Claims

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2025_03_25_cambie: Cambie's construction, recorded in the site's commentary, of a set of density 5/8 with no relation 1/a = 1/b + 1/c among distinct elements; it shows f(N) >= (5/8 + o(1))N, so f(N) is not (1/2 + o(1))N.

2025_08_11_van_doorn: Van Doorn's note proves that every subset of the first n integers of size at least 9n/10 plus a cube of a logarithm plus one contains distinct x, y, z with 1/x + 1/y = 1/z, so f(N) <= (9/10 + o(1))N for Problem 302.

2026_07_20_schuh: A partial proof claim of 20 July 2026, filed by the account 15Redstones and credited to Robert Schuh with two AI systems, that f(N) <= (373/420 + o(1))N for Problem 302; the argument is an unsigned text on a paste site.

2026_08_16_khanukov: A partial proof claim by Dmitry Khanukov, AI-assisted, first released on 16 August 2026 and filed on the site on 13 September 2026: f(N) >= (5/8 + delta)N for large N and limsup f(N)/N <= 140803024/163562355 for Problem 302.

2026_09_25_kitamura: A Lean 4 development of 25 September 2026 by Kenta Kitamura, AI-assisted, declaring limsup f(N)/N <= 0.8461739827964010 for Problem 302 through a priority recurrence over smooth blocks and kernel-checked certificates.

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