# P=W cohomology computation cross-check

Family 043: <i>P</i> = <i>W</i> for fixed-determinant SL<sub><i>n</i></sub> moduli spaces. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Compare perverse and weight filtrations for coprime fixed-determinant traceless Higgs moduli, including composite ranks.

## Applicability and commercial boundary

P=W is unrelated to computational P versus NP; complete cohomology and variant-part statements require the exact moduli data.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Identify independently computable low-rank filtrations for a research fixture.

## Evidence scope

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

[P=W in composite rank for fixed determinant](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026/P-equals-W-in-composite-rank-for-fixed-determinant-September-24-2026.pdf).