Coordinate compensation passes the small known-answer controls

The new calculation preserves tiny changes in all six coordinate controls. The original arithmetic passed three; moving only the longitude origin passed four. Compensation passes all six under the same relative comparison tolerance.

Each pair uses the same simple motion at small and large coordinate origins. Large origins make it harder to retain small additions. The original calculation loses the smallest north/east changes entirely in these fixtures and has about 1% relative error in the large-height case. Compensation keeps the rounding remainder rather than discarding it.

The largest compensated difference error is about 0.000000003 relative to the independent reference, below the fixed 0.0000001 comparison tolerance. That figure describes a mathematical software check, not measured gyro accuracy.

What was tested

The reference differentiates the discrete midpoint impulse sum without using the native derivative code or a shared truth generator. The fixtures deliberately use large coordinate origins; the one-million-metre height is an arithmetic stress case, not an aircraft observation. Gravity is constant in these origin tests so translating height does not change their physical motion.

The 46 source-bound software checks also cover all three physical candidates, both processing cases, every nuisance column, height-dependent gravity, partial packets, initial-position corrections, lever arms, longitude wrapping and forecasts without later receiver positions. The earlier inward timing convention is retained. The shared native loader avoids copying the loader into each study.

The frozen study completes all 18 tasks in 7.13 seconds, using one numerical thread, three charged compiler builds, 126 native evaluations and 16,380 conservatively counted packet-query visits. Baseline precision failures remain visible in the CSV. Task completion is separate from passing a precision check.

What remains

These short controls qualify the arithmetic for a further diagnostic, not for new scientific conclusions. They do not establish accuracy over an entire recording or resolve the previously failed fits.

The next finite comparison should test the same four exposed saved points, retain every derivative column, and repeat the original stopping check as a diagnostic without changing any fit label. It must verify the original input arrays, error operator, environment and baseline cost first. No fresh calibration campaign follows automatically.

No nonlinear fits, new noise examples, aircraft reads or protected observations were used. The original 53-stretch findings and failed calibration labels remain unchanged.

Verified report · Results CSV · Frozen plan · Previous four-point comparison · Next analyses.