Derivative bounds for calibrated packets
An inertial measurement unit (IMU) contains gyroscopes and accelerometers. The prediction-bound calculation needs to know how an IMU increment changes as calibration varies. A new exact-arithmetic component encloses that change through third order, for the stated bias/gain region and calibration path.
The component also handles the partial-packet arithmetic used when a query falls inside a packet. It rejects clock ranges that cross a packet boundary; it cannot silently treat them as one smooth interval.
Nine focused checks pass, including comparison with an independent power-series calculation at 27 parameter/path points. Denominator failures, invalid paths and unsupported clock ranges are rejected.
This supplies calibrated-increment derivatives, not complete trajectory derivatives or verified clock-partition coverage. No original measurements were read, altered or fitted. It changes no instrument scale or calibration bound.