Almost All Primes are Partially Regular
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Statement
In the circle of Kummer's regular primes and Vandiver's conjecture, the paper proves that almost all primes are partially regular, yielding a partial Vandiver theorem for a density-one set of primes, with consequences for Kubota-Leopoldt p-adic L-functions, Eisenstein congruences and K-theory torsion.
Context
Sits in the Kummer-Vandiver circle, one of algebraic number theory's oldest problem families, though the density-one statement itself was a folklore target rather than a numbered conjecture.
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"The theorem proving partial regularity for almost all primes is fully formalized in Lean/Mathlib and was produced automatically by AxiomProver from a natural-language statement of the conjecture." The human authors prepared the mathematical exposition from the formal development as reference.
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Machine check · not human verification
machine: partially checkedscope Lean formalization of the core argument; statement correspondence not independently audited
Fully formalized and kernel-checked in Lean/Mathlib, produced autonomously by AxiomProver; no independent review of the informal-to-formal correspondence yet. Tier: AxiomProver produced both the proof and the Lean statement; the correspondence to the informal claim has not been independently audited.
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