What was already known
Zeilberger computed the counts through n=40 and guessed the recurrence. Those finite values did not prove it for all n.
AI involvement
Padhi selected the challenge, directed the work, ran independent checks and rejected faulty proposals. He credits Claude with the mathematical ideas, proof and verification code.
Claude generated the proof and mathematical ideas under Padhi’s selection and falsification protocol.
Importance
Resolves a specific enumerative-combinatorics challenge with a formula and all-n proof.
Limitations
Two independent dynamic programs agreed on 56 terms, and the derived recurrence matched those terms. Those finite checks do not verify the complete symbolic proof; no complete independent check is documented.
Technical verification
Two independent dynamic programs agree on 56 finite terms and the derived operator annihilates them. That exact finite test checks cases, not the complete symbolic all-n argument; no complete human or machine check is documented.
Human understanding
Padhi explains the testing protocol, but the source credits Claude with the proof and does not document his independent explanation of its reverse-Kreweras derivation; Few is the evidence default.
Correction and publication history
Resolves a specific enumerative-combinatorics challenge with a formula and all-n proof.
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