Not evaluated
Bounded klt complements for Fano contractions (family 066)
The gist
In its release of October 6, 2026, OpenAI presents two manuscripts on bounded klt complements for Fano contractions.
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-066-bounded-klt-complements-fano-contractions-r1
@misc{discoveria-oai-fam-066-bounded-klt-complements-fano-contractions-r1,
author = {{DiscoverIA}},
title = {Bounded klt complements for Fano contractions (family 066)},
howpublished = {DiscoverIA registry, entry oai-fam-066-bounded-klt-complements-fano-contractions},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-066-bounded-klt-complements-fano-contractions#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Here “bounded” means that a quantity stays controlled by a value fixed in advance, and “klt” names a smoothness condition on the singularities of a geometric space. If the manuscripts were correct, the existence of bounded klt complements would be established for Fano contractions, a type of map between geometric spaces.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: its review field reads “unchecked”, and no third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 066.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 · Bounded-klt-complements…link only, reading not recorded
- Repositorygithub.com · Uniform-Cartier-sections…link only, reading not recorded
- Lean proofgithub.com · 066.mdpage read word for word
- Lean proofgithub.com · CartierChartCompactnessSup…link only, reading not recorded
Method
Two manuscripts dated September 25, 2026, attributed to an unreleased internal OpenAI model: “Bounded klt complements for Fano contractions” and “Uniform Cartier sections for Fano type contractions”. The formalisation is in lean/docs/066.md and lean/ComparatorChallenges/CartierChartCompactnessSupport.lean (1 Comparator statement); the family appears in the sources of formalization.yaml, and history.md reports no revision. 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 (Algebraic and complex geometry)
- In openai/math
- family 066, section “Algebraic and complex geometry”, 2 manuscripts dated Sep 25, 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 64 of 372, by family number
- Not evaluated : The generalized Mukai conjecture (family 063)
- Not evaluated : The μ-constant problem for surface singularities (family 064)
- Not evaluated : Virasoro constraints for complete intersections and projective bundles (family 065)
- Not evaluated : Bounded klt complements for Fano contractions (family 066)
- Not evaluated : The Campana–Peternell conjecture in dimension six (family 067)
- Not evaluated : Anticanonical nonvanishing under smooth semipositivity (family 068)
- Not evaluated : Quantum geometric Langlands at irrational level (family 069)
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