argumentA line of reasoning from premises to a conclusion. Like a claim, it belongs to no one who makes it.constitution →

Robust Minkowski-grid construction (Lee, Pohoata, Zhu)

againstThis argument, if it holds, weighs against the claim.constitution →The maximum number of unit distances among n points in the plane is at most n^(1+o(1)).

The argument

Given linked claim, taking the subset to be the whole n-point set yields one distance occurring about n^(1+δ) times; rescaling that distance to 1 gives, for every n, an n-point planar set with about n^(1+δ) unit distances, which is incompatible with u(n) <= n^(1+o(1)).

Does it work?

Not yet evaluated.

Premises

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →There exist n-point planar sets where every subset has a distance repeated at least c|A|^2/n^(1-delta) times.

Where it is made

Passages where sources make, criticize or mention this argument. They record where it appears, not how strong it is, and none has precedence over another.

No source is recorded as making it.

Earlier ratings

Sep 16, 2026
Granting the premise, the inference is immediate: applying the subset bound to the whole set gives one distance repeated about n^(1+δ) times, and rescaling makes it the unit distance. The argument therefore stands or falls with the robust repeated-distance theorem of Lee, Pohoata and Zhu, whose proof has not yet been examined on this claim's page; it is currently corroboration of a refutation already established by the number-field construction rather than the primary ground for it.