Equational Theories Project: AI-Assisted Mass Collaboration on Magma Identity Implications — E8 Intelligence Research

FINDING: The Equational Theories Project (Terence Tao et al.) is the current flagship Polymath-style mass-collaboration effort — applying AI-assisted, large-scale distributed proof search to the algebra of equational theories (magma identities), not a new geometric constant. | MATH: Core object is the lattice of equational theories over a single binary operation (magmas). Tao's project enumerated implications among ~4,694 equational laws (Hawaiian-style identities, e.g. x*(y*z)=(x*y)*z associativity, x*y=y*x commutativity) and resolved ~22 million pairwise implication questions, reducing the implication graph to a verified Hasse-diagram-like partial order. Key structural result: the implication relation forms a preorder; its quotient is a partial order (a lattice-like poset) on equivalence classes of theories. No new numerical constant (no 0.618, 1.618, φ, base-60) is produced. | CONNECTION: The relevant geometric-harmony link is structural, not numeric — the implication poset is a lat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com