# Triangular billiard mixing reference

Family 150: Weak mixing of triangular billiards with an irrational angle. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Dynamics researchers can compare irrational-angle triangular billiards to the claimed weak-mixing result.

## Applicability and commercial boundary

Exact irrationality, weak mixing and no stated rate do not supply practical decorrelation times or guarantee finite trajectory statistics.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Record the angle representation and distinguish weak mixing from a quantitative simulation stopping rule.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Weak mixing of triangular billiards with an irrational angle](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Weak-mixing-of-triangular-billiards-with-an-irrational-angle-October-5-2026/weak-mixing-triangular-billiards.pdf).