Not evaluated
Complex counterexamples to cancellation and affine fibrations (family 047)
The gist
On October 6, 2026, OpenAI published a manuscript, from an unreleased internal model, on an explicit failure of cancellation in complex affine spaces.
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-047-complex-counterexamples-cancellation-affine-r1
@misc{discoveria-oai-fam-047-complex-counterexamples-cancellation-affine-r1,
author = {{DiscoverIA}},
title = {Complex counterexamples to cancellation and affine fibrations (family 047)},
howpublished = {DiscoverIA registry, entry oai-fam-047-complex-counterexamples-cancellation-affine},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-047-complex-counterexamples-cancellation-affine#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The cancellation problem concerns algebraic varieties: can two of them be different and yet become equivalent once multiplied by the same affine space (a flat space)? If the manuscript were correct, it would give, according to its title, an explicit example over the complex numbers.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and no verification by a third party 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 · 047.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 · An-explicit-failure-of…link only, reading not recorded
- Lean proofgithub.com · 047.mdpage read word for word
- Lean proofgithub.com · ComplexCancellation.leanlink only, reading not recorded
Method
The manuscript “An explicit failure of complex affine-space cancellation” is dated September 23, 2026. OpenAI supplies lean/docs/047.md, which describes the scope of the Lean formalisation, with one Comparator statement (lean/ComparatorChallenges/ComplexCancellation.lean); formalization.yaml carries “review: status: unchecked”. 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 (Algebraic and complex geometry)
- In openai/math
- family 047, section “Algebraic and complex geometry”, 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
- 4 : 1 read word for word, 3 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 46 of 372, by family number
- Not evaluated : P=W for fixed-determinant moduli spaces (family 043)
- Not evaluated : The equivariant cohomological Hikita conjecture for quivers (family 044)
- Not evaluated : Counterexamples to Shafarevich holomorphic convexity (family 046)
- Not evaluated : Complex counterexamples to cancellation and affine fibrations (family 047)
- Not evaluated : A characteristic-zero counterexample to Lipman–Zariski (family 048)
- Not evaluated : A stable-coordinate counterexample in four variables (family 049)
- Not evaluated : A counterexample to Griffiths' positivity conjecture (family 050)
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