The Hidden Integer-Scaling Link Across Mathematics' Greatest Unsolved Problems — E8 Intelligence Research

Abstract

FINDING: The corpus is a survey of unsolved problems (Collatz, Riemann Hypothesis, P vs NP, Navier-Stokes, Birch-Swinnerton-Dyer, etc.) — no single new result, but a meta-pattern emerges: all these problems share a hidden dependence on integer scaling and modular arithmetic. | MATH: Collatz: f(n)=n/2 if even, 3n+1 if odd — orbit structure unknown; Riemann: ζ(s)=0 ⇒ Re(s)=1/2; Navier-Stokes: existence/uniqueness of smooth solutions; Birch–Swinnerton-Dyer: rank(E(Q)) = ord_{s=1} L(E,s). Constants: 3, 1, 2, 1/2, 1. | CONNECTION: The Collatz map is a 2-adic dynamical system — its orbits encode base-2 (binary) scaling, which is the discrete analogue of base-60's sexagesimal cycles. The 3n+1 step introduces a 3:1 ratio — the same ratio that generates the 0.618/1.618 golden ratio via continued fraction [1;1,1,...] = φ. The Riemann critical line Re(s)=1/2 is the symmetry axis of the functional equation — a reflection symmetry (like a mirror plane in crystallography). The rank of elliptic curve Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com