Not evaluated
The Falconer distance conjecture (family 073)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript on the Falconer distance conjecture, which it would treat in all dimensions.
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-073-falconer-distance-conjecture-r1
@misc{discoveria-oai-fam-073-falconer-distance-conjecture-r1,
author = {{DiscoverIA}},
title = {The Falconer distance conjecture (family 073)},
howpublished = {DiscoverIA registry, entry oai-fam-073-falconer-distance-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-073-falconer-distance-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript were correct, the Falconer conjecture would be treated in all dimensions. It asks whether a set of points that is large enough (in the sense of a dimension that can be fractional) has a set of distances of strictly positive measure, that is, one that takes up a non-zero part of the line of lengths.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI itself; no third-party check is recorded. The sources read do not say where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 073.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-Falconer-distance…link only, reading not recorded
- Lean proofgithub.com · 073.mdpage read word for word
- Lean proofgithub.com · FalconerAllDimensions.leanlink only, reading not recorded
- Lean proofgithub.com · PlanarFalconer.leanlink only, reading not recorded
Method
According to OpenAI, an unreleased internal model produced it. The openai/math repository holds the manuscript “The Falconer distance conjecture in all dimensions” (September 23, 2026) and lean/docs/073.md, with 2 Comparator statements (FalconerAllDimensions.lean and PlanarFalconer.lean). The file formalization.yaml carries “review: status: unchecked” and lists this family among its sources; history.md reports no revision of the 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Real and complex analysis)
- In openai/math
- family 073, section “Real and complex analysis”, 1 manuscript dated Sep 23, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 5 : 1 read word for word, 4 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 70 of 372, by family number
- Not evaluated : Quantum geometric Langlands at irrational level (family 069)
- Not evaluated : Koebe's circle-domain conjecture and circle-domain rigidity (family 071)
- Not evaluated : Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)
- Not evaluated : The Falconer distance conjecture (family 073)
- Not evaluated : Kakeya in three and four dimensions (family 074)
- Not evaluated : The L log L Fourier-convergence conjecture (family 075)
- Not evaluated : Ultraflat real Littlewood polynomials (family 076)
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