Collatz Conjecture Remains Unproven; Videos Cover Known Unsolved Problems — E8 Intelligence Research

FINDING: The Collatz Conjecture (3n+1) remains unproven; all other listed videos are popular expositions of known unsolved problems (Riemann Hypothesis, P vs NP, Navier-Stokes, Goldbach, etc.), not new discoveries. | MATH: Collatz map: \( T(n) = \begin{cases} n/2 & \text{if } n \equiv 0 \pmod{2} \ 3n+1 & \text{if } n \equiv 1 \pmod{2} \end{cases} \). No closed-form solution; known to hold for \( n < 2^{68} \) (verified computationally). No constants or ratios emerge from the conjecture itself. | CONNECTION: None direct. However, the Collatz map's parity structure relates to 2-adic integers (\( \mathbb{Z}_2 \)), which form a fractal tree — a self-similar structure with scaling ratio 1/2, not the golden ratios. No base-60, no crystallographic symmetry. | DEPTH: 3 — The conjecture is profound in its simplicity and resistance, but the videos provide no new math; they are educational summaries. The "hardest test" video (OkmNXy7er84) refers to the 1988 IMO Problem 6 (prove \( \frac{a^2+b^2} Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com