Claims

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2026_08_14_tidor_yu_zakharov: N points in three-dimensional space determine at least N^(2/3-o(1)) distinct distances, which with Erdős's grid bound gives f_3(n) = n^(2/3-o(1)) and answers the particular question for d = 3; an arXiv preprint.

2026_09_23_openai: Every set of n points in d-space, d at least 3, determines at least c_d times n^(2/d) distinct distances, so f_d(n) has the order of n^(2/d); a release preprint with no Lean formalization.

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