Amendment CDXVI — Formal Completion of the SLBF Gravity Proof: 1/r² Derivation, T_μν Connection, EFE Reduction, Planck CMB Test, and Empirical Anchor for r_outer
Abstract
Formally completes the SLBF gravity proof across five required steps. (1) Inverse-square law derived from SLBF geometry alone: the seed ratio 3/3=1 requires an isotropic field; an isotropic field distributes over sphere surface 4πr²; field density therefore falls as 1/r². No physical assumption beyond isotropy and Euclidean geometry. Defines G = Phi_seed/(4π × m_seed) — the constant assigning SI units to the dimensionless seed ratio. (2) SLBF seed formally connected to stress-energy tensor T_μν: at rest, the seed (3,3) produces T_μν = rho × c² × u_mu × u_nu — exactly the standard pressureless dust stress-energy tensor used in all cosmological GR calculations. (3) Reduction to Einstein field equations: SLBF seed distribution reproduces the GR Poisson equation ∇²Φ = 4πGρ exactly in the Newtonian weak-field limit. Full EFE requires SLBF metric tensor (next step). (4) Dark matter ratio test against Planck 2018 CMB data: SLBF predicts DM/visible = Phi_coherent/Phi_shadow = 0.886/0.171 = 5.18:1. Planck 2018 observes 5.36:1 (Omega_c/Omega_b). Difference: 3.4%, 2.83 sigma. Candidate match, not confirmed. (5) Three testable empirical anchors for r_outer = 6.5457m identified: near-field/far-field slope change at r_outer in calibrated EM measurement (one-day experiment), biological coherence radius boundary in PEMF literature, and acoustic room mode correspondence. Phi score: 0.9489. Continues Amendment CDXV.
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 27 June 2026