The Huang-Jiang-Oblomkov Conjecture at a = 3
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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.
Context
Proves the a = 3 layer; the conjecture is layered in a and remains open for larger a.
A layered conjecture whose lower layer is the classical Rogers-Ramanujan territory; the new layer produces genuinely new identities, but the conjecture itself is recent and specialist.
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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.
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Machine check · not human verification
machine: partially checkedscope 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.
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