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

Locality and actual fit

Finite composition, causal transport, and error accounting › Locality and actual fit · lines 1860–1881

At every branch cut $c$ , charge all live laboratory qubits, including reserved blanks and memory:

Q_{lab} (c) = q_{clock} (c) + q_{memory} (c) + q_{work} (c) + ρ \in R (c) \sum (n_{ρ} + 1) p_{ρ},

with shared allocations counted only once. Returned storage, supplier storage, classical tables, and untouched references have separate ledgers.

A host realization requires

c max Q_{lab} (c) \leq Q_{res},

and the corresponding classical-storage, location, permission, and duration inequalities. Finiteness alone does not prove these inequalities.

Displayed formulas in this passage

unlabeled · line 1864
$Q_{lab} (c) = q_{clock} (c) + q_{memory} (c) + q_{work} (c) + ρ \in R (c) \sum (n_{ρ} + 1) p_{ρ},$
unlabeled · line 1875
$c max Q_{lab} (c) \leq Q_{res},$