Not evaluated
Patterson’s first moment for cubic Gauss sums (family 023)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript said to treat, unconditionally, Patterson's first moment (an average) for cubic Gauss sums.
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-023-pattersons-first-moment-cubic-gauss-sums-r1
@misc{discoveria-oai-fam-023-pattersons-first-moment-cubic-gauss-sums-r1,
author = {{DiscoverIA}},
title = {Patterson’s first moment for cubic Gauss sums (family 023)},
howpublished = {DiscoverIA registry, entry oai-fam-023-pattersons-first-moment-cubic-gauss-sums},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-023-pattersons-first-moment-cubic-gauss-sums#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Cubic Gauss sums are sums of complex numbers from number theory. If the manuscript were correct, their first moment would be treated without relying on an unproved hypothesis, as the word “unconditional” in its title indicates.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: its review field reads “unchecked”, and no third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 023.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 · An-unconditional-first…link only, reading not recorded
- Lean proofgithub.com · 023.mdpage read word for word
- Lean proofgithub.com · PattersonFirstMoment.leanlink only, reading not recorded
Method
The manuscript “An unconditional first moment for cubic Gauss sums” is dated September 25, 2026 and attributed to an unreleased internal OpenAI model. The formalisation is in lean/docs/023.md and lean/ComparatorChallenges/PattersonFirstMoment.lean (1 Comparator statement); the family is absent from the sources of formalization.yaml, and history.md reports no revision of the 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: “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 023, section “Number theory”, 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 23 of 372, by family number
- Not evaluated : Squarefree quartics and power-free polynomial values (family 020)
- Not evaluated : A quadratic bound for Jacobsthal's function (family 021)
- Not evaluated : The weak inhomogeneous Duffin–Schaeffer conjecture (family 022)
- Not evaluated : Patterson’s first moment for cubic Gauss sums (family 023)
- Not evaluated : An asymptotic formula for the number of totients (family 024)
- Not evaluated : Erdős’s short Egyptian-fraction conjecture (family 025)
- Not evaluated : Positive lower density of large prime gaps (family 026)
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