Next steps for the NASA airborne analysis

Starting point

The preserved first study found 12 globe preferences. Completed recovery adds twenty-nine, giving 41 globe preferences, zero flat preferences and 12 unfinished comparisons among the same 53 eligible stretches. All forty-one also favor the background-field globe over the zero-field globe. Completed results now include both IMU8 and IMU21 recordings. This is a substantial empirical finding; unfinished calculations do not provide equal support for flat Earth. A calibrated statistical significance level and independent-replication count still require uncertainty validation and accounting for shared flights and instruments. The current findings and saved-result diagnosis preserve what the measurements and calculations currently show.

“Rotating globe” and “still globe” below retain the exact names used in saved fits. They compare the standard background angular-rate term with zero on the same globe geometry. They are not verdicts on the field's physical cause or on heliocentric versus geocentric cosmology. A stationary-Earth theory proposing a nonzero inertial field is not represented by the zero-field candidate. Keep model preference, free measurement of the field, and interpretation separate; see the interpretation policy.

An IMU (inertial measurement unit) measures turning and acceleration. These are survey-grade IMUs used for precision airborne mapping. Their published capabilities provide a meaningful foundation for error assumptions. Exact device characterization and producer documentation are lower-priority parallel work, not prerequisites for continuing analysis. Use available system/family specifications, empirical decoder checks and explicitly stated assumptions; investigate how those assumptions affect results. Do not transfer one configuration's exact specifications to every recording or call an assumed offset allowance measured drift. Unknown corrections matter where they prevent a particular quantity from being separated, rather than stopping all modeling.

The covariance/prediction comparison has finished with 10 of 12 fits converged; its combined comparison remains unresolved. The immediate priority is resolving as many of the remaining 38 numerically incomplete stretches as possible. The active wider run retains all 41 original recovery identities and reuses the three completed subset stretches, preserving the earlier evidence. Further diagnostic expansion is deferred. Numerical completion, fit adequacy and statistical support remain separate checks; recovering a fit does not by itself establish a calibrated scientific detection.

1. Freeze a small representative subset of the 41, covering numerical failure types and observable recording properties without choosing favorable model preferences.
2. Test a separately frozen numerical strategy and larger finite evaluation budget, retaining the physical models, calibration bounds and two processing cases.
3. Check objective agreement, valid stopping, repeatability and predicted tracks, including a completed control. Keep all original failures and results unchanged.
4. Apply the qualified method to all 41 in a separately budgeted recovery study. Preserve numerical failures and report newly complete comparisons explicitly.

The recovery preparation records all 41 unfinished stretches and selects one from each of three numerical failure categories, plus a completed control. This is metadata-only preparation; the numerical strategy and finite evaluation allowance remain to be qualified.

The continuation trial is complete: 15/24 fits passed, including all six completed controls and eight of 15 unfinished primary fits. None of the three unresolved stretches became fully resolved, so this method did not qualify for rollout. Its 24 starts cover 15 unfinished fits, six completed control fits and three perturbed-start repeats. Each allows 600 fitting sweeps plus two track checks; the 14,448-sweep ceiling estimates roughly 10–14 hours on two threads. The finite allowance is recorded in the runtime freeze. Unchanged converged reference fits are reused; original failures retain their labels.

The saved stopping audit separates four early gradient failures, four early stability failures and one budget failure. A known-answer, near-boundary software control reproduces one stopping failure; the rectangular dogbox alternative passed 30/30 software controls versus TRF 29/30. The separate rectangular proposal preserves all physical assumptions, requires fresh stability verification, and saves final Jacobians and evaluation traces. Its v2 trial is complete: 24 starts used 2,021 native sweeps; 8/24 fits passed, including all six completed controls but only two unfinished primary fits and no perturbed repeats. No test stretch became fully resolved, so qualification failed. Its saved traces and Jacobians support further numerical diagnosis; software success did not translate into all-41 recovery readiness.

