Phenomenological Correspondence Between RTLI Coherence Geometry and General Relativity Across Astrophysical Systems

This technical report presents the first systematic comparison between Relational Thermodynamic Layered Index (RTLI) coherence geometry and General Relativity’s gravitational time-dilation structure across four independent astrophysical regimes: the Cosmic Microwave Background, SPARC galaxy rotation curves, the Radial Acceleration Relation, and SPTpol galaxy clusters.

Across all datasets, RTLI coherence angles follow a monotonic inverse hierarchy that parallels the depth of gravitational potential wells predicted by General Relativity, while preserving RTLI’s characteristic internal (≈20°) and boundary (≈40°) coherence angles. A time-flow parameter,

v_t^{\mathrm{RTLI}} = w_{\mathrm{geo}} \cos\theta,

is shown to track the ordering of GR time-dilation factors, suggesting that RTLI encodes gravitational structure in an information-geometric language complementary to classical metric curvature.

The correspondence is phenomenological, not replacement: RTLI does not modify or override GR. Instead, it reveals an underlying relational structure—observable in PCA coherence, cluster scaling relations, CMB dimensional flow (ρ = ±1.000), and the universal 73/27 information split in black holes—that appears consistent with how GR organizes physical systems.

We conclude that RTLI provides a unifying information-geometric lens across cosmology, galaxies, clusters, and black holes, and merits further development as a complementary framework for interpreting gravitational phenomena.