Not evaluated
Torus polynomials and the Majority function: announced resolution of two open problems, found and formalised in Lean with GPT-6 Astra (Wesonga)
The gist
On October 13, 2026, Saint Wesonga posted on arXiv the resolution of two open problems on torus polynomials and the Majority function, results discovered and formalised in Lean with GPT-6 Astra.
DiscoverIA status on October 24, 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 24, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 24, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-wesonga-polynomes-majorite-tore-2026-10-13-r1
@misc{discoveria-wesonga-polynomes-majorite-tore-2026-10-13-r1,
author = {{DiscoverIA}},
title = {Torus polynomials and the Majority function: announced resolution of two open problems, found and formalised in Lean with GPT-6 Astra (Wesonga)},
howpublished = {DiscoverIA registry, entry wesonga-polynomes-majorite-tore-2026-10-13},
note = {Status “Not evaluated”, snapshot 1, recorded on October 24, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/wesonga-polynomes-majorite-tore-2026-10-13#releve-1},
urldate = {2026-10-24}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Torus polynomials approximate a Boolean function modulo the integers; they were introduced as a route to showing that the Majority function lies outside a class of Boolean circuits with modular gates, ACC^0. If the results held, they would answer two of the five open problems posed by Krishan and Vishwanathan, on integer lifts and explicit polynomial approximations.
What remains unclear
The Lean code comes from the author, who wrote the paper alone, and no third party has reviewed the statements or the text yet. A formalisation checks the proof of a statement, not that the statement faithfully captures the problem posed.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · arxiv.org · abs/2610.19174
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 sourcearxiv.org · abs/2610.19174page read word for word · consulted on Oct 24, 2026 ·
The results presented were discovered and formalized in Lean using GPT-6 Astra.
- Paperarxiv.org · html/2610.19174page read word for word · consulted on Oct 24, 2026 ·
We resolve two of these, concerning integer lifts and explicit polynomial approximations.
- Lean proofgithub.comlink only, reading not recorded
Method
GPT-6 Astra discovered the results and formalised them in Lean 4 with Mathlib, starting from the circuit-complexity framework Saint Wesonga had built for PARITY lower bounds. The author guided the choice of questions and the scope, and is responsible for the claims and the final text. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 24, 2026 from arxiv.org (page read, quotation checked word for word: “The results presented were discovered and formalized in Lean using GPT-6 Astra.”).
Limits
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
- Saint Wesonga, with GPT-6 Astra (OpenAI)
announced on Oct 13, 2026 - Nature
- new result
- Field
- Theoretical computer science (circuit complexity / torus polynomials)
- Checked by
- no verifier identified
- Sources
- 3 : 2 read word for word, 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
arXiv preprint, not peer-reviewed; Lean supplied by the author only; no third-party evaluation found
Source: arxiv.orgread word for word
An observation is added; none is ever erased.
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