12 Worked finite models
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12.1 Smooth branch
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For \(q=3\) and formal dimension \(d=2\), the finite levels have cardinalities
The seed zeta function is
12.2 Weighted dyadic chart
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For weights \((1,2,4)\), the counts are
The first coordinate is active immediately, the second one level later, and the third at depth five. The exact rational function generated by the code is
The negative signs in this presentation arise from moving the denominator to \(1-8T\); every power-series coefficient is positive.
12.3 Singular branch
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For \(x^2=0\) over a residue field of size three, the counts are
and
The exact branching dimension is \(1/2\).
12.4 Directed transport
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The finite graph in Figure 10 has three source components. The source-component theorem and brute-force enumeration both return the minimum seed count three.