The saved-tangent diagnosis reproduces a boundary-start stall on an independent two-parameter control. Exact-bound initialization improves completion on saved affine systems from 12/24 to 16/24; the remaining weak directions involve gravity correction and gyro gains. The boundary-aware nonlinear controls now pass 40/40 known-answer comparisons with bounded linear steps, versus 35/40 for the original method and 38/40 when only the start is snapped to the boundary. All retain the same bounds and fresh stopping checks. The separate boundary-aware archival trial is complete: 17/24 fits passed using 2,399 sweeps, including nine of fifteen unfinished primaries, all six controls and two repeats. No test stretch became fully resolved; the method did not qualify for rollout. The saved-result diagnosis separates six stationary stability stalls from one budget failure. All three predetermined primary/repeat pairs agree in cost and track to within 0.13 mm on every axis, yet have opposite stopping outcomes. Before another trial, isolate native prediction and tangent accuracy near these endpoints, keeping the physical models and bounds unchanged. Further budget alone does not address the six early stops. No archival result is relabeled by these local calculations.

The separate actual-position stability comparison checks the full model's predicted-position change instead of rejecting a correction solely on its local residual prediction. It retains gradient and objective-change limits, requires at most 1 mm axis-specific RMS movement and 1 cm at every epoch, and preserves the old rule and results. These numerical tolerances are not claims of receiver accuracy. Forty known-answer cases and independent short native motion controls pass. The new finite trial uses all primary endpoints of the completed boundary-aware study, the same four recordings, 24 starts and a 14,448-sweep ceiling. No endpoint is chosen for a favorable cost or convergence result. Both primary and perturbed starts must independently pass before an all-41 recovery freeze. This trial is now complete and qualified: 24/24 fits passed, including all controls and repeats, using 393 native sweeps. Three previously unresolved stretches consistently favor globe, giving a combined numerical tally of 15 globe, zero flat and 38 unresolved while preserving the original study.

The full recovery preparation records all 41 original unresolved stretches and their 130 unfinished fits. If the qualification passes, reusing its 15 primaries and three repeats leaves 115 primary recoveries, 38 repeated-start checks and six fresh controls: 159 starts, capped at 95,718 native sweeps. The ceiling estimate is 51–76 hours on two threads. Selection uses original completion status and UTC order, never model costs. This is metadata preparation; the qualified trial now supports the separately frozen remaining-stretch recovery. Each newly complete stretch must also pass its repeat check and fresh controls.

The wider run completed all 159 starts and 22,355 sweeps: 117 fits passed, including all six fresh controls. Eighteen original unfinished stretches pass their complete comparison and repeat, bringing the combined tally to 30 globe, zero flat and 23 unresolved. The earlier 15/0/38 tally above describes the subset stage, not current findings. The completed freeze permits no retries or use of its unused allowance.

The next priority is overlapping flight legs recorded by two instruments when one comparison finishes and the other does not. Start with the 24 October 2009 IMU8/IMU21 leg and the 26 September / 7 October 2015 loaner/DMS legs. Use the same shared UTC interval, compare per-axis raw and motion-context rate differences, and inspect model-specific costs and stopping reasons. Keep different recorders separate; an unfinished result is not an opposing shape finding. The analytics export records these pairs and descriptive measurements without new fits. A subsequent numerical comparison needs its own finite freeze; the completed recovery allowance stays closed.

The saved paired-recording diagnosis finds six overlapping recorder pairs with different completion outcomes. Each of the three priority pairs has one failed primary fit: two miss only the relative-cost stability check, while the third misses the vertical position-stability check. All three pass endpoint stationarity. Saved agreement does not relabel a failure. The bounded endpoint diagnostic checks the three failed endpoints and their three successful-recorder counterparts with sixty native evaluations maximum and zero optimizer starts. It compares repeated predictions, value/derivative implementation agreement, and full/half/quarter local corrections before any new fit policy is considered. It completed all sixty evaluations. Repeated coordinates were identical, and the value and tangent implementations agreed within 0.00025 micrometres across all evaluated points. Smaller corrections pass the measured probe checks at two failed endpoints; the October 2015 DMS endpoint still fails the cost check. A neighboring originally completed loaner endpoint also fails the newer full-correction check. The completed probe report retains these observations without changing any disposition. The next test concerns derivative accuracy and integration precision in weak calibration directions, rather than further attempts under the unchanged stopping procedure.

