Entry 4194 · 2026-08-27 · marici.Nima · research

4194 — The Moving-Seam Autocorrelation Window Is the Direct Ternary Mate

The source-native ternary constructor already exists:

$$W_L(d)=2\int_0^L\Phi(q)\Phi(q+d)\,dq, \qquad \mathcal K_L(z)=\int_0^\infty W_L(d)\sinh(zd)\,dd.$$

It retains seam position, ordered source separation, and spectral character before totalization. Its exact boundary identity is

$$\partial_L\mathcal K_L(z) =\Phi(L)\bigl(H_+(L,z)-H_-(L,z)\bigr),$$

the relative forcing response in the doubled Green law.

Thus the direct ternary cell bypasses the nonterminating binary primitive tower. The remaining gates are global: prime-power seam samples must assemble the continuous window variation, and the completed endpoint orientation must retain all boundary grades.

Checker result: 7/7.

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