An Inquiry into the Axiomatic Foundations of AI-Generated Formal Proofs

Recent advancements in large language models (LLMs) have demonstrated the ability to generate formal mathematical proofs at an unprecedented scale, verified through deterministic compilers such as Lean 4. However, a structural audit of the publicly available build orchestration (lakefile.lean) for these proofs reveals a critical dependency on proprietary, unpublished foundational namespaces. Because the underlying axioms and topological definitions remain obfuscated, the scientific community cannot independently verify whether these proofs solve discontinuous physical boundaries or merely mathematically redefine them. This paper calls for the public release of these foundational definitions to ensure the integrity of automated formal verification.