# Billiard integrability assumption audit

Family 147: The near-boundary Birkhoff conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometry researchers can distinguish an ellipse classification under a full invariant grazing foliation from a few observed caustics.

## Applicability and commercial boundary

A smooth positive-curvature convex boundary and complete annulus foliation are strong continuum conditions. Finite trajectories do not certify them or determine manufacturing tolerances.

## 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

Extract a stable numerical diagnostic only after a quantitative theorem is available.

## 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).

[Continuous Phase Foliations Create Analytic Caustic Collars](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Continuous-Phase-Foliations-Create-Analytic-Caustic-Collars-September-24-2026/paper.pdf).