Preserve the common packet clock
The complete orientation cover passes correctness but misses its improvement target. A saved-input calculation identifies a specific loss: independent packet cutoff remainders can be large even when their sum is nearly linear. This stage changes the uncertainty construction, not the physical candidates, instrument timing assumptions or original observations.
First: qualify a correlated prefix-clock component
Let packet durations be positive binary values dt_j, rounded start tags be
s_j, and exact physical prefix durations be P_j = sum(dt_1 ... dt_j).
The mathematical clipped-period sum is
S_i(t) = sum(clip(t-s_j, 0, dt_j), j<=i).
With D_i = max(abs(s_j-P_(j-1)), j<=i), monotonicity and exact telescoping give
clip(t-D_i, 0, P_i) <= S_i(t) <= clip(t+D_i, 0, P_i).
Thus its discrepancy from clip(t,0,P_i) is at most D_i, regardless of the
number of packets. Keep exact rational center/endpoints and the sum of selected
one-sided packet slopes. Bound the reference clamp's remainder at endpoints and
its two knots, then add the clock defect and center discrepancy. Include any
supplied upstream time-map remainder. Do not add independent packet kink bounds
when a common-clock bound is available.
Use a streaming prefix accumulator with work linear in packet count. Reject nonpositive durations, noncontiguous declared tags and nonfinite inputs. Keep the original left-sided boundary convention and explicitly distinguish the mathematical clipped-period map from whole-program floating-point behavior. Check against independent exact sums at every relevant knot, interval endpoint, boundary center and generated interior point, including non-dyadic periods, variable rates and repeated rounded tags.
After component tests pass, freeze a finite generated qualification. Preserve the old independent-kink method and all completed results. No native predictions, archive reads or observed fits are needed for this component.
Then: qualify regrouped native propagation separately
In a new candidate, split coordinate updates into a fixed reference-rate term times the correlated prefix clock and a residual-rate integral. Retain all calibration directions. Combine specific force and gravity before multiplying by their common partial-packet duration, so their known cancellation is not lost through separate norm bounds. Preserve unknown gains, biases, frame and time dependencies; no physical model term may be deleted.
The regrouping must reproduce the unchanged native center and its full 27-column linearization within separately stated numerical checks. Independent constant-motion/constant-force controls, packet boundaries and all candidate/ processing cases precede another generated usefulness experiment. Keep the complete orientation cover where needed. Save training inequalities, Jacobians, support certificates and each remainder term for subsequent metadata-only diagnosis. Freeze finite calls, bound steps, thread allocation and cooperative time limits before each new execution; never reuse a completed allowance.
This does not establish the physical instrument clock, a whole-program numerical certificate, actual receiver covariance, long-record usefulness or predictive adequacy. Failed qualifications block dependent observed fits. Protected ESA groups remain sealed.