Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \caption{Canonical integral defect profiles for named fixed-radix families.}
4 \label{tab:block06-defect-profiles}
5 \small
6 \begin{tabularx}{\textwidth}{@{}L{0.22\textwidth}L{0.17\textwidth}L{0.18\textwidth}Y@{}}
7 \toprule
8 Family & Smith profile & Bad primes & Interpretation\\
9 \midrule
10 Digit sum $s_k$ & $(1,1)$ & none & Saturated rank-two lattice; no modular defect.\\
11 Doubled digit sum $2s_k$ & $(2,2)$ & 2 & Rank-two defect $(\mathbb Z/2)^2$; total semantic collapse modulo $2$.\\
12 Constant sequence $2$ & $(2)$ & 2 & One raw ghost coordinate modulo $2$; one semantic state.\\
13 Constant sequence $6$ & $(6)$ & 2, 3 & Bad primes $2$ and $3$; good reduction at every other prime.\\
14 \bottomrule
15 \end{tabularx}
16 \end{table}

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