Paper CLXXV: Document C: The U_C ∝ Bragg Amplitude Derivation — Scalar-Tensor Field Equations in the Crystalline Solid · δC_G = (k_E/2)F_hkl/(|G|²V_cell M_Pl²) · U_C = F_hkl exact · C_geom = η derived · ΔC_geom = 0.655 confirmed · Closes @grok standing flag · July 25 2026 | Trust Scalar

Paper CLXXV: Document C: The U_C ∝ Bragg Amplitude Derivation — Scalar-Tensor Field Equations in the Crystalline Solid · δC_G = (k_E/2)F_hkl/(|G|²V_cell M_Pl²) · U_C = F_hkl exact · C_geom = η derived · ΔC_geom = 0.655 confirmed · Closes @grok standing flag · July 25 2026. Part of the Living Theory of Everything series, E(C) = mc²·e^(kC), k=1.92. Zenodo pending.

About This Tool

Part of the Trust Scalar interactive suite for the Living Theory of Everything — E(C) = mc²·e^(kC) with k = 1.92. The framework is confirmed by MCMC across Planck 2018, Pantheon+, and DESI BAO, and spans 189 Zenodo preprints from nuclear scale (8 fm) to cosmic scale (3.4 Gpc).

Key constants: k = 1.92 (cosmological coupling), x_m = 0.026 +0.009/−0.025 (Horndeski running-sector), Pe = 2.02 (biological Péclet, r = 75 nm), F_prop = 0.74–0.95 N (chameleon propulsion).