Finite Molecular Speeds and Rotational Relaxation: A Scleronomic Phase-Space Research Program for the Limits of Continuum Fluid Models

Abstract

This research preprint invites collaboration on the relationship between finite molecular dynamics, rotational relaxation, and the limits of continuum fluid models. It proves explicit translational-speed, angular-speed, and interacting-site-separation bounds for a fixed finite rigid-molecule Hamiltonian with Lennard–Jones site interactions. A forcing extension uses an integrable power-control envelope; positive barycentric velocity averages inherit the constituent speed bound. These results are not uniform continuum-limit estimates and do not solve the Navier–Stokes regularity problem. The accompanying calculation contains 4,096 thermal binary scattering encounters for a specified asymmetric three-site rotor. A three-mode dilute collision closure gives a mechanical-spin/stress integral-relaxation-time ratio of 1.793, with an approximate 95% sampling interval of 1.587–2.012 from 10,000 bootstrap resamples. The package includes conservation and numerical sensitivity checks, raw incoming states and encounter summaries, source code, and a central-force control. Sampling intervals do not cover closure or material-calibration uncertainty. The paper retains Cl(3,3) with signature (+++---) as a proposed scleronomic representation, supplies compatible periodic lifts and an exact conservative memory construction, and states the missing physical and analytic bridges. Conditional scale diagnostics distinguish the physical applicability of a molecular continuum approximation from mathematical claims about an idealized PDE. A source-level formalization audit explains why the inspected conditional Lean result does not establish the claimed smooth initial-value problem. The paper is open about AI assistance and unperformed work. It seeks independent replication, mathematical corrections, a controlled interaction-anisotropy sweep, fuller kinetic closures, physical calibration, and formalization repairs. No completed derivation from Cl(3,3), laboratory validation, new Lean build, or independently certified Clay solution is claimed.