Detailed study history

This page preserves the development record and intermediate outcomes. Historical counts describe their own stage, not the current combined findings. For the present result and priorities, see current findings, the short study index and next analyses.

The central question is whether recorded aircraft motion fits a globe or the specified flat disc. An IMU (inertial measurement unit) contains gyroscopes and accelerometers. The gyroscope record is the central turning measurement; GPS supplies route and timing, with receiver positions also constraining the fitted track.

This page follows the evidence and the problems each study addressed. Related software checks are grouped together. Current verified findings give the published totals; all 53 stretches and the comprehensive CSV give the individual records. Further planned work is separate.

Establishing usable observations

What the model comparisons resolved

“Resolved” here means that every required model, processing case, repeat and control passed its numerical checks. It does not mean that every model fit equally well. An unfinished calculation provides no finding in favor of either shape.

These are stages of one developing analysis, not extra independent datasets. The same stretch is counted once in the combined findings. Simultaneous instruments and shared flights also require grouping before statistical claims.

Checking why the models differ

The next measurement-contribution study has an input-dependency audit and 19 passing covariance/coordinate-projection controls. It has not yet run observed ablation fits.

The saved-primary inventory checks all 318 final primary fits. It finds 164 complete reusable artifacts and eighteen stretches with all six fits ready, while recording every missing array, time-context gap and unresolved reference. It makes no native predictions or fits.

The receiver-coordinate projection audit compares full, horizontal and height-only constraints at the saved parameters for those eighteen complete sets. All 36 horizontal-only processing-case comparisons favor globe; height-only scoring favors globe in 28 and flat in eight. No parameters were refitted. The original model results remain unchanged.

The generated-motion refitting qualification passed 24 controls before stopping at a failed height-only fit. Eighteen planned controls remain untested. All six horizontal fits reached so far passed, but their second-start checks did not run. The candidate is not qualified for observed refits; no recorded-flight result changed.

The fixed-endpoint diagnostic used 33 generated-motion evaluations to show that the proposed linear correction is too large to predict the actual fit reliably. Column rescaling gives the same result. It identifies a smaller trust-region step as the next candidate, without performing new fits or changing the failed qualification.

The complete trust-region control matrix passed sixteen of 24 generated fits and eight of twelve paired-start checks. All twelve horizontal fits passed; eight height-only fits failed the final full-range stability probe. The following sequence separately tested a local probe with unchanged numerical tolerances: all 24 fits passed, but one paired-start objective check still failed. The larger-budget continuation completed both fits in 1,035 native calls but did not resolve the height-only pair. The complete review remains unqualified at eleven of twelve passing pairs. Both coordinators completed without launching their dependent full-calibration matrix.

The horizontal-only review verifies all twelve horizontal fits and all six paired-start comparisons; it leaves height-only unqualified and preserves the failed broader gate. The subsequent horizontal full-calibration study tested all 26/27 nuisance columns: eight of twelve fits and three of six paired comparisons passed, leaving recorded-data refitting blocked.

The saved correction audit identified overlarge parameter moves in weak directions. Its separately bounded native probe check reproduced all twelve endpoints and passed all twelve regularized proposals without changing the physical objective or final tolerances. The current staged qualification passed all eight fits and five of six paired comparisons in 534 native calls. The remaining paired continuation passed both fits and all six combined pairs in 508 native calls, completing the staged horizontal-only software qualification.

The first horizontal-only recorded-flight study completed all twelve baseline reconstructions and 24 fits in 1,112 native calls. The IMU8 stretch passes all six repeats and still favors globe; the IMU21 stretch passes three of six repeats and remains unresolved in this sensitivity study. Both starts rank the models the same way. The saved-fit audit separates competing timing solutions from a marginal prediction-repeat failure and reports the large unscored height errors. The completed 28-point diagnostic isolates coupled timing/calibration and an unobserved vertical direction. The completed 29-point timing check finds no gross derivative fault and a path consistent with different locally stationary solutions, without optimization or label changes. The original 53/0/0 findings remain unchanged.

The multi-start qualification passed four known-answer systems with coupled calibration, multiple local optima, active bounds and invisible nuisance coordinates: 24 starts /166 constructed calls. The matched recorded-data follow-up completed 38 starts /2,376 native calls in 6.59 hours: both controls and 37 individual fits passed, but only two of six selected repeat comparisons passed. Specified-field globe reproduced its best predictions; the IMU21 sensitivity comparison remains unresolved. Wider timing searches are deferred while the separate gyro/acceleration contribution controls are developed.

