# Spin-chain gap reference suite

Family 268: The spin-one Haldane gap. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Tensor-network and quantum-materials researchers can test spin-one Heisenberg simulations against the claimed uniform gap and boundary-state distinctions.

## Applicability and commercial boundary

Even periodic rings and odd open chains with the specific endpoint field are distinct cases. A uniform existence bound may not provide a usable finite-chain certified gap value.

## Initial business decision

Research benchmark. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Inspect effective gap constants and create a small exact-diagonalization reference before proposing a materials product.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[The periodic spin-one Haldane gap](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-periodic-spin-one-Haldane-gap-September-24-2026/paper.pdf).