$E_{\mathrm{swarm}}(t)=\ker\begin{bmatrix}K_{\mathrm{safe}}(t)\\(I-P_{\mathrm{harm}}(t))W(t)\end{bmatrix}$
$=\ker K_{\mathrm{safe}}(t)\cap W(t)^{-1}(\ker\Delta_1(\varepsilon^*(t))).$
The executed hard law is $V=P_{E_{\mathrm{swarm}}}V_{\mathrm{goal}}$.
Evidence: E0 kernel identity; E1 projector and residual checks.
Transit: Safety Projection → Hodge Coordination → Control Law.