Problem detail · source-aware
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Godara and Sarkar proved $\mathsf{d}(H_{27})=6$ for the exponent-$p$ Heisenberg group and posed $\mathsf{d}(H_{p^3})=3p-3$ for every odd prime $p$, leaving $p\ge5$ open. The paper settles the first open case, $\mathsf{d}(H_{125})=12$, the upper bound reducing to a finite spread bound verified by exhaustive search and independently reproduced.
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.
An attribution note states the results were obtained by an AI research collaboration in which an AI system occupied the principal research seat under human direction. Claude produced the search implementations, the independent reproduction of the load-bearing computation and the write-up; a tool-free GPT-5 produced the reduction to the lemma chain and the corrected hypotheses of several lemmas.
Provider: unknown · Prompt public: unknown · Independence: unknown
No independent review, though the load-bearing computation was reproduced by a second search with a different pruning strategy. Preprint, not refereed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Settles the case p=5. The posed formula for every odd prime remains open.
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.