Proposition: Complete-channel error accounting

For compatible finite channel factors,

A complete-channel error $\epsilon$ changes any fixed reference-assisted intervention signalling value by at most $2\epsilon$. Exact physical no-signalling of the implemented network instead follows from its actual causal embedding.

Proof. Telescope the difference, replacing one factor at a time. Pre- and postcomposition by channels contract diamond norm. For a signalling comparison, the two intervened outputs each change by trace distance at most $\epsilon$. Apply the triangle inequality and take suprema. Exact causal no-signalling is Theorem thm:causal, independently of approximation.