The wider-arithmetic diagnostic now compares the same six endpoints at identical parameters and frozen local corrections. Its maximum is 84 native evaluations with zero optimizer starts. The new kernel passed exact-motion and derivative controls before archived use; it retains the equations, bounds and packet-clock branches. A completion watcher publishes the sealed report and then runs six exact-motion solver controls after the native job releases its four-thread allocation. Any subsequent observed-fit qualification still needs its own finite freeze; no old failed fit is promoted. That comparison is now complete: five of six full probes pass with wider arithmetic, including both cost-only failures; the September disc vertical failure remains. Eleven arithmetic/derivative controls and six exact-motion solver controls passed. The paired qualification trial passed all sixteen fits, including both controls and perturbed repeats, in 129 sweeps. Both previously unresolved targets now favor globe, bringing current findings to 32 globe preferences, zero flat and 21 unresolved.

The separate cost-only recovery completed all 86 starts in 891 sweeps, passing 83 fits, both controls and all twelve repeats. Nine more stretches have complete comparisons, bringing findings to 41 globe preferences, zero flat and 12 unresolved. The other three primary fits exhausted the forty-evaluation allowance. The next bounded continuation preserves models and gates while allowing up to 200 evaluations and fresh repeats/controls. The nine earlier stationarity/position-failure stretches require their own assessment. Neither prior freeze may restart or reuse its unused allowance.

Minimum solver qualification supports this recovery sequence. Additional clock, calibration, covariance, measurement-contribution and independent-flight studies can be revisited afterward; they are not prerequisites for attempting numerical recovery. No new numerical allowance is implied by this roadmap.

Priority and scope

The matched trial is now complete: 10/12 fits converged versus 11/12 in its baseline. The control kept its globe/rotation preference; the other stretch remains unresolved. The saved-fit calibration/adequacy audit now reports signed limits, parameter associations, local weak directions and residual RMS for all 318 first-pass and 12 trial fits. The two-recording residual diagnostic has completed 24 saved-parameter predictions with no refits. It reproduces baseline errors, finds temporal correlation after whitening, and exposes a large vertical clock effect. Full-flight solver qualification remains planned; the completed calibration comparisons below examine matched alternatives. The software qualification matrix now passes 34/34 predefined starts, including short independently generated IMU/GPS controls. It qualifies those small cases, not full archival optimization. The six-start clock comparison has completed with all six fits converged. Reoptimization under packet-header timing restores the control's rotating-globe vertical error to about 0.70 m and preserves its globe/rotation preference. Z-axis gain and offset still reach their bounds. The completed control's nominal-clock references remain unchanged; calibration sensitivity is the next unresolved comparison. The saved clock/calibration audit shows that gravity correction leaves its limit while Z gain and offset remain pinned. Its prepared sensitivity plan isolates each Z correction with matched zero-anchor ablations; those are diagnostic references, not asserted factory calibrations. The separately frozen 12-fit calibration comparison has completed: 11 fits converged. Gain-zero preserves globe/rotation preference under both processing cases; offset-zero remains incomplete because one still-globe fit exhausted its allowance. All four rotating-globe fits retain close track errors. No retries are authorized. The retrospective prediction trial has completed with five of six fits converged. In its fully completed processing case, horizontal prediction RMS is 2.45 m for rotating globe, 142.9 m for still globe and 166.0 m for flat disc. The second case's flat fit exhausted its allowance, leaving the combined comparison unresolved. This recording had already been examined in full; the split does not turn it into unseen-data confirmation.

