Skip to content

Erdős problem 94

Start work

Suppose nn points in R2\mathbb{R}^2 determine a convex polygon and the set of distances between them is {u1,…,ut}\{u_1,\ldots,u_t\}. Suppose uiu_i appears as the distance between f(ui)f(u_i) many pairs of points. Then ∑if(ui)2≪n3.\sum_i f(u_i)^2 \ll n^3.

Open in the state represented here.

That occurrence is one of four Erdős 94 declarations Formal Conjectures publishes, and this identity does not establish the cubic distance-multiplicity conjecture.

How far the record reaches6 of 6 stages
  1. Sourceerdos-problems
  2. StatementRetained
  3. Formal4 retained
  4. Resolutionproved (Lean)
  5. Work2 checks
  6. Decisionaccepted
  7. The questionNot reached
The accepted scope sits inside the question, and does not reach it.
Scope of what is proved
The question aboveNot established here
Proved and acceptedaccepted

For every finite planar point set P, the sum over its distinct determined distances of the unordered-pair distance multiplicities equals P.card.choose 2

Results2
For every finite planar point set P, the sum over its distinct determined distances of the unordered-pair distance multiplicities equals P.card.choose 2
Aug 18, 2026, 6:37 PM · 3 evidence items · replaces an earlier Result · current
accepted
For every finite planar point set P, the sum over its distinct determined distances of the unordered-pair distance multiplicities equals P.card.choose 2
Aug 17, 2026, 6:40 PM · 3 evidence items · replaces an earlier Result · replaced by a later Result
superseded
Checks2 scoped
Submission v3 revision fidelity
Does not establish: Correctness of the mathematical proof or a fresh kernel rebuild. Scientific acceptance, a Decision, or Standing. Provider-, host-, source-byte-, repository-, or tool-independent reproduction.
pass
Scientific meaning and state fidelity
Does not establish: A new proof, fresh kernel execution, semantic equivalence, or resolution of the cubic Erdős 94 conjecture. External source-owner review, upstream acceptance, or adoption. Scientific acceptance, a Decision, or Standing. Provider-, host-, source-byte-, repository-, or tool-independent reproduction.
pass
A check reports only its own scope. The Decision accepted the Claim, not the check.
Inspect evidenceReproduce checksStart work