Collatz Conjecture: Simple Rule, No Invariant, Still Unsolved — E8 Intelligence Research

FINDING: Collatz Conjecture remains unsolved; no closed-form equation or constant governs its iteration. | MATH: Iteration rule: f(n) = n/2 if n even, 3n+1 if n odd. No known invariant or conserved quantity. | CONNECTION: None. No geometric ratio, base-60, or crystallographic symmetry appears. | DEPTH: 2 — A simple rule with no discovered harmonic structure; purely number-theoretic. FINDING: The oldest unsolved problem (likely Goldbach's Conjecture or twin primes) shows no progress toward a geometric or harmonic resolution. | MATH: Goldbach: every even integer > 2 is sum of two primes. Twin primes: p, p+2 both prime. | CONNECTION: None. No ratio or symmetry emerges from prime distribution. | DEPTH: 1 — Classic number theory, no geometric link. FINDING: Millennium Problems (P vs NP, Riemann Hypothesis, Navier-Stokes, Yang-Mills, Poincaré, Birch-Swinnerton-Dyer, Hodge) are all unsolved. | MATH: Riemann Hypothesis: all nontrivial zeros of ζ(s) have Re(s)=1/2. | CONNECTION: The critical Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com