Claims

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1985_01_01_simpson: Simpson's 1985 proof of Znám's inequality gives n_k at most 2^(k-1) for every irreducible covering set of size k; accepted on the refereed paper.

2006_01_01_sun: Zhi-Wei Sun's theorem (Integers 2007) that for every odd prime p the divisors of 2^{p-1} p above one form an irreducible covering set, so infinitely many n qualify; accepted on the refereed paper.

2019_04_09_balister_bollobas_morris_sahasrabudhe_tiba: The asymptotic of Balister, Bollobás, Morris, Sahasrabudhe and Tiba for the number of minimal covering systems with k classes bounds the number of irreducible covering sets of size k from above; accepted on the paper.

2026_07_13_snyder: Colin Snyder's 2026 Star Fleet Math release, a Lean 4 development by its GPT-5.6 harness: exact largest modulus, smallest largest modulus k^{1+o(1)}, the reciprocal sum's order, Sun's family, and the count under two hypotheses.

2026_07_28_pickhardt: Jeff Pickhardt's 2026 manuscript with the Omniscience agent, since renamed Paratelligent, claiming the count, the least and greatest largest modulus and the reciprocal sum, with Sun's divisor family; no review.

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