# Verification report

The result is accepted by detailed self-audit of the explicit weighted
2x2 bijection, the boundary correction, Cauchy--Schwarz, Jensen, and a
bounded-test argument for total variation. No mathematical gap was found
within these statements. No independent review or formal proof-assistant
verification took place; novelty and absolute priority are not certified.

The same exact checker passes in normal and optimized Python modes:
205 margin families, 24,535 tables, and 103,262 paired legal switch edges.
Checks include all margins, the pointwise cubic cancellation, the boundary
sum, the mean inequality, a column-first counting oracle and the closed-form
two-row law. Universal results are proved analytically, not inferred from
finite samples.

Four primary-source PDFs and ten complete relevant pages were inspected.
The fixed-base cloning theorem and the growing-heavy-block theorem were
kept separate from the single-heavy-row source question. The package
records its actual visual inspection and portable rebuild in the manifest
and local readiness receipt. It is an unrefereed preprint, not a journal
acceptance, independent certification, or published DOI record.