Sunny Lines: Combinatorial Geometry and Counting Invariants in IMO 2025 Problem 1 — E8 Intelligence Research

FINDING: IMO 2025 Problem 1 introduces "Sunny Lines" — a combinatorial geometry configuration likely involving line arrangements and parity or counting invariants. MATH: No explicit equations or constants extracted from titles/descriptions; problem structure suggests combinatorial counting (e.g., number of regions, intersection points, or colorings). CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries evident from metadata. DEPTH: 2 — Standard contest problem; no fundamental constants or universal patterns revealed. FINDING: IMO 2025 Problem 2 is described as "weak revenge of geometry" — likely a synthetic geometry problem with angle chasing or cyclic quadrilaterals. MATH: No equations given; typical geometry problem may involve power of a point, radical axis, or harmonic divisions. CONNECTION: Possible hidden harmonic ratios (e.g., 0.618) if golden triangle or pentagon appears, but not confirmed. DEPTH: 3 — Geometr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com