Not evaluated
Kadison's similarity conjecture (family 288)
The gist
On October 6, 2026, OpenAI announced a manuscript filed under the title “Kadison's similarity conjecture”.
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-288-kadisons-similarity-conjecture-r1
@misc{discoveria-oai-fam-288-kadisons-similarity-conjecture-r1,
author = {{DiscoverIA}},
title = {Kadison's similarity conjecture (family 288)},
howpublished = {DiscoverIA registry, entry oai-fam-288-kadisons-similarity-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-288-kadisons-similarity-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
According to its title, the manuscript concerns Kadison's similarity theorem, approached through uniform estimates on derivations. If it held, it would provide that route to a proof.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and formalization.yaml marks it “unchecked”. No third-party evaluation is read, and the sources do not say exactly what the manuscript establishes.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 288.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 · Kadisons-similarity…link only, reading not recorded
- Lean proofgithub.com · 288.mdpage read word for word
- Lean proofgithub.com · KadisonSimilarity.leanlink only, reading not recorded
- Lean proofgithub.com · UniformCommutator.leanlink only, reading not recorded
Method
One manuscript, “Kadison's similarity theorem through uniform derivation estimates”, dated September 23, 2026. Lean supplied by OpenAI: 2 Comparator statements (KadisonSimilarity.lean, UniformCommutator.lean), described in lean/docs/288.md; family absent from the “sources” of formalization.yaml. 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 (Operator algebras)
- In openai/math
- family 288, section “Operator algebras”, 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 282 of 372, by family number
- Not evaluated : Counterexamples to Baum–Connes and Kadison–Kaplansky (family 285)
- Not evaluated : Arithmetic rigidity of lattice von Neumann algebras (family 286)
- Not evaluated : Isomorphism of free group factors (family 287)
- Not evaluated : Kadison's similarity conjecture (family 288)
- Not evaluated : The strong Kadison–Kastler conjecture (family 289)
- Not evaluated : Connes' bicentralizer conjecture and relative bicentralizers (family 290)
- Not evaluated : Toms–Winter and equivariant Jiang–Su stability (family 291)
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