The construction extends beyond this picture
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The integer waveform changes with the modulus, while the same arithmetic identity supplies it.
For general \(q\), character orthogonality gives
\[
\widehat{c_q}(k)=q\mathbf1_{\gcd(k,q)=1},\qquad
\sum_{n=0}^{q-1}|c_q(n)|^2=q\varphi(q).
\]
The associated primitive-order projector has rank \(\varphi(q)\). The general mathematical conclusions follow from the finite-sum derivations in the main paper. The source verifier separately checks its declared finite range \(2\leq q\leq64\).