Manuscript X-L-ST@1 · X-L-ST.tex · proposition · 20a32a22

Proposition: Reference-preserving route

Finite composition, causal transport, and error accounting › Regular route · lines 1802–1823 · proof included or linked

X-L-ST@1#prop:route

After hop $j$ , every payload–reference input has complete route state

ρ_{A_{j} E} \otimes i \neq = j ⨂ ω_{A_{i}} .

Arrival occurs after developed duration $ℓ / υ$ , or host duration $ℓ / (c_{h} υ)$ . The route stays in the supplied regular tube.

Proof. Each SWAP moves the entire payload and all its correlations into the next independent blank, leaving the previous slot blank. Induction proves the formula. The specified spacings and durations certify future-causal cross-port dependencies. Equation (eq:signature) gives the host duration.

Displayed formulas in this passage

unlabeled · line 1806
$ρ_{A_{j} E} \otimes i \neq = j ⨂ ω_{A_{i}} .$

Nearby in this section

section: Regular route
section: Regular route