Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \caption{Exact finite validation of the Block 04 rational-mask digital atlas.}
4 \label{tab:block04-validation}
5 \small
6 \begin{tabularx}{\textwidth}{@{}L{0.28\textwidth}Y@{}}
7 \toprule
8 Check & Recorded result\\
9 \midrule
10 Enumerated reduced unit masks & $p=2$ with $\deg A,\deg B\leq 3$, $p=3$ with $\deg A,\deg B\leq 2$, $p=5$ with $\deg A,\deg B\leq 1$; 125 masks in total.\\
11 Rational-collapse split & 51 collapse masks and 74 genuinely nonrational mask series.\\
12 Exact identities and state checks & 11391 checks; 0 failures.\\
13 Arithmetic model & exact polynomial, finite-field, Cartier-transition, and formal-series arithmetic.\\
14 Overall status & PASS.\\
15 Boundary & Finite enumeration checks the compiler, reachable Cartier module, state hierarchy, examples, and collapse classification on the declared ranges. It does not replace the unbounded proofs or classify all automatic sequences.\\
16 \bottomrule
17 \end{tabularx}
18 \end{table}

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