# Brauer character and weight counting cross-check

Family 202: The blockwise Alperin weight conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Representation software teams can compare block character counts with weight conjugacy-class counts for finite groups.

## Applicability and commercial boundary

The equality does not give an efficient enumeration of either side or a complete representation constructor.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.

## Next verification action

Identify an explicit finite group and block with independently computable counts.

## Evidence scope

The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The Blockwise Alperin Weight Conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Blockwise-Alperin-Weight-Conjecture-September-23-2026/paper.pdf).