# Quiver cohomology correspondence adapter

Family 044: The equivariant cohomological Hikita conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Organize Hikita-type correspondences between equivariant cohomology and a fixed-point scheme of a Coulomb branch.

## Applicability and commercial boundary

Loops, framings, cocharacters and stable/free gauge hypotheses matter. No generic quiver optimization speedup is established.

## 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

Inspect finite presentations and compute a small instance against existing symbolic software.

## 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).

[The equivariant cohomological Hikita conjecture for arbitrary quivers](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026/main.pdf).