# Categorical homotopy model interoperability

Family 317: Thomason model structures in all strict higher dimensions. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Investigate explicit translations between the specified strict globular category model structures and spaces.

## Applicability and commercial boundary

A Quillen equivalence does not automatically verify business processes or preserve a chosen finite encoding efficiently.

## 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 constructive functors and a small homotopy example.

## 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).

[Thomason Model Structures in Every Strict Higher Dimension](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026/paper.pdf).