What was already known
The type-D model and dualities came from earlier human work. F₂ marginals were conjectured for n=2,3, and the single-species step-ASEP limit was already known.
AI involvement
Kuan reports that Claude Opus 4.8 and Fable 5 wrote the mathematical body and proofs, with later Claude corrections to two §6 lemmas. The human author wrote the abstract and introduction and supplied the earlier model and research context.
The first-person disclosure assigns the proof-bearing mathematical body to Claude models, while Kuan guided the project and manually checked it.
Importance
Extends the marginal law to every species through a decoupling identity.
Limitations
The fixed-q cross-current covariance asymptotic remains a conjecture. The reported Lean counterpart has explicit stochastic-process interface assumptions.
Technical verification
Kuan reports a complete manual proof check. The paper also reports a Lean formalization with named hypothesis bundles for foundational stochastic-process interfaces; the exact Lean theorem-to-paper correspondence was not rebuilt here.
Formal checking
Manual verification of the paper’s proofs
- Checker
- Jeffrey Kuan, paper author
- Scope
- Theorem 8.1 Tracy–Widom marginal convergence under the stated step and fixed-q assumptions
- Basis
- Reported by the linked checker
Formalization over Mathlib, no sorry for theorem statements, with dependency graph and compiled declarations reported
- Checker
- Lean 4 formalization built with Aristotle and Claude
- Scope
- Theorem 8.1 formal counterpart and its dependencies; process-existence interfaces remain explicit hypotheses where used
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Kuan explains that each species projection is an autonomous ASEP, making the fixed-q marginal convergence a transfer of the established single-species result.
Correction and publication history
Extends the marginal law to every species through a decoupling identity.
Read this published revision