OMEGA GEOMETRY / OPERATOR BRIDGE
Single shareable package -- 7 October 2026 -- version 1.0

START HERE
Open START_HERE.html in a browser. It works offline and requires no
JavaScript, remote fonts, math-rendering service, or other web assets.
It contains the source review, complete working proofs, preservation/loss
contracts, execution scope, and source locators.

PRIMARY JULIA IMPLEMENTATION
  omega_geometry_operator_bridge.jl

Run from this directory:
  julia --startup-file=no omega_geometry_operator_bridge.jl
  julia --startup-file=no --check-bounds=yes omega_geometry_operator_bridge.jl

Julia 1.9+ is the implementation target. Standard libraries only.
JULIA STATUS: NOT EXECUTED HERE. No Julia PASS is claimed.

Use the code without automatically running its check suite:
  include("omega_geometry_operator_bridge.jl")
  using .OmegaGeometryBridge
  k = kernel_record()                 # true one-arcsecond seed, scale 1
  e = moment_ellipse(k)               # semiaxes derived from the landmarks
  T = ellipse_operator(e.R, e.r)
  chart = ellipse_affine_chart(k)     # full-kernel map and recovery metric
  B = block_truncation(e.R, e.r, 8)    # eight finite operator blocks

The infinite object is specified and proved in the note. B is a finite
truncation, not an execution of infinitely many blocks.

EXECUTED INDEPENDENT CHECKER
  verify_reference.py
  python verify_reference.py
  python -O verify_reference.py

Dependencies: NumPy and SymPy. Tested versions are in requirements-tested.txt.
The package contains the actual Python logs and EXECUTION_RECORD.txt.
Both executions exited 0, with 23 groups passed in each mode. These runs do
not execute Julia. Numerical comparisons do not replace the written proofs.

MAIN CONTENTS
  START_HERE.html                       Source-grounded proof and findings
  omega_geometry_operator_bridge.jl    Julia implementation and 21 test groups
  verify_reference.py                  Executed independent implementation
  requirements-tested.txt              Python versions used
  execution/EXECUTION_RECORD.txt        Runtime status, scope and code hashes
  execution/python-normal.txt          Actual normal-mode output
  execution/python-optimized.txt       Actual optimized-mode output
  MANIFEST.sha256                      Package file hashes, excluding itself

SCOPE
Published input: Matthew Alan Newman's Paper VII v1.6.0 and the website's
true-seed node record. The derived equal-weight, circle-centered ellipse,
affine angle-recovery chart, operator representation, weighted product,
and infinite direct sum are explicitly specified constructions here.
The original arc-and-feet curve is not a filled ellipse. The original curve
does not acquire intrinsic dimensions merely by an ambient embedding.

The package corrects the earlier file's claim about translated ellipses
and zero tails. A translated ellipse generally requires its center on the
identity tail, not zero, to preserve its numerical range.

The constant-two inequality from OpenAI family 325 is an external-theorem
application, not an independently verified claim of this package. An
explicit elementary matrix-polynomial bound is proved separately here.

SOURCE INTEGRITY
Sources were inspected through the browser. Original source bytes were not
downloaded and hashed. Source node numbers used by the checker are marked
transcriptions. MANIFEST.sha256 identifies these generated package files;
it does not certify the website, a GitHub commit, or a Zenodo byte match.

Share this ZIP as one resource. The package has not been published to the
website, assigned a DOI, saved to the user's Library, or peer reviewed.