# Distinct-distance point-set reference

Family 166: The higher-dimensional Erdős distinct-distances conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Geometry researchers can assess worst-case distinct-distance counts in fixed dimensions at least three.

## Applicability and commercial boundary

A lower bound on distance diversity is not a sensor-localization solver or a finite configuration constructor; dimension constants matter.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Identify an exact finite dataset and a use requiring this bound.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The higher-dimensional Erdős distinct-distances conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-higher-dimensional-Erdos-distinct-distances-conjecture-September-23-2026/paper.pdf).