# Verification of the Weaver coordinate cube note

The four-page manuscript gives a universal analytic proof using two credited
existence theorems: MSS Corollary 1.5 and BCMS Corollary 1.3 and its proof.
It normalizes the complement with squared norms bounded by
alpha/(1-beta), then uses Loewner order and disjoint antipodal cubes.
The exact strict-slack identity and the trivial threshold boundary are
checked in the proof. The broad AIM source is not marked solved.

The originating researcher's detailed proof and source audits are retained
in the reproducibility directory. They are not independent review or
proof-assistant verification. Akbas-Sra's prior counting result is explicitly
acknowledged, and no absolute priority or optimality claim is made.

The standalone checker uses integer and Fraction arithmetic. Its normal
Python 3.13, optimized Python 3.13 and Python 3.12 outputs agree on:

- 4,173 rational parameter cases;
- 450 noncommuting frame/free-set cases and 2,400 cube extensions;
- 30,240 whitening inequalities;
- 48,960 exhaustively counted signings;
- 1,134 repeated-coordinate count cases and five negative controls.

These are finite regressions, not exhaustive validation of all frames or
proofs of the two input theorems. The portable archive checker repeats the
same exact output without workspace dependencies. Compiler, visual-review,
archive integrity and portable-replay receipts accompany the package.

Both the built-in compiler and exported PDF compilation succeeded. All four
final pages were inspected: formulas, theorem boundaries, author footnote
and references are legible. A bibliography line-spacing warning was removed
by left-aligning the reference list; the final build has no errors, missing
glyphs, unresolved references, overfull boxes or underfull boxes.