Spacetime-Quantum Unified-Field Theory: Axiomatic Foundation, Emergent Gravity, Planck-Scale Corrections, and Consistency with the Standard Model

Spacetime-quantum unified-field theory, built on six axioms: discrete spacetime structure, spacetime-quantum coherence, energy–spacetime coupling, Lorentz covariance, hierarchical symmetry breaking, and gravity emergence. Starting strictly from these axioms, the manuscript constructs the global spacetime-quantum field and derives the master wave equation. The Einstein field equation is recovered in the macroscopic coherent limit, and a Planck-scale quantum curvature correction is introduced for quantum gravity. The standard model gauge structure SU(3)×SU(2)×U(1), including the electroweak Higgs mechanism, is retained as the established input of the theory, and its consistency with the spacetime-quantum substrate is demonstrated rather than re-derived. Gravity is shown to be a global emergent effect from collective spacetime-quanta density-gradient deformation. The strong-interaction sector is formulated with a confining (Cornell-type) potential, correcting an earlier exponentially screened form that describes color screening. One-loop heat-kernel coefficients are obtained, and falsifiable predictions for primordial gravitational waves and black-hole microstructure (logarithmic corrections to Bekenstein–Hawking entropy) are stated. This Version 3 is the corrected authoritative English manuscript, prepared for submission to Physical Review D.