The saved prediction audit now shows where prediction errors grow and how calibration changes with the fitting window. Z gain switches from −2% in whole-stretch fits to +2% in training-only fits under both processing cases; gravity correction returns to its limit. The solver-scaling comparison completed five of six fits. The sixth reached a much smaller projected gradient but did not satisfy its stopping rule; it remains unfinished. The verified-stopping comparison also completed only five of six fits and did not qualify. The saved failure audit identifies a bounded residual-step probe 1.55 times its stability limit. The next work is independent clock/calibration controls and review of numerical strategies. Predeclared prediction checks on two other recordings follow only if the numerical method qualifies and receive their own allowance. The solver and replication plan preserves those records and criteria. The six-fit allowance is spent and permits no retries. The two-recording replication still needs its own finite allowance, and calibration robustness remains a separate check.

The joint Z calibration audit now reports 27/27 converged fits on the control. All nine fixed gain/offset pairs preserve globe preference, then the specified background-field preference. The preferred cost varies 2.58%, with 0–1 remaining parameters at limits. Its advantage does not depend on the two extreme Z corrections, but this does not determine factory calibration. Two separately frozen grids now test profiled upstream removal and the earliest predeclared other recording. Both are now complete: removal converged 27/27 fits; the other recording converged 25/27, with seven complete globe preferences and two unresolved nodes. Each spent its 27-start allowance. The next saved-only audit compares remaining calibration limits and weak directions and examines the two stopping failures. The second grid checks whole-stretch robustness; held-out prediction replication remains deferred.

The saved follow-up audit now compares all 81 grid fits and checks 243 epoch residual series against their saved costs and RMS. Both unfinished fits pass saved stationarity but exhausted the solver allowance without reported success; neither is relabeled. Preferred-model costs barely change when removal is profiled, with fitted removal effectively zero on the control. No new observed starts are included in this audit.

The residual covariance audit now reports dense lag curves, cross-axis matrices and spectra for all 81 saved fits. On October 5, the preferred model's vertical innovations retain a 60-second correlation of about 0.27, with about 68% of spectral power at periods of at least a minute; September 24 shows less slow dependence. These are two recordings, not independent calibration-grid replications. The shared error-model plan sets out common cross-axis and correlated-error terms, development-only estimation and blocked prediction checks. The covariance software controls now pass all 35 checks: irregular times, cross-axis and coordinate transformations, whitening, fixed drift anchors and conditional prediction across a split. They use known covariance and residual mean; they do not include fitted-parameter uncertainty. The training/prediction controls now pass 26 checks for training-only restricted-likelihood covariance selection, linear-parameter uncertainty and covariance-choice sensitivity. They do not integrate covariance-parameter uncertainty or handle the NASA fits' nonlinear active bounds. A bounded observed comparison must specify those treatments before launch and still requires qualification and a finite allowance. The nonlinear/boundary controls now pass 25 geometry checks and an independent estimator-distribution check. They retain active parameters, identify deficient directions and preserve disconnected sampled support. They do not qualify NASA confidence intervals. The preparation plan now has a control-tested native adapter. Six independent geographic controls verify all 27 columns with 348 native software sweeps and no archive reads or observed fits. The costed comparison preparation now specifies 12 October 5 training/prediction fits under shared 10- and 300-second correlation assumptions, capped at 3,060 native sweeps with no retries. Its estimated ceiling is 154–172 minutes. The durable launcher now passes 39 worker, planning and native controls. Its separate freeze requires explicit approval of the finite allowance. Its approved 12-start comparison has completed with 10 converged fits; its combined hierarchy remains unresolved. That allowance does not authorize the separate recovery study.

The focused diagnostic plan incorporates the October 11 review, identifies tests already completed, and specifies the remaining clock, calibration, covariance and measurement-contribution work. The priorities above guide the next studies; they do not interrupt the approved numerical trial or expand the corpus.

