ONE AXIOM : The M : One Axiom

This is the foundational document of the ONE AXIOM series — the first public release of a minimal, self-contained axiomatic framework constructed from a single axiom. We introduce the axiom ∃S, M : S = {x ∈ U | M(x) = x} ∧ M = Φ(S, M) (with non-triviality: S ≠ ∅ and S ≠ U), where S is the fixed-point set of M, M is the coherence evolution operator, and Φ is the meta-operator of co-definition. Using a rigorous dual-track methodology (deductive top-down from the axiom + constructive bottom-up verification in the finite model GF(2)³), we derive — without assuming any physical law, ZFC set theory, empirical constants, or additional axioms — the complete structural apparatus that underlies both mathematics and…