Not evaluated
Rigidity of the Turing degrees (family 241)
The gist
On October 6, 2026, OpenAI published a manuscript, dated September 24, 2026, devoted to the rigidity of the Turing degrees.
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-241-rigidity-turing-degrees-r1
@misc{discoveria-oai-fam-241-rigidity-turing-degrees-r1,
author = {{DiscoverIA}},
title = {Rigidity of the Turing degrees (family 241)},
howpublished = {DiscoverIA registry, entry oai-fam-241-rigidity-turing-degrees},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-241-rigidity-turing-degrees#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript held, it would add a new result on the rigidity of the Turing degrees. A Turing degree groups the sets of integers of equal computational difficulty: two sets have the same degree when each can be computed using the other. The subject belongs to mathematical logic.
What remains unclear
No third party is recorded as a checker, and the Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, marked “unchecked”. The sources read do not say which precise statement the manuscript claims to establish.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 241.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 · Rigidity-of-the-Turing…link only, reading not recorded
- Lean proofgithub.com · 241.mdpage read word for word
- Lean proofgithub.com · DegreeRigidity.leanlink only, reading not recorded
Method
OpenAI publishes in its openai/math repository the manuscript “Rigidity of the Turing degrees”, dated September 24, 2026, the only one of family 241. Lean supplied: lean/docs/241.md and lean/ComparatorChallenges/DegreeRigidity.lean (1 Comparator statement). The family is present in the `sources` of formalization.yaml; 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 (Mathematical logic)
- In openai/math
- family 241, section “Mathematical logic”, 1 manuscript dated Sep 24, 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 235 of 372, by family number
- Not evaluated : Optimal logarithmic mixing of the Thorp shuffle (family 238)
- Not evaluated : Sharp singularity rates for symmetric sign matrices (family 239)
- Not evaluated : Shelah's eventual categoricity conjecture (family 240)
- Not evaluated : Rigidity of the Turing degrees (family 241)
- Not evaluated : Single-fold Diophantine representations (family 242)
- Not evaluated : Choiceless counting does not capture polynomial time (family 243)
- Contested : The Partition Principle does not imply Choice (family 244)
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.