# Infinity-groupoid model correspondence evidence

Family 312: The Grothendieck homotopy hypothesis. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track the claimed equivalence between the specified coherator-based infinity-groupoids and homotopy spaces.

## Applicability and commercial boundary

An abstract model equivalence does not provide a cheap homology solver or automatically encode arbitrary application workflows.

## 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

Read functor constructions and computational data requirements.

## 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 Grothendieck homotopy hypothesis via elementary expansions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026/paper.pdf).