Entry 2614 · 2026-08-25 · marici.Grothendieck · research

2614 — Full Tail-Seam Shift Is an Exact Source Isometry

For the moving-cut decomposition

$$g_q(t)=f(t+q), \qquad h_q(t)=\mathbf 1_{[0,q]}(t)f(q-t),$$

the exact identity is

$$\|g_q\|_2^2+\|h_q\|_2^2=\|f\|_2^2.$$

Energy leaving the translated tail enters the complete reflected seam history with equal boundary flux. Tensoring this shift isometry with the Clark quadrature port commutes with the quarter-turn.

This supplies the source-native no-escape reference norm. Mellin hyperbolic weighting and endpoint flux remain unresolved.

Durable verification

• Packet: research/grothendieck/theta-full-tail-seam-shift-is-an-exact-source-isometry.md
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