Supply complete native curvature bounds

Two mathematical inputs now exist: the piecewise quadrature-error allowance, and calibrated/partial-packet derivatives through third order. They do not yet provide the native quantities required by the first.

The separate third-order derivative algebra now passes independent product, reciprocal and rotation checks, with actual derivatives distinguished from factorial coefficients. Connect it to the native packet-to-position adapter next. The motion-step expressions also pass focused checks. Reuse the exact packet derivatives; do not edit frozen native engines or restart their studies.

Propagate derivative bounds through the actual rotation, midpoint velocity, position and receiver-coordinate equations. Work with the residual after the shared-source expression so known calibration nonlinearity is not bounded twice. Do not subtract two unrelated enormous ranges and call that a useful residual enclosure.

Clock treatment must identify every supported packet branch over the declared domain, verify its completeness, and bound one-sided derivative jumps. Keep ideal packet-time geometry, native cumulative floating-point timestamps and numerical execution error distinct. The quadrature component assumes a continuous residual; any discontinuity or numerical deviation needs an explicit allowance, not a missing jump entry.

Before full-history work, freeze finite controls for smooth known motion and clock-boundary crossings under all candidate/processing cases. Record measured costs, useful-width requirements and every charged evaluation. A complete native enclosure must then cover the intended history/prediction period and physical domain. The aircraft error law remains a separate requirement.

This plan supplies no new native or observed-fit allowance by itself. Every new numerical study needs a separately tested finite source/input/environment freeze. Completed studies, failed labels and original measurements remain intact.