Problem detail · source-aware
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Ballantine, Beck, Feigon and Maurischat introduced the subsum polynomial $\mathrm{sp}(\lambda,x) := \prod_i (1+x^{\lambda_i})$ attached to an integer partition $\lambda$, studied rational functions built by summing reciprocals of these polynomials over natural classes of partitions, and posed ten conjectures. Six are now proved: the ordinary and binary coprimality and divisibility conjectures, and the odd and ternary special-value and recurrence conjectures.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
AxiomProver autonomously produced Lean and mathlib formalizations and machine-checkable proofs of all six conjectures. It also discovered a counterexample to one of the conjectures as printed, so the same system both proved and refuted statements drawn from one list, which is a useful demonstration that it was reading the statements rather than pattern-matching toward the expected answer.
Provider: unknown · Prompt public: unknown · Independence: unknown
The six proofs are Lean and mathlib formalizations, so they are machine-checkable rather than dependent on refereeing. Note that the catalog has not compiled the artifact itself, so this records the authors' claim of formalization, not an independent build.
Correctness: supported · statement fidelity: audited · peer review: none
six of the ten conjectures proved; one was found false as printed and its corrected form remains open
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.