# Chromatic finite-complex existence catalog

Family 308: Finite Smith–Toda complexes at every height. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Organize Smith–Toda finite complexes at every height with a varying prime, including the explicit fourth-height prime example.

## Applicability and commercial boundary

Existence at a prime depending on height does not establish every height at one fixed prime or an efficient constructor.

## 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 cell counts, attaching maps and construction costs.

## 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).

[Finite Smith–Toda Complexes at Varying Primes](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Smith-Toda-Complexes-at-Varying-Primes-September-23-2026/paper.pdf).