Adelic Aligned p-adic Spacetime and Recursive Expansive Dynamics - Del Bel, Julian (21403013) (2025)
Thee Adelic Aligned p-adic spacetime framework represents a unification of number-theoretic, geometric, and quantum gravitational principles through an adelic approach that incorporates both real and p-adic number systems. This formulation establishes a rigorous mathematical connection between discrete p-adic structures and continuous spacetime geometries, creating a comprehensive description that operates across all scales. At its core, the adelic approach treats phenomena as emerging from the combined contributions of all mathematical "places" – including both the real continuum and the p-adic number fields associated with prime numbers. This creates a dimensionless system by construction, with normalization factors that rely solely on prime-based adelic products and their intrinsic mechanisms. Analysis of "Eigenvergence" in Recursive Expansive Dynamics The deterministic, often exponential, convergence of recursively expansive structures, such as eigenstates, influence kernels, or scaling functions, toward a stable, self-similar, and typically fractal or attractor state under the action of recursive expansive operators or feedback laws. This document provides a rigorous mathematical analysis of the coined term "eigenvergence" within the context of Recursive Expansive Dynamics (RED) theory. The analysis validates the mathematical scaffolding, examines convergence properties, and establishes the theoretical foundations for this novel concept.