Not evaluated
Fourier transforms below n log n
Family 130
The gist
In its release of October 6, 2026, OpenAI announces, using an unreleased internal model, an explicit power saving for the exact discrete Fourier transform.
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-130-fourier-transforms-below-n-n-r1
@misc{discoveria-oai-fam-130-fourier-transforms-below-n-n-r1,
author = {{DiscoverIA}},
title = {Fourier transforms below n log n (family 130)},
howpublished = {DiscoverIA registry, entry oai-fam-130-fourier-transforms-below-n-n},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-130-fourier-transforms-below-n-n#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The discrete Fourier transform breaks a sequence of values down into frequencies. According to the family's title, the saving would concern a number of operations below n log n, where n is the size of the sequence.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it as unchecked. No third-party verification is recorded, and the sources read give only the manuscripts' titles, not their statements; the expression “power saving” is not defined in them.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 130.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-explicit-power-saving…link only, reading not recorded
- Repositorygithub.com · Finite-tensor-savings-and…link only, reading not recorded
- Lean proofgithub.com · 130.mdpage read word for word
- Lean proofgithub.com · ExactFourier.leanlink only, reading not recorded
- Lean proofgithub.com · UniformFourier.leanlink only, reading not recorded
Method
The openai/math repository contains two manuscripts dated September 25, 2026, “An explicit power saving for the exact discrete Fourier transform” and “Finite tensor savings and exact Fourier circuits”, and the file lean/docs/130.md, which describes the Lean formalisation with two Comparator statements (lean/ComparatorChallenges/ExactFourier.lean and lean/ComparatorChallenges/UniformFourier.lean). The family is among the sources of formalization.yaml; history.md reports no revision of these manuscripts. 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
- Theoretical computer science
- In openai/math
- family 130, section “Theoretical computer science”, 2 manuscripts 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
- 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 126 of 372, by family number
- Not evaluated : The asymptotic Gotsman–Linial conjecture (family 127)
- Not evaluated : A factor-two approximation for shortest common superstring (family 128)
- Not evaluated : Exponential state costs for two-way automata (family 129)
- Not evaluated : Fourier transforms below n log n (family 130)
- Not evaluated : Polynomial mixing of graph switches with prescribed degrees (family 131)
- Not evaluated : A counterexample to the quadratic sensitivity conjecture (family 132)
- Not evaluated : The complexity of Weisfeiler–Leman refinement (family 133)
Related frontiers
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.