15 Boundary-localized error and claim control
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The strongest visual distinction between global Fourier reconstruction and exact packet retention is seen in a band around the discontinuity.
Conjecture 15.1: Edge-packet approximation class
There should exist natural function spaces in which a signal is represented as
\[
f=s+\sum_q a_q\mathbf1_{\Omega_q},
\]
with separate norms for smooth approximation, boundary geometry, packet amplitude, and packet identification. A projector-resolved approximation theory on such spaces should yield rates that do not mix smooth truncation error with discontinuity-location error.
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