# Spin-model continuum and mass reference calculator

Family 215: Canonical $`O(3)`$ continuum limit and exact $`O(4)`$ mass asymptotics. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Lattice-model researchers can compare O3 continuum and O4 leading transfer-gap asymptotics with numerical studies.

## Applicability and commercial boundary

Exact leading asymptotics and existence of a positive mass gap do not provide controlled finite-beta corrections or an arbitrary physical material model.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Extract the O4 coefficient into a reproducible reference curve and inspect quantitative convergence errors.

## 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 canonical massive continuum limit of the two-dimensional O(3) model](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf).