Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \caption{Exact finite validation of the Integral prime-power atlas integral and prime-power layer.}
4 \label{tab:block06-validation}
5 \small
6 \begin{tabularx}{\textwidth}{@{}L{0.31\textwidth}Y@{}}
7 \toprule
8 Check family & Recorded result\\
9 \midrule
10 Smith and modular profiles & 1984 divisibility chains of ranks one through four; moduli 2 through 24; 45632 chain-modulus cases.\\
11 Fitting and prime-power profiles & 8840 Fitting cases and 39680 prime-power profile cases over $p=2,3,5,7$.\\
12 Digit-equivariant systems & 320 exact Smith-square systems with integral and modular intertwining checks.\\
13 Orbit and completion controls & Digit-sum state formulas over four primes and 1681 bounded ghost-contraction samples.\\
14 Total exact checks & 697958; 0 failures.\\
15 Overall status & PASS.\\
16 Boundary & Bounded exact verification supports the printed formulas and examples. It does not replace the symbolic proofs or establish unrestricted integral recognition.\\
17 \bottomrule
18 \end{tabularx}
19 \end{table}

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