Claims

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1984_10_02_hegyvari: Hegyvári (Acta Math. Hungar., 1986) proves that the largest number of integers in [1, n], not required to increase, with all consecutive sums distinct lies between (1/3 + o(1))n and (2/3 + o(1))n, so f(n) is at most (2/3 + o(1))n; refereed.

1996_05_01_coppersmith_phillips: Coppersmith and Phillips (SIAM J. Discrete Math., 1996) bound sets in which no sum of 2 to 4 adjacent elements is an element, which gives f(n) at most (2/3 - 1/512)n + O(log n); refereed.

2026_07_27_lenthall_cleary: A partial proof claim of 27 July 2026: the upper bound f(n) at most n/2 plus a constant times n^{2/3}, by blocks of adaptive length, with the finite inequality in Lean 4, not built here; the bound leaves f(n) = o(n) open.

2026_08_31_pickhardt: Pickhardt's manuscript, written with the Paratelligent Research Agent: f(n) at least (4/sqrt 3 - o(1)) sqrt n by a sequence omitting one residue class mod 3, and at most n/2 + ((3/2) 2^{-2/3} + o(1)) n^{2/3} by layer packing.

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