What was already known
Amdeberhan, Shareshian and Stanley established the coarser record-partition count and asked for a composition refinement with an algebraic interpretation.
AI involvement
AxiomProver received the theorem statements without a solution and generated the proofs and Lean formalizations. Chen, Mogielnicki and Ono wrote the explanatory paper.
The source states that AxiomProver received only the three theorem statements and generated the mathematical proofs and formalization without a supplied solution.
Importance
Resolves the record-composition refinement and supplies an algebraic description.
Limitations
The authors report complete Lean proofs and provide a separate human exposition. A separate complete human check of each generated proof is not documented.
Technical verification
The authors report complete Lean 4.31.0 proofs. The released problem statement names the exact record-composition product and noncommutative lift; the released solution contains the corresponding proofs without sorry. Human exposition is not counted as a separate completed proof check.
Formal checking
Complete Lean formalization in problem.lean and solution.lean
- Checker
- Lean 4.31.0 type checker, as reported by AxiomMath
- Scope
- The record-composition product formula and noncommutative symmetric-function lift in Theorems 1.1–1.3
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human authors give a direct bijection via record blocks, derive the product formula and explain its noncommutative symmetric-function lift.
Correction and publication history
Resolves the record-composition refinement and supplies an algebraic description.
Read this published revision