Human direction and agent implementation [connes-000R]

✍️sourceAGENTDRAFTED

This is a human-directed, substantially agent-implemented formalization and exposition project. The division of work was concrete.

Human mathematical and proof direction

• selected Zhou's theorem and required completion of every Zhou-internal argument, with property (T) for \(\mathrm {EL}_3(\mathbb F_2[t])\) as the single explicit external premise;
• fixed Zhou's Sections 2–7 as the proof order and required the overview to show one construction feeding factor equivalence, property (T), ICC, and nonisomorphism; and
• required comparison of the OpenAI, Zhou, and Anthropic proofs by the algebraic information each factor forgets, followed by the EJZK formalization outlook.

Human review and exposition contract

• required literature grounding, declaration-level provenance, public privacy boundaries, and Tau Ceti rubric review;
• required Linux Comparator verification with statement and axiom checks, confinement, Lean-kernel replay, and nanoda replay, while keeping technical acceptance distinct from mathematical audit;
• specified notes about the formalization rather than a restatement of the source papers, including proof architecture, mathematical weight, special designs, the threefold motivation, proof-family comparison, and unresolved boundaries; and
• reviewed rendered output and required corrections to headings, prose, diagrams, cross-references, navigation, privacy, and publication wording.

Agent implementation and review

• reconciled the literature and public Lean sources, adapted attributed proof blocks, implemented the Lean development, and refactored its public interfaces;
• ran literature, consumer-contract, provenance, semantic, and Tau Ceti reviews; built the Comparator, documentation, and rendering infrastructure; and repaired the resulting findings; and
• drafted and revised the mathematical notes, diagrams, comparisons, and formalization estimates under the human-specified structure and constraints.

The working cycle was: human proof and review contract \(\longrightarrow \) agent implementation \(\longrightarrow \) role-separated agent review and repair \(\longrightarrow \) human inspection and correction \(\longrightarrow \) approved landing.

Agent role separation is not independent human review; the project's audit ledger records the remaining review boundary. Public proof transfers are identified in the port map.