Not evaluated
The β-Barendregt–Geuvers–Klop conjecture (family 245)
The gist
On October 6, 2026, OpenAI announced, for the β-Barendregt–Geuvers–Klop conjecture, a manuscript on weak and strong normalisation in pure type systems.
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-245-beta-barendregtgeuversklop-conjecture-r1
@misc{discoveria-oai-fam-245-beta-barendregtgeuversklop-conjecture-r1,
author = {{DiscoverIA}},
title = {The β-Barendregt–Geuvers–Klop conjecture (family 245)},
howpublished = {DiscoverIA registry, entry oai-fam-245-beta-barendregtgeuversklop-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-245-beta-barendregtgeuversklop-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
Weak normalisation means that every well-typed term has at least one sequence of reductions that ends; strong normalisation, that every sequence ends. If the manuscript were correct, it would specify in which cases computation on typed terms eventually terminates.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI: the repository marks its review “unchecked”, and no third-party verification has been found. The sources read do not give the precise statement of the result.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 245.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 · Weak-and-strong…link only, reading not recorded
- Lean proofgithub.com · 245.mdpage read word for word
- Lean proofgithub.com · TypeSystemNormalization.le…link only, reading not recorded
Method
The manuscript “Weak and strong normalization in pure type systems” is dated September 25, 2026; family 245 has only this one, filed under the section “Mathematical logic” of overview.tex. The repository contains lean/docs/245.md and one Comparator statement (TypeSystemNormalization.lean, in lean/ComparatorChallenges). The family is absent from the sources of formalization.yaml, and 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 245, section “Mathematical logic”, 1 manuscript dated Sep 25, 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 239 of 372, by family number
- 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)
- Not evaluated : The β-Barendregt–Geuvers–Klop conjecture (family 245)
- Not evaluated : Cannon's conjecture (family 246)
- Not evaluated : An infinite finitely presented residually finite 2-group (family 247)
- Not evaluated : Thompson's group F is nonamenable (family 248)
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.