% global_universality_artifacts.tex

\subsection{Artifact-level completion: report, certificate, and paired radii}
\label{sec:global-universality-artifacts}

The mathematics above naturally produces two levels of machine-checkable output.
The intent is that an independent reader can:
(i) validate the global conclusion without rerunning the full internal pipeline, and
(ii) carry forward the minimal global data needed to support later proofs.

\subsubsection*{Paired radii and the conservative scalar floor}

The robust layer distinguishes perturbations of costs and perturbations of template entries.
Accordingly, the canonical robustness radius is a pair
\(
\boldsymbol{\varepsilon}=(\varepsilon_c,\varepsilon_A)
\)
with the meaning
$\|\Delta c\|\le \varepsilon_c$ and $\|\Delta A\|\le \varepsilon_A$.
For convenience, we also record the conservative scalar floor
\(
\varepsilon_{\min}:=\min\{\varepsilon_c,\varepsilon_A\}.
\)
The scalar floor is sufficient for parameter-space cover arguments; the pair is the natural object for reproducible robustness claims.

\subsubsection*{Report versus certificate}

\begin{center}
\begin{tabular}{@{}p{0.26\linewidth}p{0.50\linewidth}p{0.20\linewidth}@{}}
\toprule
Artifact & Role & When produced \\
\midrule
\texttt{GlobalUniversalityReport} & Full region-level audit: cover data, diagnostics, and optional proofs & Always (certified or boundary) \\
\texttt{GlobalUniversalityCertificate} & Compressed carry-forward object: global bounds + witnesses + rate pack & Only when uncovered set is empty \\
\bottomrule
\end{tabular}
\end{center}

Both artifacts are explicitly specified by JSON Schemas:
\begin{itemize}[leftmargin=2em]
\item \path{global_universality_report_schema.json}
\item \path{global_universality_certificate_schema.json}
\end{itemize}

The report schema supports the paired-radius form by allowing
\texttt{epsilon\_global} and \texttt{epsilon\_star} to be either a scalar or an object with fields
\texttt{eps\_c\_star}, \texttt{eps\_A\_star}, and (optionally) \texttt{eps\_min}.
The examples in this repository use the paired form.

\subsubsection*{Compression map: report $\to$ certificate}

In the certified case, the report contains more information than downstream use typically requires.
The compression map discards only:
coverage bookkeeping (net points and intermediate certificate IDs), optional Lipschitz proof blocks, and free-text diagnostics.
It retains:
\begin{itemize}[leftmargin=2em]
\item global margins $(\gamma_0,\delta_0)$,
\item the paired global robustness radius $\boldsymbol{\varepsilon}_{\mathrm{global}}$,
\item the witness payload (uniform or chamberwise),
\item and the uniform rate pack.
\end{itemize}

This is the exact data needed to reuse the global conclusion as an input to later arguments.

\subsubsection*{Schema validation}

The schema files are included so that the report and certificate objects can be validated independently with any standards-compliant JSON Schema validator.


\subsubsection*{Machine description of the target family $\Theta$}

The global decider is a statement on a \emph{region}, so the artifacts include a separate, explicit descriptor for the parameter family.
The schema \path{theta_family_schema.json} defines a compact, model-agnostic format for declaring a target region (box/simplex/curve) together with a normalization choice.
The file \path{theta_family_example.json} records the canonical family $\Theta_{\mathrm{can}}$ from Section~\ref{sec:theta-can}.

When one invokes the ``global-on-\(\Theta\) by net + Lipschitz envelope'' route (Proposition~\ref{prop:uniform_margins_via_lipschitz}), the descriptor also makes the required continuity inputs explicit via the \texttt{net\_certification\_contract} block.
This block declares the parameter norm and conservative moduli (\(L_c, L_A, M\)) used to certify uniform positive margins from finite sampling.

To make the two global outcomes concrete, the repository also includes:
\begin{itemize}[leftmargin=2em]
\item \texttt{global\_universality\_report\_ThetaCan\_certified.json} (certified-good-global format example)
\item \texttt{global\_universality\_certificate\_ThetaCan.json} (compressed carry-forward certificate)
\item \texttt{global\_universality\_report\_ThetaCan\_atlas.json} (boundary-global atlas format example)
\end{itemize}
