Parity Invariant Proof for Infinite Visits in IMO Windmill Problem — E8 Intelligence Research

FINDING: The 2011 IMO windmill problem (Q2) is a combinatorial geometry problem about finite sets of points in general position, where a "windmill" process (alternating pivot and line rotation) always visits every point infinitely often. | MATH: No explicit equations or constants; the proof uses parity arguments and invariant properties of point-line configurations. The key invariant: the number of points on each side of the rotating line changes by ±1 at each pivot, and the total number of points is odd (2n+1). | CONNECTION: The process exhibits a cyclic symmetry reminiscent of root system reflections (e.g., A_n Coxeter group) and the alternating pivot pattern mirrors the 2-fold rotational symmetry of a regular polygon's diagonals. The invariant parity structure aligns with the crystallographic restriction for 2D lattices (only 2-, 3-, 4-, 6-fold rotations allowed). | DEPTH: 6 — The problem is a clever combinatorial invariant proof, not a fundamental discovery, but its connection to r Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com