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Not evaluated

The Boone–Higman conjecture and higher finiteness (family 250)

The gist

In its release of October 6, 2026, OpenAI announces three manuscripts on the Boone–Higman conjecture and on groups of type F-infinity, a higher finiteness property.

DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.

Status detailsDetails

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.

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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

DiscoverIA. (2026, October 12). The Boone–Higman conjecture and higher finiteness (family 250) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/oai-fam-250-boonehigman-conjecture-higher-finiteness#releve-1

BibTeX @misc, key discoveria-oai-fam-250-boonehigman-conjecture-higher-finiteness-r1

@misc{discoveria-oai-fam-250-boonehigman-conjecture-higher-finiteness-r1,
  author       = {{DiscoverIA}},
  title        = {The Boone–Higman conjecture and higher finiteness (family 250)},
  howpublished = {DiscoverIA registry, entry oai-fam-250-boonehigman-conjecture-higher-finiteness},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/oai-fam-250-boonehigman-conjecture-higher-finiteness#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/oai-fam-250-boonehigman-conjecture-higher-finiteness#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

A group has a decidable word problem when an algorithm can tell whether any product of its generating elements equals the identity element. If the second manuscript held, groups with a decidable word problem would have simple overgroups of type F-infinity. The first manuscript concerns “finite algebraic envelopes” and the Boone–Higman conjecture, and the third a “universal group” of type F-infinity.

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.

For experts

Sources, method, key facts, status history, report an error

Status

Not evaluated

Recorded on · github.com · 250.md

Step 1 of 4 on the scale: not evaluated. Next step: under review.

  1. Announced
  2. Recordednot evaluated
  3. 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.

Full history

Proofs
manuscrit : Finite algebraic envelopes and the Boone–Higman conjecture (preprints/Finite-algebraic-envelopes-and-the-Boone-Higman-conjecture-September-23-2026), manuscrit : Simple F∞ overgroups of groups with decidable word problem (preprints/Simple-F-infinity-overgroups-of-groups-with-decidable-word-problem-September-23-2026), manuscrit : A universal group of type F∞ (preprints/A-universal-group-of-type-F-infinity-September-23-2026), Lean fourni par le revendicateur : lean/docs/250.md, 3 énoncé(s) Comparator (non vérifié par un tiers)

Sources

Method

The openai/math repository contains three manuscripts dated September 23, 2026, including “Finite algebraic envelopes and the Boone–Higman conjecture”. The other two are titled “Simple F∞ overgroups of groups with decidable word problem” and “A universal group of type F∞”. The file lean/docs/250.md describes the Lean formalisation (3 Comparator statements); the family is listed 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 (Group theory)
In openai/math
family 250, section “Group theory”, 3 manuscripts dated Sep 23, 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
8 : 1 read word for word, 7 links only
This entry
AI draft, not reviewed

Status history

Only one observation so far.

  1. 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 244 of 372, by family number

See all 372 entries

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