Lawvere's Fixed-Point Theorem Unifies Cantor, Gödel, Tarski, and Turing Diagonal Arguments — E8 Intelligence Research

FINDING: Lawvere's fixed-point theorem unifies Cantor, Gödel, Tarski, and Turing diagonal arguments as a single categorical theorem: in a Cartesian closed category, if a point-surjective morphism f: A → B^A exists, then every endomorphism g: B → B has a fixed point. | MATH: Core statement — given f: A → B^A point-surjective (∀h:A→B, ∃a∈A with f(a)=h), then ∀g:B→B, ∃b∈B with g(b)=b. Contrapositive (the "diagonal" form): if g:B→B has no fixed point, then no point-surjective f:A→B^A exists. Specializations: (1) Cantor: B={0,1}, g=¬ (no fixed point) ⇒ no surjection A→2^A. (2) Gödel/Rosser: B = sentences, g = negation/consistency map, A = proofs ⇒ no surjective proof-coding. (3) Turing: B = {halt, loop}, g = flip ⇒ no total computable halting decider. (4) Tarski: B = truth values, g = liar map ⇒ no definable truth predicate. | CONNECTION: The theorem is the categorical skeleton of self-reference. No direct appearance of φ=1.618, 0.618, 0.382, 0.786, 2.618, base-60, or crystallographic root Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com