Manuscript En02-E@2 · En02-E-v2.tex · section · c2769986
Scope, dependencies, and evidence
Scope, dependencies, and evidence · lines 170–254
The construction separates the following objects:
\begin{gathered}
\text{specified field state}
\longrightarrow
\text{selected packet state}
\longrightarrow
\text{finite flagged representation},\\
\text{declared encoding interface}
\longrightarrow
\text{message channel}
\longrightarrow
\text{complete recovery protocol}.
\end{gathered}
A field state does not determine the second line.
Connections between the lines are proved only for explicitly stated
interfaces.
\paragraph{Route A.}
We construct and approximate the full selected radiation state,
including multiparticle occupation and packet correlations.
\paragraph{Route B.}
We transfer its vacuum/nonvacuum probability to an independently
specified logical benchmark. This is a nonvacuum-calibrated recovery
model, not a derived microscopic evaporation channel.
The stationary field formulation is the one specified in the supplied
Em03-A manuscript \cite{Em03A}, with the external Unruh-state
construction retained \cite{DMP}. The operational benchmark is a
specialization of the supplied En02-D model \cite{En02D}; its needed
claims are proved here.
\begin{center}
\renewcommand{\arraystretch}{1.13}
\begin{tabular}{@{}p{0.26\textwidth}p{0.27\textwidth}p{0.38\textwidth}@{}}
\toprule
Ingredient & Dependency & Status in this paper\\
\midrule
Stationary boundary covariance
& Em03-A; standard Hawking model
& Explicitly stated analytical input\\
Bulk state identification
& Dappiaggi--Moretti--Pinamonti
& External construction and Hadamard theorem\\
Radial scattering
& Specified Schwarzschild ODE
& Flux-normalized construction; approximation bounds\\
Selected density operator
& Quasifree field restriction
& Proved finite-mode representation\\
Occupation cutoff
& This paper
& Deterministic CPTP map and explicit errors\\
Message encoding and core
& Operational specification
& Additional model inputs\\
Recovery performance
& Specified channel and interface
& Analytical optima; numerical checks unexecuted\\
\bottomrule
\end{tabular}
\end{center}
\paragraph{Evidence status.}
No Python, solver, or pdfLaTeX execution is asserted.
The numerical appendix is an implementation specification, not a
results section. Analytical examples are explicitly identified.
An executed incorporation study requires actual archived runs and
inspection of their numerical and compilation records.
We use \(c=\hbar=k_B=1\), \(G>0\), and base-two entropy.
For states and channels,
\[
d_{\mathrm{tr}}(\rho,\sigma)=\frac12\left\lVert \rho-\sigma\right\rVert_1,\qquad
d_\diamond(\Phi,\Psi)=\frac12\left\lVert \Phi-\Psi\right\rVert_\diamond.Channel comparisons include arbitrary references. Matrix denotes operator norm and denotes Frobenius norm.
Displayed formulas in this passage
unlabeled · line 174
\begin{gathered} \text{specified field state} \longrightarrow \text{selected packet state} \longrightarrow \text{finite flagged representation},\\ \text{declared encoding interface} \longrightarrow \text{message channel} \longrightarrow \text{complete recovery protocol}. \end{gathered} A field state does not determine the second line. Connections between the lines are proved only for explicitly stated interfaces. \paragraph{Route A.} We construct and approximate the full selected radiation state, including multiparticle occupation and packet correlations. \paragraph{Route B.} We transfer its vacuum/nonvacuum probability to an independently specified logical benchmark. This is a nonvacuum-calibrated recovery model, not a derived microscopic evaporation channel. The stationary field formulation is the one specified in the supplied Em03-A manuscript \cite{Em03A}, with the external Unruh-state construction retained \cite{DMP}. The operational benchmark is a specialization of the supplied En02-D model \cite{En02D}; its needed claims are proved here. \begin{center} \renewcommand{\arraystretch}{1.13} \begin{tabular}{@{}p{0.26\textwidth}p{0.27\textwidth}p{0.38\textwidth}@{}} \toprule Ingredient & Dependency & Status in this paper\\ \midrule Stationary boundary covariance & Em03-A; standard Hawking model & Explicitly stated analytical input\\ Bulk state identification & Dappiaggi--Moretti--Pinamonti & External construction and Hadamard theorem\\ Radial scattering & Specified Schwarzschild ODE & Flux-normalized construction; approximation bounds\\ Selected density operator & Quasifree field restriction & Proved finite-mode representation\\ Occupation cutoff & This paper & Deterministic CPTP map and explicit errors\\ Message encoding and core & Operational specification & Additional model inputs\\ Recovery performance & Specified channel and interface & Analytical optima; numerical checks unexecuted\\ \bottomrule \end{tabular} \end{center} \paragraph{Evidence status.} No Python, solver, or pdfLaTeX execution is asserted. The numerical appendix is an implementation specification, not a results section. Analytical examples are explicitly identified. An executed incorporation study requires actual archived runs and inspection of their numerical and compilation records. We use \(c=\hbar=k_B=1\), \(G>0\), and base-two entropy. For states and channels, \[ d_{\mathrm{tr}}(\rho,\sigma)=\frac12\left\lVert \rho-\sigma\right\rVert_1,\qquad d_\diamond(\Phi,\Psi)=\frac12\left\lVert \Phi-\Psi\right\rVert_\diamond.