Claims

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2025_05_07_clemen_dumitrescu_liu: For all large n some n-point planar set has its most frequent distance occurring Omega(n log n) more times than the next one (Corollary 1.10, from Theorem 1.9); refereed in Acta Math. Hungar.

2026_07_15_snyder: For all large n some n-point planar set has its most frequent distance occurring at least n^(1+c/log log n) more times than the next one, with c = 1/50000; a Lean 4 proof is supplied, not built here.

2026_07_21_xeff: For all large n some n-point planar set has its most frequent distance occurring at least n^(1+c) more times than the next one, for an absolute c > 0, by tuning the construction behind the unit-distance disproof.

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