This roadmap authorizes no new observed starts, synthetic campaigns, deletion, resumption of completed studies or production promotion. The verified-stopping trial is complete; its six-start allowance is spent, with no retries. Any new numerical work needs a separately identified configuration and finite approved allowance. Future jobs share a four-thread total budget through the launch guard; active and historical freezes retain their original settings.

1. Qualify numerical completion

Review the matched solver trial against the preserved baseline: objective values, stationarity, stability, boundary behavior and predicted observations. A materially worse completed control or unexplained change in ranking needs investigation before expansion. Do not simply promote the 42 old budget-stopped fits that happened to pass stationarity.

Add bounded qualification controls generated independently of the fitting kernel: known interior and boundary optima, transport-only and background-rotation inputs, nearly redundant parameters, timing perturbations, and several deterministic seeded starting points. The existing analytic solver tests are a start, not an independent end-to-end IMU/GPS qualification. Check objective agreement and prediction recovery; require parameter recovery only for combinations the controls identify. Count every start and evaluation. Multi-start agreement improves confidence but does not prove a global optimum. Distinguish a converged but poor flat fit from an unfinished flat fit.

The completed software matrix already includes short independently generated IMU/GPS controls. Extend that evidence to realistic integration lengths, both clock conventions, coupled gain/offset errors, near-boundary optima and poor initial states. Compare two numerical strategies over the same feasible region. A larger evaluation-budget sensitivity is a separate future freeze, not permission to retry or relabel the original failures.

2. Explain calibration-boundary saturation

The first pass reached the Z-axis gyro-gain limit in 304/318 fits and its offset limit in 294/318. The median completed fit had 15 parameters at a limit. A constrained optimum can legitimately sit on a boundary; this frequency warrants its own audit.

For every parameter, report its physical estimate, normalized distance to each limit, upper/lower boundary counts, model/case dependence and associations with clock, mounting, speed and latitude. Examine Z-axis gain and offset together. Across-fit correlations of estimates describe the archive; they are not within-fit parameter uncertainties. Use projected gradients and available Jacobian singular vectors to examine local trade-offs. The baseline saved singular values alone; do not pretend it contains those vectors.

The completed zero-gain and zero-offset tests remove one correction at a time. The first joint grid maps combined sensitivity under header timing and no removal, preserving gradients, remaining limits and weak directions. The next two approved grids test the other processing assumption and another preselected recording, keeping remaining bounds unchanged for all three models. Further clock grids need a separate allowance. Plot feasible limits, fitted points, unfinished grid points and cost valleys. Check whether those valleys move with clock convention. Keep this separate from an absolute calibration estimate: a shallow valley can preserve a model preference while leaving its calibration poorly identified. Grid size and start allowances must be costed before approval.

Specify a small calibration sensitivity matrix before new fits, justified by published survey-system performance and the physical meaning of each error. Separate constant offset, gain error and changing drift. Vary the suspect gain/offset limits in controlled steps; hold other assumptions fixed, then test only a justified interaction. Apply every case equally to rotating globe, still globe and flat disc. Preserve preferences, failures, residuals and boundary behavior whether or not they favor globe.

Success means either explaining why a boundary is physically appropriate or showing a stable preference under defensible alternatives without systematic unexplained extremes. Do not add unrestricted time-varying bias just to improve residuals or choose limits that produce a desired shape. Exact per-unit certificates are not required to run these tests.

3. Assess absolute model adequacy

Every completed fit should report physical horizontal/vertical residuals, whitened RMS, residual quantiles/outliers and temporal dependence. Whitened residuals are errors scaled using the declared GPS covariance. Test their distribution and autocorrelation against what that covariance predicts; a small relative model cost does not establish that the covariance or preferred model is adequate.

Plot residuals against receiver speed, latitude, height, elapsed time and independently available maneuver indicators. Use measured temperature only if a documented channel exists. Elapsed time or aircraft movement must not be relabeled sensor temperature. Store epoch-level residuals and weights in a new diagnostic artifact if the old outputs lack them; generating predictions still has a numerical cost even without optimization.

