# Verification report for the unitary mixed identity

The four-page English manuscript proves a nontrivial singular mixed identity
of length at most 16q+8p+12 for PSU_n(q), q=p^e, n>=2. Combining this with
the attributed Bradford–Schneider–Thom lower bound gives Theta(q),
uniformly in dimension.

## Mathematical argument

The proof handles perpendicular transvection directions by square-zero
nilpotents and nonperpendicular directions by a nondegenerate Hermitian
two-plane. The resulting three order alternatives are combined using
separate free conjugators. Free-product normal form proves nontriviality
both before and after projectivization, including characteristic two.
The variable-length count and singular augmentation are explicit.

The manuscript's general normal-form lemma merely separates out the
argument already contained in the accepted proof. No all-family result,
exact minimum length or nonsingular construction is asserted.

## Exact diagnostics

Normal and optimized Python runs pass 7,851 transvection-pair tests,
480 complete word evaluations and ten free-product cases. The fields
have q in {2,3,4,5,7,8,9,11}; the formal-word tests also include q=101.
Reports distinguish exhaustive pair tests from tests with a fixed
first transvection. All three order branches are exercised, and the
unseparated-commutator control reduces to the empty word as expected.

The checker uses exact field tables and integer exponents, with no
floating-point proof steps and no assertions disabled by optimization.
These finite tests are supplementary diagnostics, not a proof of the
infinite family.

## Scope and review

The precise unitary theorem has undergone detailed originating-researcher
self-audit. The original OWR questions remain partially solved. Known
methods, the lower bound and the single-variable reduction are credited.
The literature review is bounded; novelty and absolute priority are not
certified. AI assistance is disclosed in the manuscript. No independent
human review or proof-assistant verification is claimed.

The publication package includes reproducibility files and source
provenance. Third-party source PDFs are not included.