Not evaluated
Choiceless counting does not capture polynomial time (family 243)
The gist
On October 6, 2026, OpenAI claimed that choiceless polynomial time with counting does not capture polynomial time; a second manuscript compares a symmetric choice with that framework.
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-243-choiceless-counting-does-not-capture-r1
@misc{discoveria-oai-fam-243-choiceless-counting-does-not-capture-r1,
author = {{DiscoverIA}},
title = {Choiceless counting does not capture polynomial time (family 243)},
howpublished = {DiscoverIA registry, entry oai-fam-243-choiceless-counting-does-not-capture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-243-choiceless-counting-does-not-capture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Choiceless polynomial time with counting is a framework of computation that never arbitrarily picks one element among equivalent ones, but can count. If the first manuscript held up, this framework would not express everything that a polynomial-time computation decides; the second would place a “witnessed symmetric choice” strictly above it.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is provided by OpenAI alone, and its review is marked “unchecked”; it is not known whether a third party has checked it. The titles do not give the exact setting or the assumptions of these statements.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 243.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 · Choiceless-polynomial…link only, reading not recorded
- Repositorygithub.com · Witnessed-symmetric…link only, reading not recorded
- Lean proofgithub.com · 243.mdpage read word for word
- Lean proofgithub.com · ChoicelessPolynomialTime.l…link only, reading not recorded
- Lean proofgithub.com · WitnessedChoice.leanlink only, reading not recorded
Method
First manuscript, dated September 23, 2026: “Choiceless polynomial time with counting does not capture polynomial time”. The second manuscript, dated September 24, 2026: “Witnessed symmetric choice is strictly stronger than choiceless polynomial time with counting”. The repository provides lean/docs/243.md and two Comparator files, ChoicelessPolynomialTime.lean and WitnessedChoice.lean; the family is noted as “présente des `sources` de 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 (Mathematical logic)
- In openai/math
- family 243, section “Mathematical logic”, 2 manuscripts 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
- 6 : 1 read word for word, 5 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 237 of 372, by family number
- 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)
- Not evaluated : The β-Barendregt–Geuvers–Klop conjecture (family 245)
- Not evaluated : Cannon's conjecture (family 246)
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