# Odd-primary Kervaire witness registry

Family 309: The Kervaire invariant problem at the prime three. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Store the claimed surviving three-primary classes and exact indices, stems and orders.

## Applicability and commercial boundary

A sparse existence result in stable homotopy is not a general homotopy-group computation algorithm.

## 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

Extract representatives and verify indexing against selected formal scope.

## 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 Kervaire invariant problem at the prime three](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026/paper.pdf).