MDFR — Vol. 1 Extract — Dynamic Model of Phase Rigidity: prime number distribution as a conservative dynamical system

The Dynamic Model of Phase Rigidity (MDFR) treats the field of integers as a conservative physical system with intrinsic time τ = ln(N), measurable thermodynamic properties, and an internal geometric structure that generates constants without calibration. This paper is an operational extract of Volume 1 (~100 pages, deposited PATAMU/SIAE November 2025). It presents seven certified results: — A deterministic prime classifier (L1) with zero observed errors on 10¹¹ integers, including all Carmichael numbers tested (30/30) — which fool probabilistic tests such as Miller-Rabin. — A second independent classifier (L2) with zero errors, structurally independent of π(N) and Li(N). — A distributional classifier (L3) with Accuracy = 1.0 on 116 numbers, superior to GUE as reference model. — Four stable constants (β = 2.0, H = 0.723, α = 1.703, H×α = 1.2384) observed simultaneously within 1% on 10¹¹ consecutive integers. — An antisymmetric Z/2Z charge structure (T11) with random probability 3.7×10⁻⁹. — A conservative Hamiltonian system with τ-dilation formally analogous to gravitational time dilation. — Statistical robustness: Z = 99.3 standard deviations from randomness (MS-03, 5000 bootstrap iterations). All results are independently replicable on SHA256-verified raw CSV files. The generative mechanism is protected as a trade secret; this paper is evaluated exclusively on its operational outputs. The model identifies Stasis = 0.5 as a geometric fixed point coinciding structurally with Re(s) = 1/2 of the Riemann Hypothesis — an emergent coincidence, not a proof. Volume 2 in preparation: formal N↔Zeta connection, L4 classifier, thermodynamic applications. Industrial directions: cryptography, energy optimisation, radio astronomy, particle physics. Priority deposit: PATAMU/SIAE 2025/02381 (deposits 274538, 275405, 277912 — November 2025).ORCID: 0009-0007-3577-9850 10.5281/zenodo.19797180