Monograph I: Bouncing Kinetics and DESI 2024 Dark Energy Audit — A Field-Ontological Resolution of Cosmological Singularities

Monograph I: Cosmology & Astrophysics Description Bouncing Kinetics and DESI 2024 Dark Energy Audit: A Field-Ontological Resolution of Cosmological Singularities This monograph analytically derives a singularity-free, geodesically complete cosmic bounce via Sobolev $W^{2,2}$ regularisation, presenting an exact audit matching DESI 2024 dark energy parameters ($w_0=-0.92, w_a=-0.38$) and early JWST galaxies ($z>10$) with a strict falsification threshold ($r < 0.001$). Problem Statement This monograph presents a rigorous field-ontological resolution to the fundamental mathematical breakdown of Big Bang cosmology at the curvature singularity. Mathematical Methodology By embedding spacetime geometry into a continuous, elastic vacuum potential field bounded by a Sobolev $W^{2,2}$ capacity constraint $\|\Phi\|_{W^{2,2}} \le \mathcal{B}_Q < \infty$, classical curvature singularities are naturally regularised into a smooth, past-complete cosmic bounce at critical density $\rho_c \approx 0.41 \rho_P$. Key Results & Empirical Audit Geodesic Completeness: Elimination of cosmological singularities without requiring speculative multiverse paradigms. DESI 2024 Dark Energy Audit: The relaxation kinetics of the elastic vacuum medium provide an exact analytical fit to recent DESI 2024 DR1 dark energy measurements ($w_0 = -0.92, w_a = -0.38$). JWST Galaxy Overabundance: Preserved topological wave knots explain the mature galaxy overabundance discovered by the James Webb Space Telescope at $z > 10$. Popperian Falsification Threshold: Establishes a strict upper limit for primordial gravitational wave tensor-to-scalar ratios at $r < 0.001$. Relation to Master Monograph This specialist monograph constitutes an integral module of the Triadic Field Ontology (Master DOI: 10.5281/zenodo.23374765).