Gravity and QEP–Ω: Mass, Gravity and Branchwise Quantum Equivalence

This fifth article in the Unified Entropic Field Theory (UEFT–Ω) series develops the gravitational foundations of entropy-dependent mass generation and formulates the Quantum Equivalence Principle (QEP–Ω) in terms of branchwise inertial and gravitational mass operators. Building on the Yang–Mills, Higgs, neutrino and unified mass structures developed in Articles I–IV, the investigation establishes a common mathematical treatment of sectoral mass, total stress–energy, spacetime curvature and quantum-state-dependent gravitational response. The formulation employs the probabilistic entropy field (S(x,t)) within an entropy-dependent gravitational effective action containing nonminimal curvature couplings and higher-derivative interactions. The principal contributions include: Derivation of metric and entropy field equations, stress–energy conservation, covariant Ward identities and gravitational backreaction. Construction of the coupled graviton–entropy–gauge Hessian and calculation of one-loop ultraviolet contributions, including nonminimal fourth-order operators, curved-background effects and gauge-field mixing. Formulation and mathematical analysis of QEP–Ω through branch-restricted inertial and gravitational mass operators, universality measures, operator-domain conditions and coherent quantum-state responses. Derivation of the relationship between gauge-invariant Yang–Mills spectral excitations, correlator thresholds, vacuum-subtracted gravitational responses and entropy-regulator stability. Development of operational acceleration and interferometric observables, including numerical sensitivity analysis and comparison with published atom-interferometry measurements. The article connects entropy-dependent particle mass generation to gravitational sourcing and develops explicit mathematical conditions for the equality of gravitational and inertial responses across admissible quantum branches. Its results integrate the gravitational, spectral, variational and quantum-equivalence constructions within a common effective-field-theoretic framework. Series context: Article V completes the five-part UEFT–Ω investigation developed during 16 October 2025–9 March 2026. Related publications: Article I — Yang–Mills: Entropic Gauge Spectra and Mass-Gap Structure. DOI: 10.5281/zenodo.23985878 Article II — Higgs: Entropy-Dependent Scalar Potential, Mass and Vacuum Structure. DOI: 10.5281/zenodo.24020439 Article III — Neutrinos: Entropic Mass Matrices, Hierarchies and Mixing. DOI: 10.5281/zenodo.24034488 Article IV — Unified Mass: Sectoral Entropy–Curvature Architecture. DOI: 10.5281/zenodo.24094559 © 2026 Nazim Ari. All rights reserved.