MOND from 5D Geometry: Quadrature Addition and SPARC Validation

Coherent Gravity Theory (CGT) — Paper Series

Description

A six-paper series presenting Coherent Gravity Theory, a geometric framework unifying Modified Newtonian Dynamics (MOND), General Relativity, quantum mechanics, special relativity, dark energy, and the fermion mass spectrum from higher-dimensional geometry.

Core claim: Spacetime includes compact extra dimensions — a Hubble-scale circle (setting the MOND acceleration scale a_0 = cH_0/(2pi)) and an S^7/Z_33 orbifold (encoding particle physics). The framework derives rather than assumes:

• The MOND interpolating function nu(x) = sqrt(1 + 1/x)
• The galaxy cluster sqrt(3) enhancement from 7D Vlasov dispersion
• The cosmological constant Lambda = 2.03 H_0^2/c2
• The Koide formula K = 2/3 for charged leptons
• A Cabibbo-angle normalization template theta_C = 45 deg / sqrt(12) = 12.99 deg (model/program; full operator reduction remains open)

Empirical validation: SPARC rotation curves (175 galaxies), X-COP cluster data (7 clusters), wide binary EFE suppression, Bullet Cluster lensing offsets.

MOND from 5D Geometry (Version 4)

Derives the MOND interpolating function nu(x) = sqrt(1 + 1/x) from a fifth compact dimension. The observable acceleration is the quadrature norm of perpendicular components (4D Newtonian + W-sector), with a geometric-mean constitutive rule g_W^2 = a_local * a_0. Validated against 175 SPARC galaxies (lowest chi^2 among tested interpolating functions). Wide binaries validated with smooth EFE suppression model (predicted 1.364 vs observed 1.363). The acceleration scale a_0 = cH_0/(2pi) emerges from the W-circle circumference.