The completed two-recording diagnostic now stores per-epoch errors under both clocks and both covariance assumptions. Its nominal rotating-globe residuals are small but retain lag-one correlations of roughly 0.42–0.76. Packet-header timing raises vertical RMS to approximately 9.2–9.4 m without changing fitted parameters. These findings prioritize the clock comparison; they neither establish a calibrated adequacy failure nor replace held-out prediction checks. Speed/course covariates in this diagnostic are coordinate-derived proxies under a reference globe metric, not recorded VTG measurements or independent evidence.

The completed covariance audit extends the saved grid epochs through 60 lags, with cross-axis covariance and low-frequency power, retaining actual time separations and cadence limitations. Irregular records receive no spectrum or resampling. These are fitted navigation errors containing receiver error, inertial error and model mismatch; they cannot alone identify receiver noise. Compare available fix-quality and precision channels without treating those indicators as measured error variance; the selected saved epochs lack those fields. Estimate and seal a shared covariance alternative on development or training observations before evaluating later predictions. Do not choose a different covariance for each physical model or calibrate a significance threshold on its own in-sample residuals.

Retain the whole-stretch fit as the primary analysis. Existing fixed-parameter 4–10-minute section checks remain useful, but are not held-out validation: the parameters saw those observations. A genuine blocked prediction check fits calibration/initialization using training receiver observations only and evaluates withheld receiver positions using the original IMU increments. Account for correlated GPS errors across the split and fitted parameter uncertainty. When a short stretch cannot support a meaningful split, report that limitation and use separate-flight validation; do not invent independent trials.

Develop and validate an absolute-fit criterion before it can authorize positive scientific support. Account for fitted parameters, active bounds, correlated errors and solver failures; do not assume a textbook chi-square cutoff applies automatically. Calibration must cover the full hierarchy, including the minimum of the two globe costs and the selection process.

Public reporting should distinguish:

• Preferred model: the complete matched comparison has a lower cost.
• Adequacy not established: required absolute-fit checks are missing or unvalidated.
• Preferred but inadequate: the relative winner fails established fit-quality checks.
• Validated support: numerical, adequacy, robustness and statistical decision checks pass.

These future labels do not retrospectively change the current findings. The existing production significance gate stays intact until the additional checks are validated.

4. Compare timing and receiver-coordinate assumptions

The selected-packet clock audit now reproduces both frozen recordings, including both time tags and native provenance. UTC elapsed time differs from nominal by about 22 ppm. Independent physical controls demonstrate how this can accumulate into substantial height error and trade off with gravity; they do not identify the NASA increment period or reproduce the full fitted calibration shift. No new observed fits or native predictions were made. The coupled three-dimensional controls now recover known motion and demonstrate both packet-endpoint compensation and its loss under independent observation times. They check the Python integration primitive and known-reference linear calibration. The separate geographic controls extend testing through both native kernels and nonlinear solvers, with independent receiver times and six free calibration/initialization/latency parameters under all three true models. Their report retains every outcome. Full nuisance freedom and long-record conditioning still need qualification before observed profiles.

