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

This preprint presents an updated English working version of the galactic Letter on the Geometric Relay Theory (GRT), developed as a Kaluza-Klein reduction of Minazzoli’s Entangled Relativity. The manuscript reports six levels of empirical evidence for structural amplification of gravity in disk galaxies under a fully frozen pipeline on a canonical 86-galaxy SPARC ring. Levels 1-4 recover the core signal already identified in earlier versions: (1) global BTFR scatter reduction, (2) intra-galaxy RAR survival under placebo permutation, (3) galaxy-by-galaxy rotation-curve correlations, and (4) universality of the structural coefficient b across sample cuts. Level 5 adds a referee-oriented HSB/LSB robustness test showing that the global gain is carried predominantly by HSB galaxies, while the LSB side remains weak and statistically fragile. Level 6 introduces a gas-weighted structural correction Q1, eff motivated by the ER-EMd correspondence, yielding an additional positive correction on the frozen pipeline and full numerical reproducibility across two independent AI-assisted implementations. This version also includes a short theoretical subsection on the characteristic relay timescale at the HI radius. In a referee-safe formulation, the result is presented as a structural consistency check rather than a closed numerical prediction: with canonical KK normalization and the natural choice |C| ~ MPl^-2, the slow relay mode acquires a characteristic frequency of order sqrt (G rhob), placing its period in the observed galactic orbital range without the need for an additional exotic scale. The purpose of this upload is to archive the updated English version of the manuscript with the six-level empirical structure, the gas-weighted correction, the HSB/LSB robustness analysis, and the cautious relay-timescale consistency subsection in a form suitable for submission, review, and citation.