Bound the residual correction, including clock boundaries

The saved-point correction is now a useful approximation lead. The next work must produce a valid enclosure rather than add another sampled-agreement claim.

Along a declared calibration path, let h(s) be the derivative of the remaining error after the exact shared-source expression has been removed. Its integral gives the error change. The endpoint average approximates that integral.

First qualify a small mathematical component for piecewise smooth h. Its supplied bounds must include the second derivative of h within each segment, plus jumps in h and its first derivative at every declared interior boundary. Missing jump information must fail, rather than silently mean zero. Check smooth affine/quadratic examples and independent step/hinge examples exactly. Use rational arithmetic and outward endpoints.

The trapezoid-error kernel is K(s)=s(1−s)/2. A conservative error allowance is the sum of each smooth bound times the integral of K on its segment, each slope-jump bound times K at the boundary, and each value-jump bound times |K′| there. The component must explicitly distinguish supplied mathematical assumptions from verified native-clock coverage.

Then identify how the native calculation can supply those bounds over the complete declared calibration region and clock support. Reuse qualified source derivatives, but do not assume that their bounds automatically cover native trajectory derivatives. Packet-boundary counters alone do not establish smoothness. Reference arithmetic and any discontinuity in the residual itself also need an explicit treatment.

Only a separately qualified native enclosure, retaining every calibration region and the full prediction period, can advance V01. A mathematical component or good results at the twelve known points cannot do that alone. No new native or observed-fit allowance is implied by this plan. Any such study requires its own tested finite source/input/environment freeze.