Not evaluated
Torus-packet equidistribution in prime, quartic, and sextic degrees (family 015)
The gist
On October 6, 2026, OpenAI claims, with an unreleased internal model, to have established the equidistribution of “torus packets” in prime, quartic and sextic 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-015-torus-packet-equidistribution-prime-quartic-r1
@misc{discoveria-oai-fam-015-torus-packet-equidistribution-prime-quartic-r1,
author = {{DiscoverIA}},
title = {Torus-packet equidistribution in prime, quartic, and sextic degrees (family 015)},
howpublished = {DiscoverIA registry, entry oai-fam-015-torus-packet-equidistribution-prime-quartic},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-015-torus-packet-equidistribution-prime-quartic#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 three manuscripts were correct, the equidistribution of these “torus packets” would be established in three cases: prime degree with arbitrary local type, primitive quartic degree for arbitrary orders, and primitive sextic degree.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) supplied by OpenAI itself contains only one statement for the family, and its tracking file marks it as unchecked. No third-party verification is recorded, and the sources read do not detail how much of the three manuscripts that statement covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 015.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 · Equidistribution-of-Prime…link only, reading not recorded
- Repositorygithub.com · …Quartic-Torus-Packets-for…link only, reading not recorded
- Repositorygithub.com · …Sextic-Torus-Packets…link only, reading not recorded
- Lean proofgithub.com · 015.mdpage read word for word
- Lean proofgithub.com · DukePrimeDegree.leanlink only, reading not recorded
Method
The openai/math repository contains three manuscripts: “Equidistribution of Prime-Degree Torus Packets with Arbitrary Local Type” (September 24, 2026), “Equidistribution of primitive quartic torus packets for arbitrary orders” and “Equidistribution of Primitive Sextic Torus Packets” (both dated October 5, 2026). The file lean/docs/015.md describes the Lean formalisation (lean/ComparatorChallenges/DukePrimeDegree.lean); the family is not among 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 (Number theory)
- In openai/math
- family 015, section “Number theory”, 3 manuscripts 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
- 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 15 of 372, by family number
- Not evaluated : Independent largest prime factors of consecutive integers (family 012)
- Not evaluated : Ostmann's inverse Goldbach conjecture (family 013)
- Not evaluated : Restricted geometric Langlands, generic Ramanujan and Arthur parameters (family 014)
- Not evaluated : Torus-packet equidistribution in prime, quartic, and sextic degrees (family 015)
- Not evaluated : Zilber–Pink in abelian varieties and the Siegel threefold (family 016)
- Not evaluated : OpenAI claims the irrationality exponent of π is 2 (family 017)
- Not evaluated : The Margulis–Platonov conjecture over global fields (family 018)
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.