Manuscript En04-A@1 · En04-A.tex · section · bab77211

The baseline prevents a magic-origin inference

The four-Majorana control is not a magic certificate › The baseline prevents a magic-origin inference · lines 1614–1660

At $g = 0$ , or at $t = 0$ , collected radiation is vacuum and $c_{R} = 1$ . Therefore

ε_{rec}^{R} = \frac{3}{4}, ε_{rec}^{B} = 0, δ_{full} = \frac{3}{4} .

Residual non-constancy is already maximal for a qubit at the initial interface: the diary is retained in the inaccessible source. Nonzero coupling is not the cause of that pre-existing non-constancy.

As collected coherent states become more distinguishable, the radiation error decreases and residual leakage can decrease. Thus this control cannot establish that added non-Clifford resources force added leakage.

No fixed qubit Pauli dictionary for the entire bosonic dynamics has been declared, and no magic measure has been evaluated for it. The control is commuting and uses no scrambling or out-of-time-order estimate. It is a recovery obstruction, not a certificate of non-local magic or geometric response.

If all bath modes are accessible,

c_{R} (t) = exp [- 2 g^{2} \int_{μ}^{Λ} \frac{1 - cos ( ω t )}{ω ^{3}} d ω] .

For a restricted packet space, a nonzero coupling need not produce nonzero collected displacement at every chosen time.

The source energy remains zero, while

E_{B} (t) = g^{2} \int_{μ}^{Λ} \frac{1 - cos ( ω t )}{ω ^{2}} d ω, E_{I} (t) = - E_{B} (t) .

This follows from coherent bath energy and total-energy conservation. It is dressing of an initially undressed preparation, not a gravitational evaporation law.

Displayed formulas in this passage

unlabeled · line 1618
$ε_{rec}^{R} = \frac{3}{4}, ε_{rec}^{B} = 0, δ_{full} = \frac{3}{4} .$
unlabeled · line 1640
$c_{R} (t) = exp [- 2 g^{2} \int_{μ}^{Λ} \frac{1 - cos ( ω t )}{ω ^{3}} d ω] .$
unlabeled · line 1651
$E_{B} (t) = g^{2} \int_{μ}^{Λ} \frac{1 - cos ( ω t )}{ω ^{2}} d ω, E_{I} (t) = - E_{B} (t) .$