‑Matter Degradation, Dark‑Energy Phase‑Transition and Equation‑of‑State Crossing: Nonlinear Phase‑Transition Model Based on Multiplicative Structure of Unified‑Field Formula and Validation against DESI 2025

Feng Dejian Independent Researcher, Founder of the Unified Cosmic Matter‑Energy Theory ORCID: 0009‑0000‑5793‑9666 Web of Science ResearcherID: PQA‑8034‑2026 November, 2026 Abstract Based on Feng Dejian’s unified‑field formula Φ = (εₓ · v² · t_int · T) / ε and its underlying postulate system, this work constructs a nonlinear phase‑transition model describing dark‑matter degrading into dark‑energy. The core result is that the multiplicative algebraic structure of the unified‑field formula naturally yields a power‑law decay solution Φ(s)=Φ₂(1‑s)^N. Far from the degradation‑driven dynamical‑failure boundary one obtains a microscopic decay index. Near this boundary, divergence of the unit‑scale intrinsic characteristic action time introduces singular dynamical corrections, yielding a cosmological phenomenological effective index N_eff≈ 2.3. We adopt published steady‑state scaling relations (v∝√T, ε∝T², εₓ·t_int=h) together with their breaking under non‑steady‑state degradation, and perform background evolutionary computations within the full FLRW interacting dark‑energy (IDE) framework. The derived model outputs are w₀≈‑0.752 and wₐ≈‑0.78, which lie within the 1σ confidence interval of the joint DESI DR2 + CMB + DES‑Y5 observational analysis. Two physical features that cannot be produced by the standard linear CPL parametrization are predicted: a dark‑energy‑density peak f(z) near z≈0.5, and non‑monotonic oscillatory behaviour of w(z) around −1. Both features receive tentative observational hints from DESI non‑parametric reconstruction. The observed crossing of w across −1 is interpreted as an apparent observational consequence of the breakdown of local unit‑scale dynamical laws close to the degradation boundary, rather than an intrinsic genuine phantom phase of dark‑energy. A revised nine‑item self‑consistency assessment and five strictly falsifiable physical predictions are presented. Supplementary material included in this manuscript contains a complete MCMC simulation protocol, stiff ODE demonstration code, dimensional‑consistency checklist, degrees‑of‑freedom accounting, Bayesian‑complexity discussion, and layered falsification criteria. Keywords: unified‑field formula; dark‑matter degradation; dark‑energy phase transition; equation‑of‑state crossing; DESI 2025; nonlinear phase transition; local dynamical‑failure boundary