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An Exact Apéry Limit for the AESZ 182 Calabi–Yau Recurrence
Abstract
A proof of the 2008 conjecture of Almkvist, van Straten and Zudilin on the Apéry limit of the Calabi–Yau recurrence AESZ 182, fully verified in Lean 4. Theorem. Let a(n) and b(n) satisfy n4u(n) = (43n4 − 86n3 + 77n2 − 34n + 6)·u(n−1) − 12(6n−7)(6n−5)(n−1)2·u(n−2) for n ≥ 2, with a(0) = 1, a(1) = 6 and b(0) = 0, b(1) = 1. Then b(n)/a(n) → 3ζ(3)/11. Method. A Laurent-polynomial period of a 3×3 determinant F, combined with its Mahler measure m(F) = 9ζ(3)/(2π2). Formal verification. This version gives a proof fully verified in Lean 4 (633 modules, standard axioms only), replacing the Hodge-theoretic argument of v8; a fresh rebuild from source reproduced it.
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Metadata
- Authors
- Shvets, A.
- Venue
- Zenodo
- Publisher
- Zenodo
- Published
- 2026-10-21
- Type
- Preprint
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