Alex Chengyu Li

Cover Relations and Lagrange Collisions in Rational Dyck Path Orders

Schiffler defined matching and Lagrange scores on rational Dyck paths, producing two strict partial orders, and asked for a path description of their cover relations and whether equal Lagrange values force isomorphic band graphs. We determine the cover relation in both orders. Ex...

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...

Proof Engine Infrastructure: A Fail-Closed Claim-Graph Method for Accountable AI-Assisted Mathematical Research

Background: AI systems can produce proof sketches, formal code, solver artifacts, and candidate strategies faster than research communities can assess them. Long-running and parallel agents can also hallucinate, lose problem context, duplicate obligations, or return incompatible...

Ballot-Admissible Fibonacci Ribbon Tableaux: Complete Enumeration for Arbitrary Alphabet Size and Fixed-Rank Asymptotics

Tenn proved the three-letter case and left the enumeration of ballot-admissible Fibonacci ribbon tableaux for alphabet sizes n >= 4 open. This work resolves that problem uniformly for every alphabet size n >= 2. Encoding ribbon columns as an alternating dominant type-A walk and c...

Influence Capacity at the Firm Level: Three-Axis Portability and Competitive Decline

This paper proposes a firm-level theory of influence capacity organized around productive capacity pi_F, mobilizable surplus mu_F, and network position nu_F. The central portability hypothesis is that ecosystem position adds predictive content for pricing power, strategic autonom...

Which Capacity Fails First? National Evidence for a Three-Axis Model of Influence

This paper develops an empirical test of a three-axis theory of national influence. It operationalizes productive capacity pi, mobilizable surplus mu, and network position nu; restricts retrospective classification inputs to information dated before scored crossings; and evaluate...

Beyond GDP: A Three-Axis Theory of National Influence Capacity

Why can a commercially small state exercise influence beyond its output, while a materially large state loses leverage when alliances, payment channels, or administrative reach fracture? This article develops a three-axis theory of national influence capacity: productive capacity...

Repeated-Endpoint Canon Permutations: Cone Walks and Spectral Geometry

This preprint solves the intermediate repeated-endpoint enumeration for canon permutations by a multichain recurrence and cone-walk model. It proves upper-boundary non-D-finiteness and exact asymptotics, and develops the associated harmonic-kernel and higher-dimensional spectral...

Hamilton Cycles and Paths in the Noncrossing Partition Refinement Graph

Let NCR(n) be the cover graph of the refinement order on the noncrossing partitions of an n-element cyclically ordered set. We determine exactly when this graph has a Hamilton cycle and when it has a Hamilton path. The graph has a Hamilton cycle exactly for n in {0,1} or even n a...

Repeated-Endpoint Canon Permutations: Cone Walks and Spectral Geometry

This preprint solves the intermediate repeated-endpoint enumeration for canon permutations by a multichain recurrence and cone-walk model. It proves upper-boundary non-D-finiteness and exact asymptotics, and develops the associated harmonic-kernel and higher-dimensional spectral...

Rigidity, Descents, and Wilf Classification in Pattern-Avoiding Canon Permutations

This focused preprint proves four conjectures on pattern avoidance in canon permutations, gives all twelve fixed-alphabet counting formulas for the 64 subsets of three-letter patterns, classifies those subsets into exactly 21 global canon-Wilf classes, and develops descent and al...

Rigidity, Descents, and Wilf Classification in Pattern-Avoiding Canon Permutations

This focused preprint proves four conjectures on pattern avoidance in canon permutations, gives all twelve fixed-alphabet counting formulas for the 64 subsets of three-letter patterns, classifies those subsets into exactly 21 global canon-Wilf classes, and develops descent and al...

Rigidity, Descents, and Cone Walks in Pattern-Avoiding Canon Permutations

This preprint proves four conjectures on pattern avoidance in canon permutations, gives all twelve counting formulas for the 64 subsets of three-letter forbidden permutations at fixed alphabet size three, and determines principal descent factorizations. It also solves the interme...

Proof Engine Infrastructure: A Fail-Closed Claim-Graph Method for Accountable AI-Assisted Mathematical Research

Background: AI systems can produce proof sketches, formal code, solver artifacts, and candidate strategies faster than research communities can assess them. Long-running and parallel agents can also hallucinate, lose problem context, duplicate obligations, or return incompatible...

Borrowed Safety: How Output-Centric AI Governance Depletes the Human Capacity It Assumes

This preprint develops the borrowed-safety thesis: output-centric AI controls can reduce visible hosted-platform risk while weakening the distributed human capacity needed to secure, verify, and govern future AI deployment. It introduces containment, incidence, regeneration, and...

When More Payoff Information Hurts: Objective Alignment under Endogenous Feasibility

This paper develops a theory of objective information value when payoff information improves but an agent incompletely represents how current actions change future feasibility. For arbitrary finite decision problems, posterior convexity is the benchmark for objective welfare to r...

Borrowed Safety: How Output-Centric AI Governance Depletes the Human Capacity It Assumes

This preprint develops the borrowed-safety thesis: output-centric AI controls can reduce visible hosted-platform risk while weakening the distributed human capacity needed to secure, verify, and govern future AI deployment. It introduces containment, incidence, regeneration, and...

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 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...