lean

Provenance

This repository is human-directed and materially AI-assisted formal research. Contribution credit and decision authority are recorded separately. Final authority over research direction, claim scope, public custody, compatibility surfaces, naming, and releases rests with the human author and operator. AI systems made substantial contributions to statements, proofs, countermodels, reviews, audits, documentation, and integration.

Human authorship and operator authority

By the operator’s account, James Beck defined the research program, selected the problems and claims to pursue, set the acceptance criteria and scope fences, and reviewed, revised, accepted, or rejected agent output throughout development. The operator alone:

At the local annotated v14.0.0 tag, whose target commit is ff491b8, all 221 reachable commits list James Beck in Git’s Author field. Co-author trailers and the functional record below identify material AI contributions; they do not transfer operator authority.

Human review is not proof evidence. Lean’s kernel checks elaborated proof terms against their declared environment. Repository gates separately check scoped build, axiom-footprint, custody, and target invariants. Operator review governs admission and the claims the project makes about checked artifacts.

AI-assisted collaboration

The work was iterative rather than a clean design-then-implementation handoff. Agents proposed formal shapes, wrote and repaired Lean, constructed adversarial examples, found false or overbroad statements, ran verification, and helped maintain the claim and custody records.

Formalization, proof engineering, and review

Lead sustained collaboration: Codex (OpenAI). The operator attributes the path through the later formalization campaign, culminating in v14, principally to Codex. Its material work included theorem and countermodel construction, proof repair, overlap and scope review, detection of vacuity and overclaim, axiom and footprint audits, documentation reconciliation, and adversarial review.

The repository preserves only part of that work as explicit attribution. Git contains the commits 8fd73eb (“codex-derived work”) and eb1ee75 (“codex audit of paper repo + other scraps”). The campaign record .governor/loop.json names Codex as hybrid builder and read-only adversarial auditor for the bounded-calculi/v7 work; docs/V9-RELEASE-LEDGER.md marks multiple formal artifacts and the Mathlib split as Codex-derived; and experiments/no_free_lift_wiring/WIRING-AUDIT.md records specific Codex-found counterexamples, scope corrections, and strengthening requests.

The operator reports additional Codex work in directed sessions and in the private research/skunkworks campaign. The public repository ties the promoted sources to reviewed source revisions, but cannot independently allocate every piece of private work among collaborators. No Codex Co-Authored-By trailer is reachable from the v14 tag; this is functional attribution from the cited records and operator account, not a claim that Codex alone originated every v14 definition or theorem.

Conceptual framing and theorem-shape critique

Lead collaboration: ChatGPT (OpenAI). It materially contributed to the conceptual and editorial loop: separating claim types, turning prose into bounded formal questions, proposing theorem shapes and countermodels, and sharpening hypotheses.

The repository records concrete examples in PAPER-MAP.md and CLAIM-REGISTER.md. ChatGPT caught the false first form of commitsToHysteretic_strict_mono, helped route the quantitative persistence proof ladder, and sharpened the witness-invariance boundary. The operator additionally attributes material contributions to the formalization-leading and runtime-conformance doctrine to ChatGPT discussions. By the operator’s account, these exchanges often shaped a statement before proof work began and therefore are not well measured by changed lines.

Implementation and repository integration

Material collaboration: Claude Code (Anthropic). Through the v14.0.0 tag, Git records 34 Co-Authored-By: Claude Fable 5 trailers and 14 Co-Authored-By: Claude Opus 4.8 (1M context) trailers. The Fable-labelled work is concentrated in the July bounded-calculi, custody-indexed, and v5–v8 campaigns. All 14 commits from the first v14 admission through v14 preparation carry the Opus trailer.

The v14 integration pass was rapid and required follow-up corrections. The history preserves that loop: stale target commentary, rung-5 public accounting, rung-7 axiom partitioning, and description-gate phrasing were corrected before the final v14 cut. Claude’s trailers are evidence of material implementation, extraction, integration, gate, and documentation work; they are not evidence of exclusive design ownership, mathematical correctness, or operator ratification.

Provenance basis and limits

This is a functional attribution record based on:

It is not a complete forensic reconstruction. Chat discussions, rejected drafts, private research-tree work, and reviews that prevented bad code may not appear in commit metadata. A commit trailer identifies collaboration on that commit, not the origin of every contained idea. A model may also have performed different roles in different sessions. The v14 ledgers record repeated adversarial review, but do not always identify every reviewing model; unnamed reviewers are not reconstructed here from inference.

Platform/tool names are used where exact model versions were not preserved. Exact version labels are repeated only where Git recorded them. The numerical Git counts above are frozen to the named v14 cut and will not silently describe later history.

What this document does not claim


This document reflects the repository state and operator record as of 2026-07-20 and may be revised when better evidence appears.