All 24 geographic fits passed the predefined convergence/prediction checks. Their calibration audit shows why this is insufficient: micrometre track errors coexist with up to 0.647°/hour Z offset error in the short synthetic tracks, and all 12 near-boundary fits reach the offset limit. The completed interval controls separate those effects: all nine new fits passed, offset errors shrink approximately with interval squared, and added roll reduces the remaining error by another factor of 34–42. This identifies a numerical/geometry mechanism in the synthetic controls, without establishing the NASA boundary mechanism. The original-rate correction comparison has now completed: all nine new fits passed, and combined coning/rotating-force corrections reduce offset error to at most 0.000377°/hour across the three supplied truths. Both globe controls recover within 0.000011°/hour. Conditioning remains weak; these noise-free, six-parameter controls do not qualify noisy or full archival fits. The latitude/convention extension has also completed: all 24 fits at ±45° pass, with offset errors below 0.00079°/hour and no calibration limits reached. Opposed starts and roll/unequal timing retain the improvement. Correcting already-compensated inputs instead introduces error. A six-fit NASA integration comparison has completed with unchanged header timing, bounds and solver: four fits converged and both zero-field globe fits exhausted their budgets. The 27-column derivative check has passed for all three candidates; global optimizer qualification remains distinct. Do not upsample observed packets or double-correct the archive. The saved integration audit preserves the original findings and identifies no improvement in Z boundary saturation. Its staged profile plan proposes 27 fixed gain/offset comparisons, roughly 6–7 hours, under original integration and one processing case first. Implement/test its worker and obtain a separate finite allowance before execution. The profile worker now implements fixed-coordinate reoptimization, final derivative capture and recovery; preparation starts no fits. The integration alternative is not ready for corpus rollout.

The control's matched reoptimized clock comparison is complete: all six fits converged, the close rotating-globe fit returned, and globe/rotation preference survived. It shows that calibration can absorb much of the fixed-parameter clock effect; it does not establish the physically correct integration interval. Z gain and offset remain at their limits.

First audit packet timestamp quantization, interval distributions, cumulative elapsed-time drift, rate changes and discontinuities, separately from the period represented by each increment. Compare nominal timing with header timing without selecting the convention that gives the preferred model its smallest cost. Use independent packet-jitter controls and available decoder-validation channels to investigate the distinction. Group1 remains fused navigation and supplies no independent Earth-model evidence. Then a separately frozen extension can test the other preselected recording and the joint calibration profiles under both clocks. Report costs, ranking, completion, calibration and prediction quality, including incompatible or inconclusive timing evidence.

Then compare full three-dimensional receiver positions with horizontal-only observations, an altitude-only diagnostic and justified height/geoid perturbations. Preserve original reported heights and geoid separations. Clearly identify which coordinates enter the objective, initialization and motion screening. Removing altitude from the objective alone does not mean it disappeared from the complete procedure. Check identifiability after each ablation; an insufficient observation set cannot supply a positive conclusion.

Transform covariance consistently with any coordinate representation. Equivalent representations of the same physical observations should agree numerically; do not compare arbitrary coordinate units as if they carried equal information. For an axis ablation, use its appropriate covariance rather than dropping components after joint whitening. Receiver latitude/longitude remain outputs of a geodetic navigation system; these tests isolate their influence, not replace them with raw GNSS ranges. Raw ranges are a possible later extension, not a blocker for the present archive study.

Applanix V6 section 3.3.2.1 documents Group 10001 as primary-receiver output. The planned versioned supplement will retain per-file receiver-type codes, original NMEA identifiers, stream hashes and historical version/layout evidence. Receiver output is distinct from fused Group 1 navigation; that source distinction does not establish independence of coordinate assumptions. See the provenance record.

The deferred measurement-contribution study separates gyro increments, acceleration increments, gravity and coordinate metric. Include a receiver-constrained gyro prediction where its frame and attitude assumptions can be stated explicitly. An ablation must define its replacement constraints and initialization, not silently supply missing gyros from fused attitude. Check whether non-gyro inputs can reproduce the distinction under comparable freedom. Report interacting channels and lost identifiability rather than an invented percentage of evidence attributable to one sensor. The original measurements and primary comparison remain unchanged.

Stage these comparisons rather than immediately multiplying every timing, calibration and coordinate option into a large grid. Freeze each small matrix and its compute budget before fitting, and add combinations only when earlier diagnostics justify them.

5. Account for completion selection and dependence

Report completion by model: rotating globe 43/106, still globe 73/106, flat disc 72/106. Analyze its relationship to pre-fit observables: duration, latitude, ground speed, heading evolution, recorded IMU type and installation signature. Keep fitted Jacobian conditioning in a separate numerical diagnostic; it is not an independent pre-fit observable. With only 53 stretches, prefer a small descriptive analysis to an overfitted prediction model. Do not select new intervals by whichever model finishes.

