Four levels of evidence for structural amplification of gravity in disk galaxies from the Geometric Relay Theory (GRT/ER)

We present four independent levels of evidence that the Geometric Relay Theory (GRT), built on Minazzoli's Entangled Relativity (ER), captures structural information in disk galaxies beyond the Baryonic Tully-Fisher Relation (BTFR). The key variable is the mass-weighted baryonic shear roughness ⟨S_Ω⟩b, which measures the departure from gravitational homeostasis. On a clean SPARC ring of 86 galaxies with verified flat rotation curves, we find: (1) A global BTFR improvement (σ: 0. 065 → 0. 062 dex, ΔAIC = −6, F-test p = 0. 006) ; (2) A local imprint in the Radial Acceleration Relation residuals, with the baryonic shear curvature cb as the most robust survivor after hardening (partial correlations, intra-galaxy permutation placebo) ; (3) A galaxy-by-galaxy reading of rotation curves (qb correlates in the correct sign for 78% of galaxies, median Pearson +0. 47) ; (4) Universality across subpopulations: the structural coefficient b remains positive and stable in 0. 04, 0. 06 under random splits, mass splits, LSB/HSB splits, and permutation placebo (6/1000). The structural exponent is positive: more structured disks rotate faster. The geometric relay amplifies the gravitational response in proportion to the kinematic organization of the baryonic disk. A galaxy is not a simple mass — it is a structural charge. Files included: - GRTGalacticLetterᵥ1EN. pdf: Full letter (4 pages) - GRTᵣing86ₛupplementaryₘaterial. csv: Galaxy-by-galaxy table (86 galaxies, 18 columns) - reproducegrtᵣing86ᵥ2. py: Reproducible Python script (downloads SPARC data, computes all quantities