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1 \begin{table}[htbp]
2 \centering
3 \caption{Exact finite validation of the Fixed-radix regular atlas fixed-radix regular atlas.}
4 \label{tab:block05-validation}
5 \small
6 \begin{tabularx}{\textwidth}{@{}L{0.27\textwidth}Y@{}}
7 \toprule
8 Check & Recorded result\\
9 \midrule
10 Exhaustive finite-state enumeration & base 2 over $\mathbb F_2$ through 3 raw states: 5,898 raw candidates, 2,830 leading-zero-consistent candidates, 94 distinct minimized automata; base 2 over $\mathbb F_3$ through 3 raw states: 19,830 raw candidates, 6,990 leading-zero-consistent candidates, 297 distinct minimized automata; base 3 over $\mathbb F_2$ through 2 raw states: 258 raw candidates, 170 leading-zero-consistent candidates, 26 distinct minimized automata.\\
11 Automatic-to-linear checks & 86,207 exact checks; 83 minimized automata with strict state-to-rank compression.\\
12 Unbounded regular examples & Polynomial sequences $n^m$ for bases 2 and 3 through degree 6, plus digit sums in bases 2, 3, and 4; 2,438 exact checks.\\
13 Combined Fixed-radix regular atlas checks & 89,055 checks; 0 failures.\\
14 Overall status & PASS.\\
15 Boundary & The computation validates the bounded automata and named exact examples. It does not prove an all-radix, all-ring, semiring, or all-moduli minimality theorem.\\
16 \bottomrule
17 \end{tabularx}
18 \end{table}

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