Manuscript VII-J-ST@1 · VII-J-ST.tex · proposition · f1f1d82c

Proposition: Complete-channel error ledger

Approximate simulation and the Hamiltonian comparison · lines 1077–1096 · proof included or linked

VII-J-ST@1#prop:telescope

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For compatible sequences of channels,

Every encoding, clock, controller, transition, communication, decoding, and failure output must be compared on matching interfaces.

Proof. Replace one factor at a time. The resulting telescoping sum has one channel difference in each term. Composition with channels contracts the diamond norm. Use the triangle inequality and divide by two.

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