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Module 03 / 04
Choose the best feasible degraded configuration.
It remains a valid special case. The revision does not discard it; it specifies the conditions under which it is safe to use.
Initial formulation
Choose the best feasible degraded configuration.
\[
c^*(t)\in\operatorname*{arg\,max}_{c\in\mathcal C_{feas}(\rho(t))}S(c,\rho(t)).
\]
This formulation was sufficient for EXP‑03: two faults, a finite graph and a local stability gate.
It remains a valid special case. The revision does not discard it; it specifies the conditions under which it is safe to use.
Control the trajectory of an extended system state.Open section
Current formulation
Control the trajectory of an extended system state.
\[
Z(t)=\langle x,\rho,cfg,\alpha\rangle,
\qquad
\mathcal R=\mathcal R_{phys}\cup\mathcal R_{epist},
\qquad
G_e=(\mathcal C,\mathcal T).
\]
\[
\pi^*\in\operatorname*{arg\,max}_{\pi\subset G_e}\int_0^T S(Z(t))\,dt,
\qquad
t_{k+1}-t_k\ge\tau_d,
\qquad
\tau_d>\frac{\ln\mu}{2\gamma_{min}}.
\]
Capability gives the objective; the graph gives the guaranteed set; timing constrains when the architecture may change.
The revised model produced consequences that the initial formulation could not express.Open section
Results that changed the design
The revised model produced consequences that the initial formulation could not express.
Model deactivation thresholdFor low relative influence, critical validity approaches \(e^{-1}\approx0.368\): below it, removing a degraded model can increase capability.
Catalogue composition dominates tuningRemoving the worst-conditioned configuration reduced the required dwell time by 5×, versus at most 1.78× across decay-rate tuning.
Trajectory planning changes the safety outcomeIn the reference verification, unsafe operating time decreased from 3.55% to 1.90% with only a 0.12% loss in mean capability.
Validity management has mission valueValidity-aware resource allocation increased mean capability from 0.8918 to 0.9420 in the reference model.