Parity Invariant in Windmill Pivoting, Not Metric Harmony — E8 Intelligence Research

FINDING: The 2011 IMO windmill problem is a combinatorial-geometry invariant about rotating a line through point sets, not a metric harmony result. | MATH: Given n points in general position, a "windmill" line pivots on a point, alternating pivot points; the invariant is that for odd n, some point is always the pivot (parity/alternation argument). No explicit constants or ratios emerge. | CONNECTION: None to golden ratios, base-60, or crystallographic symmetry — the structure is purely incidence/order-theoretic. | DEPTH: 4 (clever but isolated; no universal constant or deep structural link). FINDING: Mock USAMO 2012 #5 and USAMO 2008 #2, 2010 #4 are standard olympiad geometry — likely angle chasing, cyclic quadrilaterals, or power of a point. No equations or constants provided in the search results. | MATH: Unspecified — no extractable formulas. | CONNECTION: None discernible from metadata alone. | DEPTH: 2 (no mathematical content extracted). FINDING: Hilbert geometry volume growth Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com