The Axiom Profile of Mathlib

Every theorem in a proof library rests on a measurable set of axioms, and a library’s distribution of those sets — its axiom profile — is a fact about the mathematics, not an opinion about it. This paper measures the profile of the entire Mathlib library: 707,053 declarations at a pinned commit, each declaration’s transitive axiom closure computed from a content-addressed archive of the elaborated terms, certified against the Lean kernel by full replay. The findings: 25.09% of Mathlib (177,395 declarations) depends on no axioms at all; only 23 distinct axiom profiles occur in the whole corpus, and 99.96% of declarations lie on the Boolean cube over three axioms — propositional extensionality, quotient soundness, and choice; the library contains zero incomplete proofs. Choice reaches half the corpus (50.84%), but its entry structure is extraordinarily narrow: every choice-dependent declaration reaches the axiom through a frontier of just 206 declarations that use it directly, and a structural counterfactual over the dependency graph shows 55.4% of all choice-dependence flowing through three generic classical-instance gateways jointly. The measurement separates two things the per-declaration view conflates: mathematics that needs choice, and mathematics that inherits choice from shared infrastructure. Every figure is recomputable from the query outputs deposited with this paper.