Alex Chengyu Li

Beyond Kernel Verification: The Missing Engineering Layer of Mathematics

AI systems can now produce mathematical arguments and formal proof code quickly. This does not make verification a single solved problem. A Lean file may compile while the announced theorem still depends on an unresolved citation, transport, computation, or project axiom. Even af...

Beyond Kernel Verification: The Missing Engineering Layer of Mathematics

AI systems can now produce mathematical arguments and formal proof code quickly. This does not make verification a single solved problem. A Lean file may compile while the announced theorem still depends on an unresolved citation, transport, computation, or project axiom. Even af...

Lagrange Collisions and Cover Relations for Rational Dyck Paths

Schiffler associated matching and Lagrange orders to rational Dyck paths and posed two problems about their equality and cover relations. We first classify the band-graph isomorphism classes at a fixed coprime endpoint: every class is an orbit of an explicit reversal involution a...

Beyond Kernel Verification: The Missing Engineering Layer of Mathematics

AI now generates mathematical arguments and proof code faster than communities can verify, understand, and reuse them. Building on a program already spanning claim-level verification, proof infrastructure, and kernel-closed mathematics, this paper identifies two engineering failu...

Beyond Kernel Verification: The Missing Engineering Layer of Mathematics

Artificial intelligence and autoformalization are moving mathematics from proof scarcity toward proof abundance. Terence Tao has described the resulting pressure: proof generation and formal verification may accelerate faster than exposition, publication, digestion, and canonical...

Proof Engine Infrastructure: A Claim-Graph Framework for AI-Assisted Mathematical Research

AI systems can rapidly produce proof sketches, programs, formalization fragments, solver instances, and candidate proof strategies, but these outputs do not share a common evidentiary status. This paper introduces Proof Engine Infrastructure, an architecture for converting untrus...

Erdős Problem 848: A Kernel-Checked Proof of the Exact Extremal Bound

For every integer N ≥ 1, the maximum cardinality of a set A contained in [1,N] for which ab+1 is nonsquarefree for every a,b in A is exactly the number of integers n ≤ N with n ≡ 7 (mod 25). The proof uses an exact Hall reformulation, an exact prefix-colouring certificate through...

Erdős Problem 848: A Kernel-Checked Proof of the Exact Extremal Bound

For every integer N ≥ 1, the maximum cardinality of a set A contained in [1,N] for which ab+1 is nonsquarefree for every a,b in A is exactly the number of integers n ≤ N with n ≡ 7 (mod 25). The proof uses an exact Hall reformulation, an exact prefix-colouring certificate through...