Parity Invariant Solves IMO Windmill Problem — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22841437
Primary Topic
Intelligence, Security, War Strategy
Type
preprint
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preprint

Parity Invariant Solves IMO Windmill Problem — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Intelligence, Security, War Strategy
preprint

Parity Invariant Solves IMO Windmill Problem — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The 2011 IMO windmill problem is solved by a parity/invariant argument on the number of "pivot" lines crossing a fixed point, not by any metric or ratio. | MATH: The core invariant: For a windmill with n points in general position, as the pivot moves, the number of points on each side of the rotating line changes by ±1 per step; the invariant is the parity of the count of points on one side (mod 2). Specifically, if n is odd, the line can be made to pass through any point as pivot; if n is even, the invariant forces the pivot to alternate between two disjoint sets of points. No equations beyond parity (mod 2) and the pigeonhole principle on the sequence of pivots. | CONNECTION: None to golden ratio, base-60, or crystallographic symmetry. The structure is purely combinatorial — the "windmill" is a rotating line through a point, and the invariant is a Z/2Z parity. However, the underlying symmetry is the dihedral action of the rotating line on the point set, and the invariant is Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Intelligence, Security, War Strategy
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Parity Invariant Solves IMO Windmill Problem — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS