Triadic Field Ontology: A Unitary, Relational Field Theory of Emergent Matter, Timeless Wheeler-DeWitt Geometry, and Decentralized Entropy Self-Regulation

The Triadic Field Ontology resolves the Ex-Nihilo paradox ($0 = 0$) and central physical curvature singularities ($\mathcal{K} \to \infty$) through a continuous, stretched quantum field geometry. Rather than creating matter ex nihilo, the framework establishes an elastic scalar field $\Phi$ with a non-trivial vacuum expectation value $\langle 0 | \Phi | 0 \rangle \neq 0$ ($0 \neq 0$, $90^\circ$ latency $\frac{1}{4}\pi$). Under critical energy density, transversal waves buckle into a $270^\circ$ phase arrest ($\frac{3}{4}\pi$) and condense into 3D standing soliton waves ($0 \neq 1$), generating rest mass $m = h\nu/c^2$ and charge $q$. Quantum-geometric protective shields based on $W^{2,2}$-Sobolev regularity limits ($\mathcal{B}_Q$) prevent physical singularities: black holes are regularized into geodetically complete Planck stars, while the Big Bang paradox transitions into a past-complete bounce. Internal relational time $\tau$ emerges via Page-Wootters projection relative to local quantum reference frames ($\mathrm{QRF}_{\text{bio}}$). Incorporating recent empirical data from DESI 2024, lattice QCD, JWST $z > 10$ galaxy abundances, and B-mode polarization bounds ($r < 0.001$), this paper presents a unified, testable, and strictly falsifiable framework for quantum gravity and cosmology.