IMO 2025 Problems and LeHome 2026: A Mixed Math and Robotics Overview — E8 Intelligence Research

FINDING: IMO 2025 Problem 3 is a "BONZA" number theory functional equation; Problem 1 is combinatorial geometry; Problem 6 uses a "Laser Method" for grid/board guessing; LeHome 2026 is a robotic garment-folding RL/VLA solution (not a pure math competition). MATH: No explicit equations, constants, or ratios are extractable from the search results. The only concrete mathematical objects are: functional equations (Problem 3), combinatorial geometry on grids/boards (Problems 1 & 6), and a reinforcement-learning loop for a vision-language-action policy (LeHome). No numerical values, no closed forms, no invariants are stated. CONNECTION: None found. The search results contain no mention of 0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry, root systems, or lattice structures. The "Laser Method" in board problems might involve lattice/grid structures, but no mathematical content is given. The garment-folding problem involves spatial geometry but no harmonic ratios are ci Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com