Entanglement Entropy: Unifying the Quantum Origins of Gravity, Mass, Time, and Cosmic Structure

File 1 — Entanglement Entropy: Unifying the Quantum Origins of Gravity, Mass, Time, and Cosmic Structure This paper introduces a single real scalar field, Sent(x)S_{\text{ent}}(x)Sent(x), that encodes local deficits of vacuum entanglement and whose gradients produce gravitational phenomena. Mass is identified with information via a universal conversion constant κm\kappa_mκm (kg/bit), with the electron providing the calibration point and operational anchor (one bit in the free-fermion baseline). On galactic scales, solutions of the entanglement–Poisson limit reproduce flat rotation curves and the Baryonic Tully–Fisher scaling, without invoking particulate dark matter. Black holes appear as maximal-deficit configurations, linking the field-theoretic picture to the Bekenstein–Hawking area law and clarifying the role of horizons as entanglement boundaries. The framework also sketches how temporal order and the “many pasts” structure of histories can emerge from coarse-grained entanglement flow, connecting information geometry to causal structure. Across these domains, a single constant κm\kappa_mκm ties particle masses to large-scale dynamics. File 2 — Supplement: Group Field / Tensor Underpinnings of the Entropic Scalar EFT This supplement develops microscopic underpinnings for the macroscopic SentS_{\text{ent}}Sent field using group-field/tensor-network constructions. It shows how spin-network–like degrees of freedom, coarse-grained over layers, yield an area-law capacity corrected by diffusive channel sharing, thereby motivating the universal +1/2+1/2+1/2 “sharing” exponent in the renormalization of κm\kappa_mκm. The coarse-graining flow explains how a continuum scalar description and its effective coupling κ=1/κm\kappa = 1/\kappa_mκ=1/κm emerge from discrete information carriers, while a geometric sharing factor gshareg_{\text{share}}gshare enters the normalization. The same microstructure clarifies why horizons extremize entanglement deficits and how macroscopic curvature responds to microscopic connectivity. Conceptually, the construction links “many pasts” to sums over entanglement graphs, with classical spacetimes arising as typical coarse-grained phases. The result is a concrete bridge from group-field/tensor microdynamics to the effective entanglement-scalar EFT used phenomenologically. File 3 — Derivations and Numerical Validations for the Entropic Scalar EFT This technical companion fixes the covariant action, equations of motion, and stress–energy for SentS_{\text{ent}}Sent, and establishes units and normalizations unambiguously. A top-down derivation of κm\kappa_mκm runs from the Planck scale to the electron’s Compton scale with total exponent 5/25/25/2 (area law +2+2+2 plus channel-sharing +1/2+1/2+1/2), producing a no-fit prediction that matches the electron calibration at the ∼0.1%\sim 0.1\%∼0.1% level. The nontrivial +1/2+1/2+1/2 sharing exponent is validated independently by outward-biased random-walk numerics and a layered random-tensor network. SentS_{\text{ent}}Sent is defined operationally as a vacuum-subtracted von Neumann entropy; a free Dirac excitation yields a universal 111-bit baseline, while interacting toy models (Gross–Neveu; mini-Yukawa) demonstrate that interaction-generated mass shifts track interaction-generated entanglement in the weak-coupling regime. In the static limit, solving the disk Green’s function gives ΔS(R)∝[1+ln⁡(R/Rd)]\Delta S(R) \propto [1+\ln(R/R_d)]ΔS(R)∝[1+ln(R/Rd)] and, via a linearized entropic force law, recovers the Baryonic Tully–Fisher relation with the correct slope and a physically set zero-point. Together, these results make the framework tightly constrained and reproducible from definition to prediction.