Kill Switches

Three load-bearing kill switches are published with this paper, in Claim / Test / Status / Recovery form. Appendix C carries more than twenty further falsification criteria at four levels.

KS-O.1 — Drift-discipline duality.

Claim. In any system with entropic drift, holding non-zero structure requires continuous, non-zero control input.

Test. Exhibit a system with entropic drift that maintains its structure indefinitely under zero control input (Appendix C, D1).

Status. LIVE — EMPIRICAL.

Recovery. If a drift-free maintenance regime is demonstrated, Derivations I–II fall and the discipline result is void.

KS-O.2 — Capacity horizon.

Claim. Every embodied system has a maximum control capacity u_max; once required maintenance ax exceeds u_max, structure decays even at maximum effort, and collapse is deterministic.

Test. Exhibit a system that reliably maintains or grows structure while required maintenance persistently exceeds its capacity (Appendix C, D3).

Status. LIVE — EMPIRICAL.

Recovery. If capacity is effectively unbounded, the event-horizon result (Derivation III) fails.

KS-O.3 — Exit optimality.

Claim. When a system’s structural dynamics guarantee net loss over any sufficient horizon, withdrawal dominates every admissible strategy.

Test. Exhibit a structurally negative-sum system in which continued participation beats withdrawal over the long run (Appendix C, D9).

Status. LIVE — EMPIRICAL.

Recovery. If forced persistence in a structurally negative-sum environment improves long-run survivability relative to exit, the exit theorem (Derivation IX) fails.