Not evaluated
The higher-dimensional Erdős distinct-distances conjecture (family 166)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on the higher-dimensional Erdős distinct-distances conjecture.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-166-higher-dimensional-erdos-distinct-distances-r1
@misc{discoveria-oai-fam-166-higher-dimensional-erdos-distinct-distances-r1,
author = {{DiscoverIA}},
title = {The higher-dimensional Erdős distinct-distances conjecture (family 166)},
howpublished = {DiscoverIA registry, entry oai-fam-166-higher-dimensional-erdos-distinct-distances},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-166-higher-dimensional-erdos-distinct-distances#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript were correct, it would bring a result on the higher-dimensional Erdős distinct-distances conjecture. The title repeats the name of the conjecture, and the sources read do not say what the manuscript establishes exactly. Higher dimension means points located by more than two coordinates.
What remains unclear
No Lean file (Lean is a language in which a computer checks every step of a proof) is supplied, and no third-party evaluation is recorded. It is not known whether specialists have reviewed the manuscript.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · The-higher-dimensional…link only, reading not recorded
Method
According to CONTENTS.md, family 166 comprises one manuscript: “The higher-dimensional Erdős distinct-distances conjecture”. It is dated September 23, 2026 and filed under the section “Combinatorics” of overview.tex. history.md reports no revision of this manuscript. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Combinatorics)
- In openai/math
- family 166, section “Combinatorics”, 1 manuscript dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 160 of 372, by family number
- Not evaluated : Counterexamples to Ryser's covering and Gyárfás's tree-cover conjectures (family 162)
- Not evaluated : Hindman's finite sums and products conjecture (family 164)
- Not evaluated : Exact crossing numbers of complete and complete bipartite graphs (family 165)
- Not evaluated : The higher-dimensional Erdős distinct-distances conjecture (family 166)
- Not evaluated : Pinned distances and a power saving for planar unit distances (family 167)
- Not evaluated : Combinatorial invariance of Kazhdan–Lusztig polynomials (family 168)
- Not evaluated : The Shareshian–Wachs e-positivity conjecture (family 169)
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