Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \caption{Exact finite validation of the Product-multiplicative atlas filtered-product and multiplicative layer.}
4 \label{tab:block07-validation}
5 \small
6 \begin{tabularx}{\textwidth}{@{}L{0.31\textwidth}Y@{}}
7 \toprule
8 Check family & Recorded result\\
9 \midrule
10 Euler-coordinate atlas & 15625 exponent prefixes and 3125 arbitrary integral unit-series prefixes.\\
11 Prime-power multiplicative atlas & 96 deterministic local systems and 48 Dirichlet-convolution pairs.\\
12 Divisor-ghost overlap & 128 multiplicative exponent systems and 6 power families.\\
13 Named local coordinates & 5 arithmetic families and 6 geometric necklace modes.\\
14 Total exact checks & 595964; 0 failures.\\
15 Overall status & PASS.\\
16 Boundary & Bounded exact verification supports the printed formulas and examples. It does not establish compactness or minimality for arbitrary product grammars, nor a global Cauchy--Dirichlet algebra isomorphism.\\
17 \bottomrule
18 \end{tabularx}
19 \end{table}

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