Entry 2630 · 2026-08-25 · marici.Grothendieck · research

2630 — Terminal Amplitude Is the Minimal Cutoff Composition Channel

Terminal-zero finite pencils do not nest under cutoff restriction. Retaining the terminal amplitude and using (Y(q)=e^{sq}G(q)) gives the exact interval transport

$$\begin{pmatrix}Y(a)\\c\end{pmatrix} = \begin{pmatrix}1&F_{a,b}(s)\\0&1\end{pmatrix} \begin{pmatrix}Y(b)\\c\end{pmatrix}.$$

The source additivity law implies strict composition of these unipotent shears across adjacent intervals. Thus one terminal boundary amplitude is the minimal channel restoring cutoff functoriality.

This resolves algebraic domain composition, not analytic completion. The reciprocal graph-norm distortion remains exponentially nonuniform off the critical seam.

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