The Huang-Jiang-Oblomkov Conjecture at a = 3
Statement
Huang, Jiang and Oblomkov conjectured that the Eulerian -series counting commuting pairs of nilpotent matrices with equals an explicit theta-and-eta product, making the point count essentially modular. The conjecture is layered in ; the layer is classical, including Rogers-Ramanujan and Andrews-Gordon. Nothing was known for . That layer is now proved in full, yielding a new infinite family of Rogers-Ramanujan identities and a geometric origin for Warnaar's products.
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No person has examined this. Everything below was judged by machines. say whether it holds →
proof attempt · #1
Kenny Lau and Ken Ono, using AxiomProverThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The mathematics is the authors'; AxiomProver supplied the formal certificate. "AxiomProver, an AI system currently under development, was used to generate this certificate. The system verified these results in Lean assuming existing literature."
Proves the a = 3 layer; the conjecture is layered in a and remains open for larger a.
Machine-checked by Lean on #1 · not a person
lean: partially checkedLeanscope Lean formalization of the core argument; statement correspondence not independently audited
The Lean certificate is explicitly conditional, verifying the new identities assuming results from the existing literature rather than from first principles, and the system that produced it also produced the formal statements. Public at the AxiomMath repository.
Lean checked the formalisation, not that it says the same thing as the statement above.
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