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Not evaluated

Optimal logarithmic mixing of the Thorp shuffle (family 238)

The gist

In its release of October 6, 2026, OpenAI claims, using an unreleased internal model, that the Thorp shuffle (a card shuffle) achieves optimal-order mixing.

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). Optimal logarithmic mixing of the Thorp shuffle (family 238) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/oai-fam-238-optimal-logarithmic-mixing-thorp-shuffle#releve-1

BibTeX @misc, key discoveria-oai-fam-238-optimal-logarithmic-mixing-thorp-shuffle-r1

@misc{discoveria-oai-fam-238-optimal-logarithmic-mixing-thorp-shuffle-r1,
  author       = {{DiscoverIA}},
  title        = {Optimal logarithmic mixing of the Thorp shuffle (family 238)},
  howpublished = {DiscoverIA registry, entry oai-fam-238-optimal-logarithmic-mixing-thorp-shuffle},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/oai-fam-238-optimal-logarithmic-mixing-thorp-shuffle#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/oai-fam-238-optimal-logarithmic-mixing-thorp-shuffle#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

If the result held, it would concern the speed at which this shuffle mixes a deck. The titles of the manuscripts in the family refer to partial permutations, Fourier bounds and “coordinate sweeps”.

What remains unclear

The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its formalization.yaml file marks it “unchecked”. No third-party verification is recorded. The title of the family speaks of optimal “logarithmic” mixing, but the sources read do not give the exact bound.

For experts

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

Status

Not evaluated

Recorded on · github.com · 238.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 : Optimal-order mixing of the Thorp shuffle (preprints/Optimal-order-mixing-of-the-Thorp-shuffle-September-26-2026), manuscrit : Random coordinate frames and partial permutation laws (preprints/Random-coordinate-frames-and-partial-permutation-laws-September-26-2026), manuscrit : From partial permutation information to Fourier bounds (preprints/From-partial-permutation-information-to-Fourier-bounds-September-26-2026), manuscrit : Conditional information under deterministic coordinate sweeps (preprints/Conditional-information-under-deterministic-coordinate-sweeps-September-26-2026), manuscrit : Conditional permutations in a revealed switching environment (preprints/Conditional-permutations-in-a-revealed-switching-environment-September-26-2026), manuscrit : Routing densities and representation contraction for Thorp sweeps (preprints/Routing-densities-and-representation-contraction-for-Thorp-sweeps-September-26-2026), manuscrit : Row–column symmetry and contraction of coordinate sweeps (preprints/Row-column-symmetry-and-contraction-of-coordinate-sweeps-September-26-2026), manuscrit : Random-subspace tests and trace smoothing for coordinate sweeps (preprints/Random-subspace-tests-and-trace-smoothing-for-coordinate-sweeps-September-26-2026), manuscrit : Compatibility entropy and the spectrum of a Thorp sweep (preprints/Compatibility-entropy-and-the-spectrum-of-a-Thorp-sweep-September-26-2026), manuscrit : Signed tensor densities and diagram budgets for the Thorp shuffle (preprints/Signed-tensor-densities-and-diagram-budgets-for-coordinate-sweeps-September-26-2026), manuscrit : Conditional coordinate sweeps and analytic transfer (preprints/Conditional-coordinate-sweeps-and-analytic-transfer-September-26-2026), manuscrit : A strict four-row permanent inequality and permutation moments (preprints/A-strict-four-row-permanent-inequality-and-permutation-moments-September-26-2026), Lean fourni par le revendicateur : lean/docs/238.md, 13 énoncé(s) Comparator (non vérifié par un tiers)

Sources

Method

The openai/math repository contains 12 manuscripts for this family, all dated September 26, 2026, including “Optimal-order mixing of the Thorp shuffle”. The file lean/docs/238.md describes the Lean formalisation, with 13 Comparator statements (13 files under lean/ComparatorChallenges/). The family is present in the `sources` of formalization.yaml; 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 (Probability and statistical mechanics)
In openai/math
family 238, section “Probability and statistical mechanics”, 12 manuscripts dated Sep 26, 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
27 : 1 read word for word, 26 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 232 of 372, by family number

See all 372 entries

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