Massively Parallel Collaborative Theorem-Proving in Equational Theories of Magmas — E8 Intelligence Research

FINDING: The Polymath Project (Gowers 2009; Tao et al.) demonstrates that large-scale open collaboration can solve research-level mathematics, and Tao's newer Equational Theories Project extends this to machine-assisted, massively parallel theorem-proving over algebraic identities. MATH: Core object = equational theories of magmas (sets with one binary operation ∗). An identity like x∗(y∗z) = (x∗y)∗z (associativity) defines an equivalence class of algebras; the project maps the implication graph between ~4,694 distinct equations in 3 variables, i.e. a directed graph on the lattice of equational consequences. Key structural quantities: number of equations E ≈ 4,694; implication edges form a partial order (preorder) whose Hasse diagram encodes which identities imply which. Implication is transitive and reflexive → the object is a preorder/lattice, not a numeric constant. CONNECTION: The implication structure is a **lattice/poset** — the same algebraic object type as root systems and crys Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com