Manuscript X-H-ST@1 · X-H-ST.tex · proposition · 943aa27e

Proposition: Reference-preserving finite route

Scheduled locality, regular transport, and resources › A nonempty regular transport route · lines 1884–1909 · proof included or linked

X-H-ST@1#prop:route

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For every $ρ_{A_{0} E}$ , after hop $j$ the state is

ρ_{A_{j} E} \otimes 0 \leq i \leq n i \neq = j ⨂ ω_{A_{i}} .

The logical payload channel is the identity with every reference. Arrival is at

t_{d} + ℓ, T_{d} + ℓ / c_{host} .

All routes remain in the regular tube.

Proof. Each SWAP moves the whole payload factor, including its reference correlations, to the next blank and leaves the previous factor blank. Induction proves the state formula. Station spacing $ℓ / n$ and tick duration $ℓ / n$ give null cross-port dependencies; same-station dependencies are timelike.

Displayed formulas in this passage

unlabeled · line 1888
$ρ_{A_{j} E} \otimes 0 \leq i \leq n i \neq = j ⨂ ω_{A_{i}} .$
unlabeled · line 1894
$t_{d} + ℓ, T_{d} + ℓ / c_{host} .$

Proposition: Reference-preserving finite route

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