Not evaluated
The quasilinear PCP-for-PPAD conjecture (family 136)
The gist
On October 6, 2026, OpenAI announced a quasilinear reduction for the PCP-for-PPAD conjecture, 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-136-quasilinear-pcp-ppad-conjecture-r1
@misc{discoveria-oai-fam-136-quasilinear-pcp-ppad-conjecture-r1,
author = {{DiscoverIA}},
title = {The quasilinear PCP-for-PPAD conjecture (family 136)},
howpublished = {DiscoverIA registry, entry oai-fam-136-quasilinear-pcp-ppad-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-136-quasilinear-pcp-ppad-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript were correct, it would bring, according to its title, a quasilinear reduction for the PCP-for-PPAD conjecture. A reduction turns one problem into another, and quasilinear means growth only slightly faster than the size of the input. PCPs are proofs that can be checked by reading only a few pieces of them chosen at random, and PPAD is a class of computational problems of which finding an equilibrium is an example.
What remains unclear
No Lean proof (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party assessment is recorded. The sources read give only the manuscript's title, not its exact statement.
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 · The-PCP-for-PPAD…link only, reading not recorded
Method
The openai/math repository contains one manuscript, “The PCP-for-PPAD conjecture: a quasilinear reduction”, dated September 25, 2026. It is filed under the section “Theoretical computer science” (overview.tex). The file lean/docs/136.md does not exist, and OpenAI's README states that not all manuscripts have a Lean formalisation. history.md reports no revision of this manuscript. 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: “Not all have accompanying Lean formalizations.”).
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
- Theoretical computer science
- In openai/math
- family 136, section “Theoretical computer science”, 1 manuscript dated Sep 25, 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 132 of 372, by family number
- Not evaluated : The complexity of Weisfeiler–Leman refinement (family 133)
- Not evaluated : Generalized star height at most three (family 134)
- Not evaluated : Sharp homogeneous depth-five complexity of matrix products (family 135)
- Not evaluated : The quasilinear PCP-for-PPAD conjecture (family 136)
- Not evaluated : One-tape time simulation in two-fifths-power space (family 137)
- Not evaluated : Subset Sum in O(2^(0.49n)) time (family 138)
- Not evaluated : Subpolynomial queries for log-concave sampling (family 139)
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