This work was produced within the Bolzano project (https://bolzano.app), using AI systems for mathematical research and manuscript preparation. The listed authors contributed to the project and the preparation of this release. The manuscript received only limited human checking.

Text origin: primarily AI-generated.
Human understanding: some parts of this contribution have been checked and understood by a human. The manuscript received only limited human checking.
Automated editorial and literature checks are not human verification.

The binary rank-metric average-radius result was already known and is explicitly credited. The claim here is the all-fixed-finite-field square-matrix version, with a bound uniform in the capacity gap. No decoding algorithm, rectangular-model extension, or complete Lean verification is asserted.
