# Molecular-to-kinetic simulation validity planner

Family 364: Kinetic limits and fluctuations over the Boltzmann lifespan. First source-informed review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Molecular and kinetic researchers can compare marginal statistics and fluctuation observations across a regular Boltzmann lifespan and record admissible potential and initial-density conditions.

## Applicability and commercial boundary

The Boltzmann–Grad statement is a limiting result on intervals with a uniform Gaussian regularity bound, not an explicit finite-particle error budget. The fluctuation result uses exact microscopic-expectation centering and finite-dimensional distribution convergence, not automatically a uniform finite-sample confidence band.

## Initial business decision

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

## Next verification action

Inspect convergence rates, effective constants and centering cost before proposing an uncertainty-calibration package.

## 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

- [The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf)
- [Hard-sphere fluctuations on the regular Boltzmann lifespan](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026/paper.pdf)