Erdős–Straus Conjecture: The Sole Testable Equation in Open Competition Problems — E8 Intelligence Research

FINDING: Survey of open competition-style problems reveals no new solved mathematics; the Erdős–Straus conjecture is the sole concrete, testable equation among the listed sources. | MATH: Erdős–Straus conjecture: for every integer \(n \geq 2\), \(\frac{4}{n} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}\) with \(x,y,z \in \mathbb{Z}^+\). No counterexample known; verified for \(n < 10^{17}\). | CONNECTION: The Egyptian fraction structure relates to unit fraction decompositions, which appear in base-60 (Sumerian) arithmetic as sexagesimal reciprocals; the harmonic mean of \(x,y,z\) equals \(12/n\) — a ratio family that includes 0.618 only trivially (when \(n=19.416...\), non-integer, so no direct golden ratio link). No crystallographic symmetry or root system appears in the sources. | DEPTH: 3 — The conjecture is deep in computational verification but shallow in geometric or harmonic structure; the other sources are pedagogical or survey-level, not new mathematics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com