Spahn and Zeilberger's Third Challenge: Holonomicity of the Restricted Permutation Counts
candidateconfidence 50%
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Precise statement
Spahn and Zeilberger's third challenge asks whether the restricted permutation counts $a_{r,s}$ and $b_{r,s}$ are holonomic for all $r, s > 1$. Answered affirmatively.
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fidelity, correctness, priority, or novelty.
What AI did
Claude
The paper's division of labour, in its own words: the model "generated the mathematical ideas, the proofs, and the verification code", while the author "selected the problems and determined when a line of attack should be abandoned; executed all computations, on hardware the system could not access; designed and enforced the verification protocol". It adds that neither role was passive: the system did not merely formalise ideas supplied to it, and the author did not merely execute instructions.
Checked by this site on 21 August 2026 against the paper (arXiv:2608.11290v2): the division of labour is verbatim as quoted, all five challenges are reported fully solved, and two further problems are reported only partial and are NOT entered here. The paper states a four-principle verification protocol that distinguishes proved, machine-verified and supported claims, and ships code and verification scripts. Those scripts were not re-run here. Days-old preprint, no independent review.
Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
The source status is candidate and must not be represented as solved.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.