Claims

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2016_09_28_lagarias: Lagarias's 2016 Monthly paper publishes a reconstructed proof of Crampin and Hilton's 1972 negative answer: the set has O(T^(τ1+ε)) elements up to T with τ1 ≈ 0.900526, so density zero; refereed, accepted by the curator.

2026_06_19_axiommath: AxiomProver's Lean 4 file, posted to the site's thread in June 2026, proves that the set generated from 1 by 2x+1, 3x+1 and 6x+1 has lower density zero; not built or audited by this corpus.

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