OpenAI · 364-02 · 2026-09-23 · Partial differential equations
Hard-sphere fluctuations on the regular Boltzmann lifespan
preprints/Hard-sphere-fluctuations-on-the-regular-Boltzmann-lifespan-September-23-2026
Family 364. Kinetic limits and fluctuations over the Boltzmann lifespan.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Derives the nonlinear Boltzmann equation from three-dimensional grand-canonical Newtonian gases throughout every regular kinetic interval with uniform Gaussian decay. Stable finite-range radial potentials may have attractive wells and a singular repulsive core; initial pair exclusion and spatially summable Gaussian density and gradient bounds are assumed. A companion gives finite-dimensional hard-sphere Gaussian fluctuations, centered at the exact microscopic expectation and governed by the linear fluctuating Boltzmann equation.
We prove a finite-dimensional central limit theorem away from equilibrium for a deterministic grand-canonical hard-sphere gas in three dimensions. The initial probability density is smooth, with spatially summable Gaussian velocity bounds on the density and its spatial gradient. The limit holds on every finite interval on which the classical Boltzmann solution has uniform Gaussian velocity decay. The empirical measure is centered by its exact microscopic expectation. Its fluctuations converge to the Gaussian solution of the linear fluctuating Boltzmann equation.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.