Manuscript Hawk02-B@2 · Hawk02-B.tex · section · 95ea744f

Correct analytical targets

Reported Python diagnostics › Correct analytical targets · lines 1443–1496

For this run,

q = \frac{1}{8}, p = \frac{7}{8}, c_{d} = \frac{3}{4},

and

α_{1} = - \frac{i}{2}, α_{2} = - \frac{i}{2}, α_{3} = - \frac{i}{2 2} .

Thus $(p_{1}, p_{2}, p_{3}) = (1/2, 1/4, 1/8)$ and $\sum_{j} p_{j} = 7/8$ .

Quantity	Exact value	Decimal value
Survival $q$	$1/8$	$0.125$
Single-cell recovery	$3/32$	$0.09375$
Single-cell leakage	$3/32$	$0.09375$
Two-cell recovery	$183/1024$	$0.1787109375$
Time-resolved recovery	$3/32$	$0.09375$
Fixed-mode error after time pinching	$15/32$	$0.46875$
Internal-label-dephasing error	$17/32$	$0.53125$
First-cell-only collection error	$3/8$	$0.375$
Detuning Duhamel allowance	$3/10000$	$0.0003$

The fixed-mode time-pinching coefficient is

a = \frac{( 1/2 ) ^{2} + ( 1/4 ) ^{2} + ( 1/8 ) ^{2}}{7/8} = \frac{3}{8} .

The table's control values follow from the analytical propositions. The script checks the corresponding matrix identities or Bell witnesses; its manifest does not separately print all these values.

Its printed targets are

q = 0.12500000000000006, single recovery = single leakage = 0.09375000000000004,

two-cell recovery = 0.1787109375, Duhamel allowance = 0.00030000000000000003.

Their small departures from the rational targets are floating-point representations, not new physical effects.

Displayed formulas in this passage

unlabeled · line 1446
$q = \frac{1}{8}, p = \frac{7}{8}, c_{d} = \frac{3}{4},$
unlabeled · line 1450
$α_{1} = - \frac{i}{2}, α_{2} = - \frac{i}{2}, α_{3} = - \frac{i}{2 2} .$
unlabeled · line 1477
$a = \frac{( 1/2 ) ^{2} + ( 1/4 ) ^{2} + ( 1/8 ) ^{2}}{7/8} = \frac{3}{8} .$
unlabeled · line 1485
$q = 0.12500000000000006, single recovery = single leakage = 0.09375000000000004,$
unlabeled · line 1490
$two-cell recovery = 0.1787109375, Duhamel allowance = 0.00030000000000000003.$