Build a grouping ledger using verified dates, platform information, time overlap, source aliases and installation continuity. Distinguish a POS system identifier from a physical IMU serial number. Where actual flight or device identity is uncertain, record that and use conservative grouping. Several stretches or simultaneous IMU streams from one flight must not become several independent confirmations. Hold out whole supported flight or installation groups for replication; never randomly split overlapping samples.

Joint calibration across stretches is a later useful test only where installation continuity is supported. Matching configuration bytes alone do not justify it. Model appropriate temporal changes equally for every candidate and charge its added complexity. Manufacturer replies can improve that support without holding up the other audits.

Rotation-field follow-on and publication

The saved solver diagnosis separates the remaining numerical stopping issue from calibration ambiguity. A verified-stopping candidate passed cheap known-optimum and false-stop controls, but its completed six-fit airborne comparison did not qualify. Later actual-position qualification passed its observed control and repeat checks, recovering three complete globe comparisons. The wider recovery is complete, yielding 30 globe preferences, none for flat and 23 unresolved stretches at that stage. The subsequent paired wider-arithmetic trial added two complete comparisons; the cost-only recovery adds nine more. Current findings are 41 globe preferences, zero flat and 12 unresolved. Preserve the original 12 resolved and 41 unresolved results alongside new recovery evidence; software controls alone do not relabel them.

The rotation-field proposal remains separate: fit a retained background vector freely and examine latitude/altitude/velocity dependence. Report its measured properties without assigning a physical cause. Competing causal explanations need distinguishable quantitative predictions to be tested with this archive. It will reuse the numerical, adequacy and dependence checks above. It need not wait for an exact hardware identification, but unknown upstream subtraction must not be fitted as though it were independent of an unknown original field strength.

Before field fitting, audit rank using the archive's actual latitude, heading and supported installation groups. Test the columns for north amplitude, east component and vertical amplitude against installation-specific gyro offsets and upstream removal. Report weak combinations and coverage; configuration similarity alone does not establish shared calibration. This geometry check precedes fitting a common magnitude or testing solar versus sidereal rate.

Its precision stage will also ask whether the freely measured magnitude distinguishes 15.0000°/hour from 15.0411°/hour. First establish the field's direction and latitude pattern; then use a separately selected longer-record inventory, shared calibration only within supported installation epochs, and whole-flight held-out checks. Refit nuisance parameters when profiling both rates. Gain, clock scale and unknown upstream subtraction can remain indistinguishable from a change in magnitude, so longer recordings alone do not settle the question. Report unresolved cases explicitly. This tests the period, rather than absolute astronomical phase, and requires a separately approved bounded numerical trial.

Publish methods and empirical conclusions at the level actually supported. A methodological paper can describe the inverse-navigation framework and verified controls even when many real fits remain unfinished. Stronger empirical claims require adequate, robust comparisons and genuinely independent replication. Continue preserving original increments, receiver observations, selection, failures, source/environment hashes and complete reporting receipts. Keep consumer-IMU development secondary; it does not resolve these archival questions.

Secondary branch: stationary consumer crowdsourcing

The passenger-flight proposal is superseded by the stationary A/B experiment. Collection now uses a solid level support, a marked horizontal axis and repeated same-face 180° reversals. Aircraft identity and flight dashboards are removed from the active app flow. Historical aircraft simulations and frozen research remain preserved.

The signed-rate diagnostic is implemented and does not use latitude or an expected amplitude. Next priorities are independent slow-turn response tests, sub-count sensitivity, temperature/stability and reversal/alignment controls, then calibrated uncertainty. Only after sealing per-recording methods should a separate population estimator fit the latitude curve, preserving instrument/day/site dependence and all failures. The ground experiment neither replaces NASA analysis nor inherits its thresholds.