Coupling Entropy Difference Gravity: An Emergent Quantum-Gravity Framework Reconciling General Relativity and Quantum Mechanics, with Cosmological Applications

General relativity and quantum mechanics rest on incompatible pictures of spacetime, while the physical nature of dark matter, dark energy, and the 120-orders-of-magnitude discrepancy in the cosmological constant remains unexplained. This preprint proposes Coupling Entropy Difference Gravity (CEDG): gravity emerges macroscopically from the difference between the Bekenstein–Hawking holographic entropy ceiling of a spacetime region, S_BH = k_B·A/(4ℓ_P²), and the von Neumann entropy S_vN of the quantum degrees of freedom it contains. A dimensionless coupling factor η = ΔS/S_BH = 1 − S_vN/S_BH scales every gravitational source term. From four experimentally grounded axioms — holography, quantum unitarity, the laws of thermodynamics, and the equivalence principle — the framework derives, with no free parameters: the entropic force law F = η·GMm/R²; the modified field equation G_μν = η·(8πG/c⁴)T_μν, which reduces exactly to Einstein's equations at η → 1; automatic singularity avoidance (η → 0 as bulk entropy saturates the holographic bound); and parameter-free reproduction of the gravitational-to-strong-force hierarchy (~10⁻³⁸) for nucleons. Cosmological consequences follow without dark-matter particles or a cosmological constant: galaxy rotation-curve flatness from the entropy profile of baryonic reservoirs; gravity–baryon separation in merging clusters such as the Bullet Cluster via shock-generated entropy loss of the intracluster gas; vacuum-energy decoupling that suppresses the QFT vacuum contribution by the observed ~120 orders of magnitude; and late-time self-acceleration through an evolving η(z) in the Friedmann equation. Every result is explicitly labeled Theorem, Proposition (with its auxiliary hypothesis), or Conjecture, so the theory's empirical exposure is transparent to referees. Four exclusive falsifiable predictions are stated in analysis-ready form: (P1) linear correlation between rotation-curve flatness and host-galaxy baryonic entropy proxies (SDSS-MaNGA/DESI); (P2) linear lensing-weakening versus shock-entropy maps in merging clusters (Chandra/XMM archival data); (P3) supernova Hubble-diagram residuals tracking η(z) (Pantheon+/JWST); (P4) local-type primordial non-Gaussianity with f_NL = 2–5 (CMB-S4/DESI bispectra). This record contains the complete rewritten and formally reconstructed edition (v2) in three full parallel languages: English, Simplified Chinese (简体中文), and Japanese (日本語), each typeset with identical equations and numbering. Author: Yue Xiangrui (岳祥瑞), Independent Researcher. Original concept April 2026; this reconstruction adds the theorem–proof architecture and quantitative consistency checks. License: CC BY-NC-SA 4.0.