Not evaluated
The purely cosmetic surgery conjecture for knots in S³ (family 306)
The gist
On October 6, 2026, OpenAI published a manuscript on purely cosmetic surgery on knots in the three-sphere, from an unreleased internal model.
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-306-purely-cosmetic-surgery-conjecture-knots-s-3-r1
@misc{discoveria-oai-fam-306-purely-cosmetic-surgery-conjecture-knots-s-3-r1,
author = {{DiscoverIA}},
title = {The purely cosmetic surgery conjecture for knots in S³ (family 306)},
howpublished = {DiscoverIA registry, entry oai-fam-306-purely-cosmetic-surgery-conjecture-knots-s-3},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-306-purely-cosmetic-surgery-conjecture-knots-s-3#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
This manuscript belongs to topology (section “Topology” of overview.tex). If the manuscript were correct, it would provide a result on the conjecture the family is named after.
What remains unclear
The sources read do not state the manuscript's result. No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and the sources read report no third-party assessment.
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 · Purely-Cosmetic-Surgery…link only, reading not recorded
Method
The manuscript “Purely cosmetic surgery on knots in the three-sphere”, dated September 23, 2026, is the only one of family 306 listed in CONTENTS.md of the openai/math repository. There is no lean/docs/306.md; the repository README states: “Not all have accompanying Lean formalizations.” 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).
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 (Topology)
- In openai/math
- family 306, section “Topology”, 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 300 of 372, by family number
- Not evaluated : From ordinary to strong pure infiniteness (family 303)
- Not evaluated : The Hilbert–Smith conjecture in every dimension (family 304)
- Not evaluated : Counterexamples to disk embedding and Wall's manifold conjecture (family 305)
- Not evaluated : The purely cosmetic surgery conjecture for knots in S³ (family 306)
- Not evaluated : Failure of rational injectivity for maximal coarse assembly (family 307)
- Not evaluated : Smith–Toda complexes at every height with varying primes (family 308)
- Not evaluated : The Kervaire invariant problem at the prime three (family 309)
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