Regroup propagation around the common time coordinate

The correlated prefix clock passes its finite independent qualification. The next candidate uses that mathematical component in the native-history uncertainty construction. Preserve every physical model, source observation, parameter bound and completed freeze. No observed Earth-model fit is planned at this stage.

Coordinate updates

Choose a fixed coordinate-rate reference from the declared expansion center. Write each position update as a reference-rate term times cumulative elapsed time plus an integral of deviations from that reference rate. Accumulate the residual integral separately, then reconstruct the complete position bound using the qualified correlated prefix clock at each step. Do not subtract two already widened interval positions to obtain that residual.

Every intermediate state still needs a complete enclosure: use the prefix's actual center, exact time endpoints and globally bounded remainder, including its cutoff kink while the prefix ends inside the uncertain query interval. The final common-clock cancellation must not discard real intermediate uncertainty. Keep the initial position variation and every calibration/time cross term. Rounded start-tag defects remain explicitly bounded.

Force and gravity

Corrected full-packet delta-V and gravity share the same partial duration. Express the specific-force rate using the fixed complete packet period, combine its rotated value with gravity, and then multiply by the common partial duration. This preserves a known cancellation before applying norm bounds. Keep unknown bias/gain effects, attitude variation, Coriolis/transport, removal and changing gravity. Regrouping is algebraic; it cannot remove an unfavorable physical term or impose level flight.

Qualification before a usefulness run

Implement the new construction in a separate module, using the existing qualified primitive bounds. Do not edit the completed geographic/history sources. Test exact-clock and constant-rate identities, stationary-force cancellation, nonzero calibration centers, timing boundaries, all three candidates and both processing cases. Compare centers and all 27 tangent columns against the unchanged native engine. Independent known-motion controls remain necessary; sampled parameter probes alone do not prove a global numerical enclosure.

Save every training inequality, normalized Jacobian, center, coordinate scale, support certificate and remainder contribution. Test that no future truth enters region selection or reference construction. Keep scientific outputs abstaining when any required bound or measurement assumption is unsupported.

Measure component cost with cheap local controls, then freeze a separate finite qualification and a distinct usefulness comparison. Declare identities, native evaluations, bound/packet steps, all source/input/environment hashes, four-thread allocation and cooperative time limits before each execution. No retries, expansions, process signals or reuse of completed allowances.

The remaining gates include long-record usefulness, global numerical treatment, training-only calibration provenance, actual receiver-error adequacy and independent confirmation. The successful scalar-clock component alone does not satisfy them. Protected ESA groups remain sealed.

Clock qualification · Common-clock mathematics · Canonical roadmap.