Finite polynomial data and arithmetic enclosure

Sampling the residual at solver output times does not certify this supremum. The trace norm is not a holomorphic integrand in general; an analytic integration routine must not be applied to it without an appropriate enclosure argument. The conservative cellwise bound above avoids that issue.

If a piecewise approximation has jumps instead of matching endpoints, variation of constants additionally charges the trace norm of every jump before the observation time. A certificate must either verify continuity or include those jump terms.