AxiomProver autonomously proved Fel's open conjecture on alternating syzygy power sums in numerical semigroups, generating a fully verified Lean formalization from natural-language input alone. Using exponential generating functions, it derived explicit formulas linking these sums to gap power sums and universal symmetric polynomials (echoing Ramanujan's work). This milestone—detailed in arXiv:2602.03716—marks the first AI-settled research-level problem in theory-building math, with zero human guidance in the core proof search and verification
