Recursive-Dimensional Mathematics From Prime Fractals to Hyperspace Geometry

This work bridges ancient mathematical insights, modern adelic quantum arithmetic, and hyperdimensional recursive dynamics to a framework for number theory, spacetime geometry, and quantum physics. By revisiting the Rhind Papyrus and Diophantus’ contributions, this scaffolding uncovers proto-quantum arithmetic systems embedded in ancient Egyptian fraction decompositions and algebraic methods. These historical constructs are reinterpreted through adelic frameworks that unify real and and p-Adic geometries, revealing deep connections between additive decompositions, multiplicative structures, and normalization principles akin to quantum mechanics. Designed to explore the oscillatory and temporal behaviors of physical systems through recursive geometry and cyclic field structures. Grounded in the interplay of fundamental constants such as π and ϕ, RDM proposes a self-referential model of time and space evolution where dimensional transitions are encoded through golden-ratio-based scaling and hybrid harmonic transformations. By integrating datasets derived from gravitational wave frequencies, recursive time intervals, and harmonic eccentricities, the theory develops a hierarchical scheme of nested fields that modulate physical behavior across scales. Central to the framework is the “cykloid influence” hypothesis, positing that spacetime oscillations are governed by recursive curvature events that influence localized energy fields. The paper outlines recursive harmonic tables, proposes scaling laws linking temporal and spatial observables, and introduces new visualizations of singularity-driven field behavior. This approach aspires to unify aspects of field dynamics, geometric recursion, and cosmological scaling into a cohesive mathematical and physical narrative.