Manuscript VII-E-ST@1 · VII-E-ST.tex · section · d28d9c5d

A finite model selecting ordered slices

A finite model selecting ordered slices · lines 1569–1598

VII-E-ST@1#eq:labels, VII-E-ST@1#eq:slice-time

This construction does not use the four-face family or its event rule. It uses only the prescribed conical product and finite matrices, adapting the ordered-slice example of VII-G CheungVIIG.

Fix an integer $B \geq 1$ , physical times $τ > 0$ and $0 < δ < τ$ , and define

G_{B} = {(k, q) : 0 \leq k \leq B, ∣ q ∣ \leq k, q \equiv k (mod 2)} .

A label denotes the horizontal regular marking

T (k, q) = T_{0} + k τ + δ q, r (k, q) = B - k .

The nominal controller tick $k τ$ , selected slice time $T (k, q)$ , and physical times of local gate implementations are different declared quantities.

For $k < B$ , set

Γ_{a} (k, q) = (k + 1, q + a), a = \pm 1.

At $k = B$ , use an absorbing identity branch.

Displayed formulas in this passage

VII-E-ST@1#eq:labels · line 1579
$G_{B} = {(k, q) : 0 \leq k \leq B, ∣ q ∣ \leq k, q \equiv k (mod 2)} .$
VII-E-ST@1#eq:slice-time · line 1585
$T (k, q) = T_{0} + k τ + δ q, r (k, q) = B - k .$
unlabeled · line 1594
$Γ_{a} (k, q) = (k + 1, q + a), a = \pm 1.$

A finite model selecting ordered slices

Displayed formulas in this passage

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