The Windmill Problem: The Only Verified Core of the 2011 IMO Claim — E8 Intelligence Research

FINDING: The 2011 IMO "windmill" problem (Q2) is the only extractable mathematical core; the 2026 problem is unverified, and the "hardest ever" claim is unsubstantiated without the actual problem statement. | MATH: The windmill problem: Given \(n\) points in general position, a "windmill" process rotates a line about a pivot point, switching pivot to the point just passed. Prove: for \(n ≥ 3\), there exists a line and a starting pivot such that the process visits every point infinitely often. Key invariant: the number of points on each side of the rotating line remains constant (equal to \( n/2 \) or \( n/2 \)) — a discrete conservation law. | CONNECTION: The constant-side-count invariant mirrors the balance of a root system's hyperplane arrangement (e.g., \(A_n\) root system: each hyperplane splits points into two equal-cardinality sets). The rotation angle sweeps \(2π\), and the pivot sequence cycles through all points — a cyclic symmetry of order \(n\) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com