Geographic predictor/corrector and observation bounds
This extends the completed local-step controls through the actual native geographic update and antenna observation. It uses generated inputs only. Previous studies and kernels remain unchanged.
Bound construction
Carry scalar intervals separately from nominal-value/change/remainder bounds. This preserves asymmetric physical domains, including removal [0,1] centered at either endpoint and a positive period whose symmetric outer ball crosses zero. Intersect valid mathematical enclosures without clipping measurements.
Implement scalar product, inverse, sine/cosine and positive-domain powers with global derivative/remainder bounds over their declared intervals. Keep latitude, longitude and height in separate radian/metre components. Preserve continuous longitude. Reject polar or metric-denominator crossings rather than repair them.
Mirror the native step exactly: old coordinate rates; midpoint coordinates; first context using old rates; first local velocity estimate; revised rates at the same midpoint using average velocity; revised context; second local step from the original state; coordinate update using revised rates. Then rotate the lever arm and map it with the candidate metric at the predicted position.
Allow a declared period within one packet and scale corrected full-packet increments by that same fraction. Retain period/calibration cross terms. Physical Coriolis and upstream removal remain distinct. This does not cover a receiver-time interval crossing into another packet.
Independent qualification
Use one unchanged C-kernel wrapper for full state and antenna values. Compile the unchanged C++ tangent source separately and compare all 27 normalized parameter columns with independent complex-step derivatives. A separate reference uses matrix exponentials, linear solves and geographic formulas; it does not call the bound implementation or repository step.
Seventy-two fixed cases: three candidates, latitudes ±65°, fixed removal or profiled removal centered at zero/one, narrow/broad calibration, and fixed- endpoint/interior timing. Each uses 64 predeclared probes in the complete normalized box. Other parameter centers are nonzero. Interior timing spans fractions [0.3,0.7] and is centered at one endpoint of that interval; endpoint timing is fixed. Keep the timing column in every case and report when fixed. Longitude cases cross the conventional ±180° display boundary without wrapping.
All parameter limits, sources, compiler configuration/binaries and numerical
environment are frozen before execution. Compare native observations and
coordinates in a fixed metre scaling at the seed location. Limits are 2e-8 m
for value discrepancies, 2e-10 m/s for velocity, 2e-12 for rotation and 1e-6 m
per normalized parameter for derivative discrepancies. Compare global Taylor
remainders with their analytic bounds plus those numerical tolerances and
2e-12*norm(linear_term). Report roundoff-limited checks separately when a
remainder bound is smaller than the comparison tolerance. These tolerances
are not formal long-record rounding certificates.
Limits: 72 identities, 4,608 probes, 4,680 C step calls, 72 C++ tangent calls, 6,624 independent reference calls, 300 cooperative seconds, one worker/four threads. Zero original reads, archive-native sweeps, optimizer starts or retries. Reserve the complete per-identity allowance before execution; preserve failures and never refund interrupted charges. No signals or process termination.
Remaining scope
Short-step success does not establish useful bounds over a complete recording. Repeated-step support, timing across packet boundaries, numerical enclosure and shared observational covariance still precede a new archive prediction study. No protected ESA observations or existing Earth-model fits are evaluated.