_HERE.html provide
the all-point, arbitrary-parameter and infinite-dimensional arguments.

Source node numbers were transcribed from the inspected website export.
The comparison is not a byte-level hash verification of the source JSON.
Original website/PDF/GitHub bytes were not downloaded to this container:
network resolution and the download tool failed. Browser retrieval worked.
No repository commit hash was established in this review.

No physical experiment, published-paper amendment, independent peer review,
complete website audit, entire repository review, or universal unification
is asserted by this record.