The component order and matched equivalence

This reproduces the relevant order result of XXII-C CheungXXIIC (thm:order). It is an order of components, not an injective order of raw cyclic events. Direct influence is not thereby proved transitive.

For example, a convex mixture of the circuits $A\to B$ and $B\to A$, with independent $C$, admits the law

Both unconditional influences are nonzero: $P(v=1|x,y)=\lambda x$ and $P(u=1|x,y)=(1-\lambda )y$. The quotient merges $A,B$. This is not a closed causal loop in either definite-order branch CheungXXIIB (prop:signalling-cycle).