Manuscript VIII-C@3 · VIII-C-v3.tex · section · 3b070436

Initial state, token, and permissions

An explicit promised sourced history › Initial state, token, and permissions · lines 1443–1483

VIII-C@3#eq:source-state, VIII-C@3#eq:hybrid

Use a surviving source qubit with

A_{src} = L (C^{2}), B_{src} = Z, κ = 1.

For the $q = 6$ history, supply token $m_{src} = 1$ , and take

z_{+} = 6 arctan (1/64), ρ_{+} = \frac{1}{2} (I + z_{+} Z) .

Because $0 < z_{+} < 6/64 < 1$ , $ρ_{+}$ is a state and

Tr (ρ_{+} Z) = z_{+}, μ_{0} + Tr (ρ_{+} Z) = μ_{1} .

The same word is defined on every state satisfying this fixed-token promise, including compatible spectator extensions.

Initially install $Π_{μ_{0}}$ , independently of the source state, and set

s = - 1, ν_{G} = ν_{src} = 1, module = slice,

with incoming mode and source stage zero. All original names occupy valid persistent incoming labels. Choose $d \geq 1$ , $Δ τ = 1$ , and slots $k = 0, \dots, 5$ . Each flow segment has $v_{s} = 1/2$ .

The chronological word is

W = G_{- 1 \to - 1/2}; S_{tab}; G_{- 1/2 \to 0^{-}}; E_{3 - 6}; G_{0^{+} \to 1/2} .

Displayed formulas in this passage

VIII-C@3#eq:source-state · line 1450
$z_{+} = 6 arctan (1/64), ρ_{+} = \frac{1}{2} (I + z_{+} Z) .$
VIII-C@3#eq:hybrid · line 1474
$W = G_{- 1 \to - 1/2}; S_{tab}; G_{- 1/2 \to 0^{-}}; E_{3 - 6}; G_{0^{+} \to 1/2} .$
unlabeled · line 1446
$A_{src} = L (C^{2}), B_{src} = Z, κ = 1.$
unlabeled · line 1456
$Tr (ρ_{+} Z) = z_{+}, μ_{0} + Tr (ρ_{+} Z) = μ_{1} .$
unlabeled · line 1464
$s = - 1, ν_{G} = ν_{src} = 1, module = slice,$