# Kinetic solution selection and conservation audit

Family 363: Nonuniqueness with local conservation for the hard-sphere Boltzmann equation. First source-informed review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Kinetic solver teams can record the solution class and selection principle instead of treating conservation and entropy checks as sufficient evidence of a unique trajectory.

## Applicability and commercial boundary

The latest hard-sphere periodic construction has two solutions with common initial data and exact local conservation. The selected formal scope covers the older renormalized nonuniqueness result; the newer local conservation refinements are outside that scope. A nonunique weak class does not show every smooth or discretized problem is nonunique.

## Initial business decision

Prototype evidence workflow. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.

## Next verification action

Define an export schema for solution class, initial data, conservation checks, entropy conditions and solver selection; use a bounded example without claiming to reproduce the full construction.

## Evidence scope

The catalog statement and main-paper abstract or introductory theorem passages were individually reviewed. Available family-level scope documents were inspected, with attention to version differences and exclusions. This is a first application triage, not a full proof audit or independent Lean verification. Family 376 has nine paper abstracts inspected; selected scopes are not assumed to cover all nine papers in full. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Pinned sources

- [Nonuniqueness with local conservation for the hard-sphere Boltzmann equation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-with-local-conservation-for-the-hard-sphere-Boltzmann-equation-October-5-2026/paper.pdf)
- [Nonuniqueness for the periodic hard-sphere Boltzmann equation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf)
- [Selected formal scope](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/363.md)