Human direction and agent implementation [connes-000R]
Human direction and agent implementation [connes-000R]
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.
Human direction in recent refactoring
- requested repeated searches against the pinned Mathlib API, simplification of the challenge, and proof golf while preserving the exact theorem contract;
- treated heartbeat overrides as performance and refactor signals, required measured thresholds, and requested review of overlapping APIs and preparation of the Palomar metadata; and
- required the companion notes to track the Lean changes and identified
Agent implementation and review
- reconciled the literature and public Lean sources, adapted attributed proof blocks, implemented the Lean development, and refactored its public interfaces;
- implemented the resulting Mathlib reuse, action-indexed definitions, challenge and proof golf, measured heartbeat cleanup, and bicommutant simplification;
- ran full builds, Linux Comparator and nanoda checks, Lean-kernel replay, and clean-room reviews; reconciled the changes with the literature and public source; and repaired the resulting findings; and
- prepared the Palomar metadata and public documentation, then synchronized 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.