Claims

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2026_08_26_pr_huang: A research note and Lean project posted on the forum under the name Pr_Huang prove that no representation of 1 with all consecutive gaps at most 2 has largest denominator up to 4e9, extended on 2026-09-10 to about 3.74e60.

2026_09_02_ramji: An AI-generated Lean development orchestrated by Reza Ramji proves that every representation of 1 by distinct unit fractions with largest denominator at most about 8.59e23, later about 3.21e958, has a consecutive gap of at least 3.

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