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The Small Davenport Constant of the Heisenberg Group of Order 125

Godara and Sarkar proved d(H27)=6\mathsf{d}(H_{27})=6 for the exponent-pp Heisenberg group and posed d(Hp3)=3p−3\mathsf{d}(H_{p^3})=3p-3 for every odd prime pp, leaving p≥5p\ge5 open. The paper settles the first open case, d(H125)=12\mathsf{d}(H_{125})=12, the upper bound reducing to a finite spread bound verified by exhaustive search and independently reproduced.

Result
Proved(see note)
Status
Resolved
AI contribution
AI-discovered
Method
Computation
Field
Additive Combinatorics, Zero-Sum Theory
Posed by
Naveen K. Godara, Siddhartha Sarkar
Year posed
2025
Years open
1y
Solved
2026-07-15
Model
Claude + GPT-5
Vendor
OpenAI; Anthropic
Collaborators
Patrick White
Verification
Unreviewed
Publication
Preprint
Significance
10 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What was actually shown

Settles the case p=5. The posed formula for every odd prime remains open.

What the AI did

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.

Verification

No independent review, though the load-bearing computation was reproduced by a second search with a different pruning strategy. Preprint, not refereed.

Sources

Changelog3 changes
  • Matarisvanset More links to “problem-record: Godara & Sarkar 2025: Conjecture statement | https://doi.org/10.1142/S0219…”, also Year posed, Posed by, Significance note, Vendor
  • Rasmus Lindahlchanged Short name from “Davenport, H_125” to “Davenport, $H_{125}$”
  • Rasmus Lindahlchanged Short name from “Davenport, $H_{125}$” to “Davenport, H_125”

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