Propagating uncertainty through the force calculation

All 30 nonlinear force-box checks pass, including comparisons with an independent Cartesian trajectory calculation for all three candidates and six motion types. No original recordings or fitted results are used.

The acceleration-only diagnostic asks whether the measured force magnitude is compatible with the force needed to follow the receiver trajectory. That calculation is nonlinear: latitude changes the coordinate metric, while rates, accelerations, gravity and background-field assumptions interact. A tangent calculation or a few sampled perturbations need not bound that response.

What the new calculation does

It takes explicit lower/upper bounds on the nine receiver-derived quantities: position coordinates, their rates and their accelerations. Separate intervals declare gravity and the candidate's background field. Interval operations carry these bounds through the geographic metric, transport terms and required force. The resulting three component intervals then bound the force magnitude.

The calculation uses the same declared ellipsoidal globe and stationary-disc metrics as the existing exact-trajectory adapter. It does not infer geometry, calibration or a background field from the error bounds. Zero-field candidates cannot receive a nonzero field allowance. Boxes crossing the supported polar domain or a nonpositive metric are rejected.

This supplies the nonlinear step following the derivative-error bounds. It avoids replacing a bounded nonlinear response with an unqualified linear standard error. It may be loose: discarding dependencies between coordinates can only enlarge the mathematical enclosure. Overlapping boxes do not prove that one common calibration and trajectory fits a complete recording.

Verification and remaining limits

Independent Cartesian differentiation supplies the reference force on stationary, slow, eastbound, northbound, changing-course and climbing examples. Interior and boundary perturbations remain within the propagated boxes. Other checks cover gravity ranges, point-valued inputs and invalid physical domains.

Arithmetic widens interval endpoints by one representable floating-point value. This is not a formal certificate for every mathematical-library rounding error. The bounds are deterministic under their supplied physical envelopes, not calibrated confidence intervals or evidence of measured instrument accuracy.

The next gate assembles this prediction bound with common time support, increment/count uncertainty, continuous-force averaging and sensor calibration. The same declared allowances must apply to all candidates. An uninformative result is retained, rather than tightening uncertainty to obtain separation. The main 53-stretch result is unchanged.

Implementation · Independent checks · Contribution overview · Roadmap.