Four Unsolved Math Problems and a Video Paper: A Search Result Survey — E8 Intelligence Research

FINDING: Search results surface four distinct unsolved/classic problems (Hadwiger-Nelson, odd perfect numbers, Josephus, Catalan's conjecture) plus an unrelated omnidirectional video quality paper; no single unified discovery. | MATH: Hadwiger-Nelson: chromatic number χ(ℝ²) ∈ {5,6,7} (unit-distance graph); odd perfect numbers: σ(n)=2n, n odd — none known; Josephus: J(n,k) = (J(n−1,k)+k) mod n, J(1,k)=0; Catalan: xᵃ − yᵇ = 1, only 3²−2³=1. | CONNECTION: Hadwiger-Nelson lower bound 5 arises from the Moser spindle (7 vertices, 11 edges) — a unit-distance graph with no obvious crystallographic symmetry; upper bound 7 from hexagonal lattice tiling (base-60-adjacent hexagonal symmetry, 60° angles). Odd perfect numbers relate to Euler's form n = p^α · m² with p ≡ α ≡ 1 (mod 4) — no direct golden-ratio link. Josephus has modular arithmetic, no geometric constant. Catalan's conjecture is purely Diophantine. | DEPTH: 3 — the results are a list of known open problems with no new mathematical extr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com