Claims

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1987_01_01_berger_felzenbaum_fraenkel: The six-prime corollary of Berger, Felzenbaum and Fraenkel (Acta Arith. 1987): the least common multiple of the moduli of a distinct odd covering has at least six distinct prime factors; accepted on the refereed paper.

2017_03_06_hough_nielsen: Theorem 1 of the Duke paper (2019): every distinct covering system has a modulus divisible by 2 or by 3, so an odd covering must have a modulus divisible by 3; accepted on the refereed paper.

2018_11_08_balister_bollobas_morris_sahasrabudhe_tiba: Theorem 1.4 of the Inventiones paper (2022): the least common multiple of the moduli of a distinct covering system is divisible by 2, 9 or 15, so an odd covering's period is divisible by 9 or 15; accepted on the refereed paper.

2019_01_31_balister_bollobas_morris_sahasrabudhe_tiba: Theorem 1.1 of the Algebra & Number Theory paper (2021): every finite covering system with distinct square-free moduli greater than one has an even modulus, settling the odd square-free question; accepted on the refereed paper.

2026_01_11_gebyjaff: A Lean development posted by gebyjaff on 11 January 2026, generated with Archivara and Aristotle, deriving that no odd distinct covering system exists from the Hough–Nielsen theorem and an unproved good-fibre axiom; claimed.

2026_05_02_lee: Jinook Lee's five-page note and Lean development of 2 May 2026, audited by Aristotle, claiming that no covering system with distinct odd moduli exists; its central axiom was shown false as encoded and the author conceded; rejected.

2026_07_28_mian_siddique: Mian and Siddique's theorem of July 2026, with a Lean 4 development, that every covering system with distinct odd moduli greater than one has least common multiple above 10000; the bound is known and the Lean unbuilt here.

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