Entropic Scalar EFT: From Entanglement Microstructure to Gravity and Cosmic Structure

We propose that the vacuum is not an inert stage but a finite-capacity entanglement substrate, and that matter is the localized depletion of that capacity. On this view, inertial mass is the entanglement content of a defect, gravity is the long-wavelength relaxation of the surrounding substrate, and the galactic excess usually attributed to dark matter is the extended reach of that relaxation rather than a separate particulate component.

The main result is a closed conditional derivation of the static weak-field sector. A minimal tetrahedral boundary ensemble, together with a one-bit fermionic defect anchor,
turns the ultraviolet problem into a finite counting problem. Admissibility weighting, edge transport, finite-loop dressing, continuum matching, and source projection then determine the coefficients of a scalar entanglement EFT. In the resulting weak-field limit, Newtonian gravity, the galactic acceleration scale, the radial-acceleration relation, and leading no-slip lensing structure arise from one coefficient chain, without per-galaxy interpolation functions or phenomenological tuning.

The same construction also gives a non-gravitational route to the substrate length scale by treating the electron as the lightest elementary defect. The induced gravitational scale agrees with the observed Newton constant to about one percent, providing a quantitative cross-check on the matched weak-field normalization. The proposal is therefore not simply a scalar addition to general relativity: the metric field and the entanglement scalar are two continuum expressions of the same finite-capacity medium.

Time-dependent transport, cosmology, strong-field black-hole physics, and the Many-Pasts interpretation are developed as further consequences of this ontology. These sectors are not presented with equal closure. The static weak-field derivation is the central completed result; the cosmological, strong-field, and microscopic boundary sectors remain conditional or frontier completions where explicitly stated.