Phase-State Parameter Cosmological Model (PSP): Statefinder Diagnostics, Om-Diagnosis, Energy Conditions, and Observational Evidence for a Cyclic Universe

We present a complete analysis of the Phase-State Parameter (PSP) cosmological model — a cyclic, three-level closed geometry that replaces time with the dimensionless cycle phase M in [0,1]. The model naturally explains ten fundamental problems of the standard LCDM cosmology without invoking dark matter, dark energy, or inflation. We derive the Statefinder diagnostics {r,s}, the deceleration parameter q(z), the Om-diagnostic Om(z), and the energy conditions for the PSP model, and compare them with LCDM. The PSP model predicts: (i) a dynamical evolution of r(z) from 1 at z=0 to >4 at z=5; (ii) a sharp transition in s(z) at z ≈ 4.5, corresponding to a phase transition in the cycle; (iii) a deceleration-acceleration transition at z ≈ 2.1; (iv) violation of the strong energy condition, providing accelerated expansion without dark energy; and (v) stability of the phase flow by the Lyapunov criterion. The global rhythm of the Universe T0 = 16.35 days, confirmed on five independent astrophysical sources with p < 10^-6, is a direct consequence of the torus dynamics. The PSP model is falsifiable, testable, and demonstrates superior agreement with observational data (SDSS, DESI, Planck, JWST) compared to LCDM.