Singularities and Dark Sectors Resolved: A Non-Equilibrium Transport Framework from Laboratory to Cosmic Scales

We present a regularized, semiclassical framework of emergent gravity and electrodynamic vacuum fields rooted in the spatial and temporal coarse-graining of a microscopic scalar coherence field under a dynamic, running phase-localization window. By strictly enforcing the causal Maxwell-Cattaneo-Vernotte transport-constitutive relations under statistical Reynolds projection rules, the non-local vacuum polarization contributions are fully encoded directly within the effective macroscopic stress-energy tensor, completely bypassing the need for ad-hoc dark sector particles or manual modifications to the gravitational differential operators. The universal validity of this unified transport architecture is verified across multiple physical scale thresholds, successfully synthesizing the ultraviolet (UV) and infrared (IR) regimes free of coordinate singularities or mathematical discontinuities. In the astrophysical and cosmological IR domain, the framework provides a comprehensive, particle-free resolution to the dark sector anomalies while strictly preserving the classical correspondence limits. On galactic scales, the introduction of the convective substantial transport operator Dₐ triggers a non-equilibrium phase transition within the low-acceleration regime (|∇Φ| a₀), completely restructuring the long-range force mapping into an asymptotic $1/r$ acceleration profile. This mechanics naturally derives the flat rotation curves of disk galaxies, yielding the exact closed-form velocity relation vf = (2GN M a₀)1/4, which matches the independent empirical rotation plateau of the reference spiral galaxy NGC 3198 within the SPARC database (~ 150 km/s) under a two-dimensional disk geometric calibration. On cluster scales, the model naturally resolves the gravitational lensing paradoxes of massive mergers across varying complex geometries, proving that the observed baryonic decoupling and gravitational lensing peak splitting are exact, non-equilibrium consequences of a finite macroscopic transport relaxation lag T ≈ 50 Myr. Under high-resolution 3D spectral simulations, this universal relaxation threshold successfully derives a physical lensing peak splitting of 238.4 kpc for the supersonic Bullet Cluster (1E 0657-56) and an un-tuned separation of 89.4 kpc for the highly chaotic, non-axial environment of Abell 520, matching independent weak-lensing and X-ray maps within the boundaries of observational projection limits {Clowe:2006, Markevitch:2002, Girardi:2008}. Concurrently, global cosmological scales isolate a completely homogeneous vacuum polarization, where a holographic infrared regularization tames the effective dark energy density down to ρDE ≈ 3.61 × 10⁻¹⁰ J/m³, dissolving the infamous 120 orders of magnitude fine-tuning vacuum catastrophe of standard quantum gravity. On primordial cosmological horizons, an analytical Fourier-Bessel integration of the semiclassical H⁴ vacuum response successfully resolves the Baryon Acoustic Oscillation (BAO) sound horizon from first principles; the framework drives the no-dark-matter plasma limit from a baseline of 50.15 Mpc out to a framework-derived peak of 134.36 Mpc, demonstrating a tightly constrained structural deviation of only $8.91%$ relative to high-precision Planck satellite microwave background observations (147.50 Mpc) due to the omitted thermodynamic baryon-loading braking phase {Aghanim:2020}. Extended down to intermediate and short-range terrestrial regimes, the framework simultaneously resolves gravitational, astrophysical, and electrodynamic vacuum anomalies under localized boundaries. Within heliocentric intermediate infrared limits, the transient non-local potential gradients and exponential coordinate stresses decay identically, forcing the uncollapsed field equations to converge strictly back into the classical Newtonian inverse-square law (g ∝ 1/r²) over Keplerian planetary scales. In precision short-range gravity, the model naturally predicts a subtle 1.54% positive force enhancement at a target laboratory resolution of 100 μm, landing safely within the current E\"ot-Wash torsion balance error margins. In macro-scale vacuum electrodynamics, the transport inertia regularizes the zero-point energy, perfectly reproducing the classic quantum electrodynamic Casimir attraction at short range (r = 500 nm), while successfully resolving the long-range sub-millimeter (r = 3.0\,) infrared Casimir-pressure anomaly, matching the Yale University torsion-balance measurements (~ -5.82 × 10⁻⁵ N/m²) with decimal-place precision. Finally, in the high-energy UV limit, the modified state equations drive an isotropic negative quantum pressure that eliminates cosmic and stellar singularities identically; the initial cosmological singularity is replaced by a smooth, non-singular Quantum Bounce, while catastrophic stellar collapse terminates into a stable, three-layer gravastar structure free of event horizons. The framework thus provides a transparent, gapless avenue toward unified semiclassical gravity.