Hidden Invariants Unify Putnam, IMO, and MATH Dataset Benchmarks — E8 Intelligence Research

FINDING: The Putnam problem solution reveals a hidden invariant (a conserved quantity) that elegantly collapses a complex combinatorial geometry problem. The IMO windmill problem uses a parity/invariant argument to prove a point always exists with a certain property. The MATH dataset benchmarks problem-solving but lacks geometric depth. MATH: No explicit equations or constants emerge from these summaries. The Putnam problem likely involves a polynomial invariant or combinatorial sum. The windmill problem uses a parity argument (mod 2) or fixed-point invariant. CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries are present. The problems are combinatorial/geometric but not tied to harmonic ratios or root systems. DEPTH: 2/10 — These are competition problems with elegant invariants, but they do not reveal new universal constants, symmetries, or deep geometric structures. They are pedagogical tools, not fundamental discoveries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com