What This Establishes and What Remains Open

What it closes. The autonomous operator is fully specified — law (dx/dt = −ax + u), least-cost solution (u = ax), capacity limit (u ≤ u_max), method (minimise control variance), and filter (zero response to verified noise). Coupled operators are specified by the link, the cascade, and the firewall. Exit is specified as optimal stopping. The terminal ethic is grounded structurally: mutual non-extraction between self-maintaining agents is the control-theoretic content of kindness.

What remains open. Debt D1 (partially closed): Theorem VI.2 establishes network containment — the persistent set is net-positive — conditionally on the operator properties. What remains owed is the quantitative within-class criterion: the precise conditions on the drift rates, control margins, and coupling strength under which a link is net-positive, together with the basins and the collapse rates.

Structural relationships. AP02 is the human-scale projection of AP01’s programme (Appendix A). Its six axioms A1–A6 are projections of {S, B, R, C} (Appendix B): A1 and A3 and A6 from Axiom C, A2 from Axiom R, A4 from Axioms B and R, A5 from Axiom B. AP43’s four-term system supplies the reading apparatus the operator of AP02 acts through.