AdS Geometry as a Relational Antenna: A Geometric Diagnostic Framework for Holographic Coherence

Related work: De Jesus, Elias. (2026). Geometric Necessary Conditions for Holographic Correspondence: A Thales Framework Diagnostic for AdS/CFT Structure. Zenodo. https://doi.org/10.5281/zenodo.18394570 This work proposes a diagnostic reinterpretation of Anti–de Sitter (AdS) geometry within the Relational Thermodynamic Layered Index (RTLI) framework. Instead of viewing AdS spacetime solely as a fixed geometric background, the AdS–CFT system is described as a graded-index wave structure whose properties can be characterized by dimensionless relational ratios. These ratios do not introduce new dynamics but serve as organizing parameters for known holographic features. Three recurring RTLI ratios are examined: (i) an approximate 2:1 ratio between fast (quantum-dominated) and slow (geometry-dominated) propagation channels, (ii) an approximate 5:1 ratio between short and long characteristic timescales, and (iii) a characteristic angular separation of order $40^\circ$ that appears in wave-transmission and quasinormal-mode (QNM) phase structure. These quantities are interpreted as descriptive markers of how coherence and variance are distributed between boundary and bulk degrees of freedom. Within this perspective, quasinormal modes may be viewed as standing-wave solutions of an effective relational cavity, with their spacing, damping rates, and phase organization constrained by these dimensionless ratios. The framework yields qualitative, testable expectations for harmonic clustering, lifetime hierarchies, and angular distributions in the complex-frequency plane, without asserting exact numerical predictions. The purpose of this work is not to modify the AdS/CFT correspondence, but to provide a compact geometric and information-theoretic vocabulary for organizing existing results. The proposed interpretation is intended as a diagnostic aid, and its utility can be assessed through comparison with established numerical and analytical studies of AdS quasinormal modes.