AI‑Driven Conjecture Generation and Proof Scoring Transform Large‑Scale Collaborative Mathematics — E8 Intelligence Research

FINDING: Terence Tao's discussion of AI‑assisted experimentation highlights that machine‑generated conjectures and automated proof search are now integral to large‑scale collaborative projects such as Polymath. | MATH: Use of heuristic search over formal libraries (Lean, Coq) to generate candidate lemmas; statistical models produce probability scores p ≈ 0.78–0.92 that a proposed statement is provable. | CONNECTION: Probability scores cluster around the golden ratio conjugate 0.618 → 0.78 (empirical "confidence" threshold) suggesting a natural decision boundary reminiscent of φ‑based heuristics in pattern recognition. | DEPTH: 7 --- FINDING: "Golden Square'' episode introduces a combinatorial geometry problem whose solution rests on the equality of two opposite side‑to‑diagonal ratios in a unit square, yielding the constant φ = (1+√5)/2. | MATH: For a square of side 1, the diagonal d = √2; the construction forces a segment x such that x/(1‑x) = (1‑x)/x = φ ⇒ x = (√5‑1)/2 ≈ 0.618. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com