Reproduction tutorial · September 10, 2026
Independent verification of a published Lean artifact
These tutorials test the mechanism behind each paper at a practical scale. They do not reproduce frontier-scale headline results unless explicitly stated.
Source of this tutorial
This tutorial tests the mechanism behind reviewed development 03 in the immutable briefing of September 10, 2026.
Scope and limits
- Reproduction level
- artifact verification, not rediscovery
- Claim under test
- whether the published formal artifact builds cleanly offline and whether the machine-checked statement is the statement being claimed.
- Excluded claim
- this tutorial does not reproduce the discovery run, the roughly 10,000 concurrent agents, the 88 hours of discovery plus 17 hours of formalization, or the 130 billion output tokens.
- Reader, effort, and cost
- comfort with Lean and Mathlib; 6 to 12 hours; a workstation with sufficient memory. Near-zero cost beyond compute you already own.
- Prerequisites
- Lean toolchain manager, Git, and an offline build cache.
Canonical resources
- Vendor result announcement: https://openai.com/index/navier-stokes-solution/ (opens in a new tab)
- Artifact notice: Verify against the canonical repository referenced by the announcement. Discovery-run logs, agent orchestration code, and token accounting were not available for independent audit at review time.
Project plan
| Step | Stage | Effort |
|---|---|---|
| 01 | Pin the canonical repository | 45 minutes |
| 02 | Clean offline build | 2 to 6 hours |
| 03 | Statement audit | 2 hours |
| 04 | Axiom and sorry audit | 1 hour |
| 05 | Report | 1 hour |
01Pin the canonical repository(45 minutes)
Clone the canonical repository and record the commit hash, the Lean toolchain version, and the exact Mathlib revision from the lockfile.
02Clean offline build(2 to 6 hours)
Build from a clean checkout with the network disabled after dependency fetch. A build that requires unpinned downloads is a finding, not a pass. Artifact: full build log with timings.
03Statement audit(2 hours)
Read the top-level theorem statement and every definition it depends on. Confirm the formal statement matches the informal claim, including quantifiers, regularity assumptions, and the meaning of the singularity condition.
04Axiom and sorry audit(1 hour)
Print the axiom dependencies of the main theorem and search the tree for
sorry, admitted results, and unproven custom axioms. Record anything beyond the standard Mathlib axiom set.05Report(1 hour)
Publish the commit hashes, toolchain versions, build log, axiom list, and a plain-language restatement of exactly what was checked and what was not.
Controls, failure modes, and safety
Controlled variables
repository commit, Lean toolchain, Mathlib revision, build environment, and offline mode.
Failure modes
assuming a green build proves the informal claim, missing an added axiom, auditing a statement weaker than the announced result, and unpinned dependencies.
Safety
read-only verification of published mathematics. No safety hazard.