Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \caption{Exact local Mahler and polyphase examples used in Local Mahler-polyphase atlas.}
4 \label{tab:block08-examples}
5 \small
6 \begin{tabularx}{\textwidth}{@{}L{0.31\textwidth}L{0.29\textwidth}Y@{}}
7 \toprule
8 Example & Source Mahler data & Refined data or rank\\
9 \midrule
10 \(x^2\), branch 2q+0 & \( (0, 1, 2) \) & \( (0, 4, 8) \)\\
11 \(x^2\), branch 2q+1 & \( (0, 1, 2) \) & \( (1, 8, 8) \)\\
12 \((1+2)^x\), branch 2q & \(c_r=2^r,\ 0\leq r\leq4\) & \(d_k=8^k,\ 0\leq k\leq4\)\\
13 \((1+3)^x\), branch 3q & \(c_r=3^r,\ 0\leq r\leq4\) & \(d_k=63^k,\ 0\leq k\leq4\)\\
14 \((1+5)^x\), branch 5q & \(c_r=5^r,\ 0\leq r\leq4\) & \(d_k=7775^k,\ 0\leq k\leq4\)\\
15 mod-2 rank distribution, M=2,d=3 & \( (2, 2) \) & \( (4, 4) \)\\
16 \bottomrule
17 \end{tabularx}
18 \end{table}

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