Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 166-01. The higher-dimensional Erdős distinct-distances conjecture
Manuscript map · lines 5505–5514
OpenAI@2026-10-07#rem:oai-p-166-01
Authors: OpenAI. Family 166.
Title: The higher-dimensional Erdős distinct-distances conjecture.
Abstract: For every fixed integer d ≥ 3, we prove that every set of n ≥ 2 distinct points in ℝd determines at least $c_d n{}{2/d}$ distinct distances, where $c_d{}gt 0$ depends only on d. This resolves the higher-dimensional Erdős distinct-distances conjecture positively.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros