Manuscript Oai365-A@1 · Oai365-A.tex · proposition · a3840e3d
Proposition: Component order and finite futures
Quantum-process data and the event carrier › Unconditional signalling · lines 292–304 · proof included or linked
Oai365-A@1#prop:order
Collapse strongly connected components and order the quotient by reachability. The result is a partial order. Every component has at most three components in its future, including itself.
Proof. Reachability is reflexive and transitive. Mutual reachability is exactly the equivalence relation being collapsed, so the quotient is antisymmetric. A directed path stays within one trial, whose graph has three vertices.