The Prime-Prime Lattice (PPL) and Non-Equilibrium Open Wave Dynamics: Part II: The Kuramoto Model as the Generative Foundation of Fields, Macroscopic Spacetime Phase Transitions, and the Observational Validation of the 4/3 Critical Ratio via GW170817

Abstract

Building upon the mathematical foundation established in Part I, we reformulate non-linear synchronization dynamics and general relativity within the Prime-Prime Lattice (PPL) space. We establish the renormalized, additive-free Kuramoto model as the absolute ontology and generative foundation for all physical ``fields.'' Instead of postulating fields as primary entities, we demonstrate that all field vibrations emerge naturally as the collective phase-locking envelopes of infinite-dimensional prime oscillators, structurally tuned by Minimal-Step Prime Pairs (MSPP) acting as a non-equilibrium open system. By treating the spacetime metric not as a passive continuous fabric but as the spatial gradient of this collective Kuramoto coherence, we extend the classical framework of Einstein's general relativity. We resolve classical metric singularities by reforming the line element multiplicatively, exposing how the classical relativistic thermodynamic limit of $3/4$ undergoes a multiplicative inversion to clamp at the stable unitary ratio of $4/3$. In this Version 2 revision, we expand our empirical validation beyond the initial GW170817 event to an out-of-sample dataset of $N=420$ gravitational wave events from the LIGO/Virgo/KAGRA O4 observation run. Utilizing the deterministic Universal Jacobi Mapping $\mathcal{J}$ to extract sub-harmonic periods $T_0$, we demonstrate that the PPL model converges to the theoretical infrastructure floor $C=0.1454\text{ s}$ with a log-space coefficient of determination $R^2=0.9843$ and a decisive log Bayes factor $\ln B_{\mathrm{PPL/GR}}=32.08$, definitively ruling out overfitting and classical general relativistic divergence.