Recorded acceleration-magnitude envelope assessment

Scope and identities

Use the two previously selected development recordings: IMU8 stretch b365bdf39150ee6afc303ac1 and IMU21 stretch 7df21c836bec5751f83c0cce. Selection is inherited unchanged from the earlier hardware-diversity comparison, not chosen for this diagnostic's output. This is retrospective development evidence, not untouched confirmation.

On each stretch, use one-second windows centered at 10%, 50% and 90% of its saved duration. Use all supported receiver epochs within 16 seconds of each center for a degree-four local polynomial. Reject insufficient support, receiver gaps over two seconds, longitude chart discontinuity or physical domain failures. Keep every exclusion. Do not search for replacement windows.

Assess all three candidates under nominal 5 ms and packet-header integration interval hypotheses. Both share the first saved interval origin. Allow one common receiver/IMU offset in ±0.15 seconds. Keep only whole packets whose possible support is inside the one-second window, and average every candidate over exactly that retained interval union. No Group-1 attitude or gyro values enter the scalar diagnostic.

Declared uncertainty alternatives

Cross two receiver-coordinate boxes (1 m and 5 m horizontally and vertically) with two acceleration-calibration boxes (gain ±1%, offset ±0.05 m/s²; gain ±15%, offset ±0.25 m/s²). These are sensitivity hypotheses, not verified per-unit specifications or confidence intervals. The wider calibration box matches earlier development limits; the narrower box tests an alternative without claiming manufacturer support. Each axis has a shared constant calibration interval; box propagation relaxes the dependence across packets.

Convert horizontal distance bounds to latitude/longitude bounds using 6,300,000 metres and the minimum cosine over receiver latitude plus its latitude error. Reject unsupported polar bounds. This is an explicit coordinate error convention under conventional receiver coordinates, not raw GNSS ranging.

The degree-four Taylor envelope declares absolute derivative bounds by order for latitude/longitude/height, in radians/metres and seconds:

These explicit smoothness assumptions cover the Taylor remainder only when they hold. They are not inferred from a low polynomial residual. Record observable envelope conflicts, but absence of a conflict does not verify unobserved high-frequency motion.

Use apparent gravity 9.70–9.90 m/s², one count per delta-velocity component, the separately recorded IMU8/IMU21 conversion hypotheses, a corrected body-force direction-rate bound of 1 rad/s and a continuous scalar magnitude-rate bound of 2 m/s³. Periods are exact under each named integration hypothesis; frequency error and time-varying latency are not implicitly covered. None of these assumptions may be changed after viewing this assessment's outcomes.

Regression weighting is a fixed identity matrix, not an estimated covariance. Coordinate measurement/truncation boxes propagate deterministically through all nine trajectory quantities and the nonlinear candidate force calculation. Do not shrink deterministic errors as independent noise. Estimate the force box at every retained packet midpoint; include continuous averaging and common offset bounds. Preserve physical and numerical failures separately.

Finite allowance and outputs

• Two strict, hash-checked source extractions; no downloads or new selections.
• 24 receiver-operator batches: two recordings × three windows × two clocks × two receiver-error boxes; at most 256 operators each, 6,144 total.
• 144 candidate identities: those 24 batches × two calibration boxes × three candidates; at most 256 force boxes each, 36,864 total.
• Zero optimizer starts, zero native trajectory integrations and no retries.
• One worker, four total numerical threads, 30-minute wall ceiling.

Charge each extraction, operator batch and candidate identity before work. Interrupted identities remain charged. Source/input/environment hashes and immutable artifacts must verify before continuing unfinished work. Completed work never restarts. Preserve selected counts, timestamps, interval membership, receiver inputs, parameter assumptions, outputs, exclusions and hashes.

Publish a compact table and CSV of measured/predicted envelopes and minimum gaps for every identity, with unsupported intervals visible. Overlap is only a non-exclusion by a necessary scalar constraint; it is not complete-history feasibility. Disjoint boxes indicate incompatibility under the stated bounds, not calibrated significance. Every scientific decision remains abstain. Compare descriptively with the saved complete-observation findings, without refits or relabeling earlier sensitivity failures.

Combined controls · Roadmap.