Not evaluated
Squarefree quartics and power-free polynomial values (family 020)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on squarefree values of quartic polynomials and power-free values of polynomials.
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-020-squarefree-quartics-power-free-polynomial-r1
@misc{discoveria-oai-fam-020-squarefree-quartics-power-free-polynomial-r1,
author = {{DiscoverIA}},
title = {Squarefree quartics and power-free polynomial values (family 020)},
howpublished = {DiscoverIA registry, entry oai-fam-020-squarefree-quartics-power-free-polynomial},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-020-squarefree-quartics-power-free-polynomial#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 establish, going by its title, a result on the squarefree values (not divisible by any square of an integer other than 1) taken by polynomials of degree four, and another on the power-free values of more general polynomials. The repository files this family under the section “Number theory”.
What remains unclear
No check of the Lean supplied by OpenAI (a language in which a computer checks every step of a proof) by a third party, nor any other independent assessment, is recorded. The sources read detail neither the exact statement of the manuscript nor how much of it the Lean covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 020.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 · Squarefree-values-of…link only, reading not recorded
- Lean proofgithub.com · 020.mdpage read word for word
- Lean proofgithub.com · PowerFreeValues.leanlink only, reading not recorded
Method
The manuscript in the openai/math repository is titled “Squarefree values of quartics and power-free values of polynomials” and is dated September 24, 2026. OpenAI supplies lean/docs/020.md and one Lean file, lean/ComparatorChallenges/PowerFreeValues.lean (one Comparator statement); formalization.yaml carries “review: status: unchecked” and lists the family in its sources. 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 020, section “Number theory”, 1 manuscript 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
- 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 20 of 372, by family number
- Not evaluated : OpenAI claims the irrationality exponent of π is 2 (family 017)
- Not evaluated : The Margulis–Platonov conjecture over global fields (family 018)
- Not evaluated : The p-adic section conjecture (family 019)
- 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)
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