A (p,q)-adic Generalization of the Collatz Conjecture — E8 Intelligence Research

Abstract

FINDING: Collatz conjecture generalized to (p,q)-adic analysis, revealing a framework for studying iterative dynamics over mixed-radix number systems. | MATH: The standard Collatz map: \( T(n) = n/2 \) if \( n \) even, \( T(n) = 3n+1 \) if \( n \) odd. Generalized to (p,q)-adic: \( T_{p,q}(x) = x/p \) if \( x \equiv 0 \mod p \), else \( T_{p,q}(x) = qx + 1 \). Key constants: \( p=2, q=3 \) for classical case. No new constants or ratios reported in the provided summaries. | CONNECTION: No explicit geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, or crystallographic symmetries) found in the video descriptions. The (p,q)-adic approach may implicitly involve lattice structures in p-adic spaces, but this is not stated. | DEPTH: 6 — The generalization to (p,q)-adic analysis is a significant mathematical extension, potentially linking number theory, dynamical systems, and p-adic geometry, but the provided summaries lack specific equations, constants, or geometric connections. Th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com