State of Proof

2026-08-01-openai-nonsofic-group · Group theory

The unit group of the binary Leavitt algebra L_F₂(1,2) is not sofic

Intake record · four gates mapped · no audit gate has run

Current record status

What this docket currently establishes

Intake record · four gates mapped · no audit gate has run. This docket identifies what has been checked and what remains open. It does not validate or reject the manuscript's headline claim beyond the explicitly stated scope.

Claim
The unit group of the binary Leavitt algebra L_F₂(1,2) is not sofic
Source version
Updated Ten Advances manuscript · updated 2026-08-06
Source SHA-256
ebc561ab5c53dbd240e17a8fdb6fffeb648591eca85dbfc7466f563638f8c566
Source locked
Last material update
Next open step
Reconcile the substantively revised August 6 prose with the August 2 Lean commit before any formal replay is treated as relevant

One-minute summary

Chapter 3 of OpenAI's updated Ten Advances manuscript claims that the binary Leavitt algebra's unit group is not sofic. The pinned Lean commit predates a substantive prose revision by four days. Paper-to-Lean and version correspondence is therefore the first gate; no build or mathematical audit has run.

Scope of this docket

The planned audit covers original-to-revised source lineage, paper-to-Lean correspondence, a fresh pinned formal replay, the exact hypotheses of cited theorems, and an independent specialist reconstruction of the revised proof.

Claim and dependency map

  1. G1 · claim mapped

    Paper-to-Lean and August 2/August 6 version correspondence

    Depends on: original PDF · revised PDF · pinned commit

  2. G2 · claim mapped

    Fresh pinned formal replay and axiom closure

    Depends on: G1

  3. G3 · claim mapped

    Cited-theorem hypothesis table

    Depends on: primary literature

  4. G4 · claim mapped

    Independent audit of the revised expander and Leavitt-algebra route

    Depends on: G1 · G3

Evidence routes

formal
Planned: build and kernel-check the pinned Lean target, then keep its result separate from prose correspondence.
literature
Planned: exact-hypothesis table for every load-bearing cited theorem.
expert
Planned: independent group-theory reconstruction of the August 6 proof route.

Findings and scope limits

  1. No Lean build, replay, or mathematical audit gate has run in this lab.

  2. The August 2 Lean commit predates the substantive August 6 manuscript revision, so repository proximity cannot establish correspondence.

Open Steps—where expert eyes are needed

Group theory and formal verification · audit not started

Which exact Lean endpoints, witnesses, and definitions correspond to the revised paper's unit-group claim?

The formal artifact predates the revised proof and may encode a materially different route or endpoint.

Source record and provenance

The updated Chapter 3 is the audit target. The original PDF is preserved separately. No journal or referee disposition is asserted in the locked sources.

Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case.

Retrieved .

Version and record history

  1. new docket

    2026-08-01-openai-nonsofic-group

    Updated and original manuscripts plus Lean commit locked; four gates mapped; no gate run

  2. source updated

    2026-08-01-openai-nonsofic-group

    OpenAI published a substantive Chapter 3 revision; the August 2 Lean commit predates it

Statuses describe evidence collected for a defined scope. They are not peer-review decisions, publication recommendations, or certificates of mathematical truth.