Not evaluated
Counterexamples to Zariski's multiplicity conjecture (family 059)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, counterexamples to Zariski's multiplicity conjecture, a question in geometry.
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-059-counterexamples-zariskis-multiplicity-r1
@misc{discoveria-oai-fam-059-counterexamples-zariskis-multiplicity-r1,
author = {{DiscoverIA}},
title = {Counterexamples to Zariski's multiplicity conjecture (family 059)},
howpublished = {DiscoverIA registry, entry oai-fam-059-counterexamples-zariskis-multiplicity},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-059-counterexamples-zariskis-multiplicity#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Zariski's multiplicity conjecture states that two ambiently homeomorphic hypersurfaces near an isolated singularity have the same multiplicity, a number measuring how “pinched” the surface is at that point. This means that a homeomorphism of the surrounding space carries one onto the other. If the manuscripts held, ambiently homeomorphic hypersurfaces with different multiplicities would exist, which would contradict the conjecture; their titles cite multiplicities two and three, then four and five.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment 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 · 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 · …hypersurfaces-of…link only, reading not recorded
- Repositorygithub.com · …germs-in-C4-with…link only, reading not recorded
Method
In the openai/math repository, family 059 comprises two manuscripts: "Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three" (dated September 24, 2026) and "Ambiently homeomorphic isolated hypersurface germs in ℂ⁴ with multiplicities four and five" (dated September 27, 2026). No revision is reported in history.md. The absence of Lean is inferred from the absence of the file lean/docs/059.md; OpenAI's README states that not all manuscripts have a Lean formalisation. 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 (Algebraic and complex geometry)
- In openai/math
- family 059, section “Algebraic and complex geometry”, 2 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 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 58 of 372, by family number
- Not evaluated : Termination of fourfold minimal model programs (family 056)
- Not evaluated : Campana's abelianity conjecture and special varieties (family 057)
- Not evaluated : The Kollár–Pardon universal-cover conjecture (family 058)
- Not evaluated : Counterexamples to Zariski's multiplicity conjecture (family 059)
- Not evaluated : The Global Spherical Shell conjecture (family 060)
- Not evaluated : The LeBrun–Salamon conjecture and projective contact classification (family 062)
- Not evaluated : The generalized Mukai conjecture (family 063)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.