The channel-removal controls pass 25 known-answer software checks. They expose the orientation freedom left without gyroscopes and define an acceleration-magnitude diagnostic without using fused attitude. This is software groundwork, with no new archived-data fits.

The fitting-error audit found median horizontal errors of about 0.068 m for the globe with the specified background field, 29.5 m for zero-field globe and 47.1 m for the disc on the same original twelve stretches and two processing cases. These are in-sample errors under each candidate's declared geometry, not independent prediction accuracy.

Finding and testing numerical failure mechanisms

Software controls have known answers. They check the calculations; they do not add flight evidence. A method that passes them must still be checked on the recordings.

| Complete timing-boundary review | Verified companions, controls and repeat agreement; added one globe preference, bringing the total at that stage to 48 globe / 0 flat / 5 unresolved. |

| Adjacent-boundary trial and complete review | Explicitly checked a neighboring timing boundary; both controls and the target pair passed in 44 calls, adding a globe preference: 49 globe / 0 flat / 4 unresolved. | | Clustered-boundary diagnostic and complete review | Located a stable point among closely spaced timing boundaries; both controls, all six primaries and the required diagnostic repeat pass, adding one globe preference: 50 globe / 0 flat / 3 unresolved. | | Remaining timing profile | All ten checks passed: both starts agree at each fixed offset under both processing assumptions; free-time completion remains untested by this diagnostic. | | Matched free-time test | Both controls passed, but all four target fits failed the full stopping gate despite close repeat agreement; the tally stays unchanged. | | Remaining-endpoint audit | Separates timing-only stationarity failure from fresh-correction failure and places the endpoints near integration boundaries, using saved data without refitting. | | Matched two-case boundary diagnostic | Both controls and the profiled-removal pair passed; both unsubtracted endpoints stopped at the probe-spacing guard. The tally stays unchanged. | | Narrow-boundary clock audit | Verified distinct, correct clock states below the fixed spacing guard, motivating a separately qualified numerical check; no native calls or model fits. | | Representable timing probes | All 31 software checks and all four observed checks passed; 56 native evaluations verified the two blocked endpoints and fresh controls with unchanged scientific stopping limits. | | Complete two-case review | Verified all six primary fits and both required repeat pairs from saved evidence, adding one globe preference: 51 globe / 0 flat / 2 unresolved. | | Final two-stretch audit | Separated geometry guards, unchecked neighbors and unstable calibration corrections in nine saved outcomes; no new integrations or fits. | | Focused nearby timing pair | Both controls passed; both targets stopped before evaluation because of a saved-context representation error. | | Corrected receiver context | Completed 54 native calls without software errors; both controls passed, but both targets failed the fresh right-side correction despite close repeat agreement. | | Saved correction systems | Reproduced a successful local-solver status with a worse affine objective than the feasible zero step, using six saved-system solves and no native predictions. | | Range-scaled affine correction | Passed 33 software checks and all four observed checks in 54 native evaluations, retaining all physical bounds and full native stopping limits. | | Complete scaled-correction review | Verified all six primaries and both processing-case repeat pairs, adding one globe preference: 52 globe / 0 flat / 1 unresolved. | | Last-stretch field-endpoint checks | All six checks passed in 100 native evaluations, including both processing-case pairs; the separate zero-field timing disagreement remains. | | Last-stretch zero-field timing profiles | All eight fixed-time fits and two controls passed in 132 evaluations; four repeat comparisons reproduced the two competing offsets. | | Last-stretch free-timing comparison | Both controls passed; four repeatable target fits failed full stability in 190 evaluations, leaving the last stretch unresolved. | | Last-stretch saved correction audit | Isolated a large proposed timing move almost at a packet transition; fixed-time corrections are micrometre-scale, and affine scaling alone does not fix it. | | Last-stretch two-sided timing checks | All four zero-field endpoint checks and both fresh controls passed in 102 evaluations; both processing-case repeat pairs agreed. | | Final complete model review | Verified six model/case primaries, four repeat pairs and two fresh controls, completing recovery at 53 globe / 0 flat / 0 unresolved; preserved all 28 focused outcomes. |

Supporting controls and earlier simulated-flight work

The remaining timing/calibration comparison examined eight outstanding endpoint pairs using saved data only. It distinguishes widely separated timing solutions from nearby solutions with calibration-stability failures, guiding the next matched profile without changing the published tally.

What comes next covers unfinished comparisons, measurement-channel checks, reserved-observation prediction, freely estimating the rotation field and the proposed solar-versus-sidereal rate test. The ground experiment is a separate consumer-IMU project under development.