Libidinal routing

What the plate operates. Proposition 7' establishes that the four registers become dependently distributed under closed-loop joint observation through $O$. The plate visualizes the cross-register mutual information $I_{{\Pi }_t}(u^i;u^j)$ forming over time.

Why the off-diagonals grow. Each platform observation $y_s$depends jointly on multiple registers (the platform's $O$ is non-separable). Observing $y_s$ introduces posterior dependence between registers via explaining-away — a textbook property of Bayesian networks. Over many observations, mutual information accumulates on every off-diagonal cell.

The coupling rates. Different register pairs couple at different rates. The plate uses an illustrative set:

• S-C (somatic-cognitive): fastest. Engagement events couple somatic and cognitive registers directly through attention.
• S-K (somatic-kinaesthetic):fast. The body's rhythms entrain to the platform's.
• C-K, C-P: medium.
• S-P, P-K: slowest. The political register has its own dynamics; coupling to the somatic and kinaesthetic registers proceeds more slowly.

What the proposition authorizes the prose to claim. The four registers are libidinally routed under the closure. Subject, Citizen, Person, Consumer are no longer dynamically decoupled. They are dependently distributed via the platform's observation channel. Lyotard's libidinal economy claim — desire flowing across registers without respect for analytic separations — is what the closed loop produces operationally.