Unified Quantum Gravity (UNI–QG) via Vinay's Energy–Acceleration Law: Finite-Identity Quantum Closure with Reproducible Tests from Quantum to Cosmology

I present Unified Quantum Gravity (UNI–QG) formulated through Vinay’s Energy–Acceleration Law, a finite-identity kernel in which dynamics arise from gradients of a causal-step density field along an invariant causal sequence. The framework assumes that physical identity is finite and conserved, yielding discrete causal updates with a well-defined continuum limit. At the quantum level, closure of finite causal loops enforces an integer action condition, providing a physical origin for quantization and discrete quantum transitions. Standard quantum mechanics is recovered in the appropriate limit, while quantum “jumps” are interpreted as reallocations of finite causal identity between allowed causal loops, without introducing additional quantum postulates or new particle species. At the level of fundamental interactions, the same finite-identity kernel reproduces known forces as limiting or band-structured regimes of a single dynamical law. In the smooth-gradient regime it recovers Newtonian gravity and Einstein general relativity; in the corresponding transverse shear regime it recovers the Lorentz-covariant Maxwell equations and Lorentz symmetry; and in higher-density resequencing and locking regimes it reproduces phenomenology associated with weak and strong interaction regimes, without introducing separate force fields or additional free constants. In gravity and compact objects, the theory yields an Energy–Acceleration tensor that reproduces general-relativistic dynamics in the weak-field regime and replaces classical singularities with finite-core structures. This leads to testable consequences for black-hole interiors, gravitational-wave ringdown, and horizon-scale observables, while remaining consistent with current constraints. On Solar-System scales, the framework reduces smoothly to Newtonian and post-Newtonian dynamics, predicting only extremely small deviations that remain well below present experimental bounds. In cosmology, the kernel generates a predictive expansion history that advances the baryon-drag epoch and reduces the sound horizon (typically zdrag ⁣∼ ⁣1650z_{\mathrm{drag}}\!\sim\!1650zdrag∼1650, rd ⁣∼ ⁣137 Mpcr_d\!\sim\!137\,\mathrm{Mpc}rd∼137Mpc), enabling consistency between late-time distance probes and BAO-scale constraints through invariant combinations such as X≡H0rd/cX \equiv H_0 r_d / cX≡H0rd/c. The model is tested against SN Ia, BAO, Lyα\alphaα, and cosmic-chronometer data. On galactic scales, the identical fixed kernel is applied unchanged to galaxy rotation curves, reproducing rotation-curve systematics and the radial-acceleration relation without invoking dark-matter halos or galaxy-level tuning. The framework is further tested against early-galaxy UV luminosity functions, showing agreement with current JWST observations and predicting a faint-end luminosity floor without additional astrophysical parameters. Pre-registered, Occam-penalized predictive tests. Earlier pre-registered formulations of the framework were explicitly challenged on grounds of model flexibility and Occam penalties. In response, the results presented here adopt pre-registered, Occam-penalized, no-retuning tests: all structural constants are fixed in advance, and the same kernel is applied unchanged across quantum, gravitational, cosmological, galactic, and early-galaxy regimes. No sector-specific tuning or auxiliary components (such as dark-matter halos or ad-hoc early-time modifiers) are introduced. Falsifiability. The framework admits a single locked falsification criterion: if late-time distance data robustly constrain the invariant combination X≡H0rd/cX \equiv H_0 r_d / cX≡H0rd/c outside the predicted interval under standard systematic treatments, the causal finite-identity branch tested here is ruled out. Additional falsifiers include failure to reproduce the galaxy radial-acceleration relation without dark matter or the absence of the predicted UVLF faint-end turnover. This Zenodo release includes the main paper, supplementary material, and replication packages (software, instructions, and reference outputs) enabling independent reproduction of the cosmology, galaxy-rotation, and UVLF analyses.