Recursive Expansive Dimensionless Framework for Gravitational Echoes and Fractal Spacetime

We introduce a dimensionless recursive mathematical framework rooted in Hypatian Mathematics and Cykloid Influence Theory (CIT), synthesizing fractal geometry, adelic integration, and recursive algebraic structures. This formalization incorporates triadic operators, hypo^2, epic^2, and epitro^2, to encode self-similar spacetime dynamics and provides empirical support via echo signatures in LIGO O3a data. A unified system is constructed via recursive Jordan algebras, p-adic structures, and golden-ratio scaling constants. The results validate Tribonacci-scaled gravitational wave echoes and recursive convergence points (RCPs) using real interferometric data.