Geometric Measurements of the Axiom of Choice in Neural Proof Embeddings
The axiom of choice has divided the foundations of mathematics for over a century, but the distinction between classical and constructive proofs has remained a philosophical and methodological one. We use Lean 4's kernel-level tracking of axiom dependence to show that the axiom of choice has a measurable geometric correlate in proof space that obeys a one-parameter mixture law and has operational consequences for neural theorem provers. To do this, we partition $471{,}260$ declarations of Mathlib by transitive dependence on the axiom of choice and represent a filtered population of $42{,}355$ traced theorems by their sequences of tactic invocations. We use the constructive proofs in this ...
| Authors | Rodrigo Mendoza-Smith |
|---|---|
| Primary category | cs.LG |
| Published | 26 June 2026 |
| Last updated at source | 26 June 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.