Refining the globe-versus-disc comparison

The pilot is complete: two recordings favor globe and then rotation across all four cases; none has a complete flat-favoring result. Four recordings lack complete comparisons. See the pilot findings and the subsequent 53-stretch findings. The sections below preserve the method and development sequence.

The initial calculation needed refinement before its fit differences could be used scientifically. The main issues are unfinished optimization and calibration freedom large enough to absorb the predicted signal. Sensor quality alone does not establish how much of that freedom is needed in these particular logs.

At 140–256 m/s, the spherical horizontal curvature scale is about 4.5–8.3 degrees per hour. The historical stress test permits a constant offset of ±20 degrees/hour per axis. The corresponding centripetal acceleration scale is approximately 0.003–0.010 m/s²; each acceleration axis permits ±0.25 m/s². These comparisons use an explicit 6,371 km spherical radius. They are predicted scales, not measured Earth signals or the complete globe/disc difference.

On a steady interval, a nearly constant model contrast can be traded against an unknown constant IMU offset. A deterministic algebraic check shows that an 8-degree/hour constant gyro contrast disappears completely inside the current 20-degree/hour offset envelope; a 1-degree/hour envelope leaves 7 degrees/hour. This does not show that the actual flight contrast is constant. It explains why more observations of the same geometry cannot by themselves establish calibration. Changing speed/direction, independent calibration and controls can break that trade.

What the refinement should do

1. Resolve numerical optimization first. Use accurate derivatives, parameter scaling and staged initialization. Finish with all declared nuisance parameters free within the same stated bounds. Diagnose actual gradients and derivative stability; do not accept a tiny optimizer step as evidence of a minimum. Validate the new solver before spending another observed-data fitting allowance.
2. Ask globe versus disc explicitly. Treat the rotating and stationary globe as a two-member family, preserving the separate rotation question. Compare the family's best profile with the disc only when all contributing candidate profiles are resolved. Local convergence still does not establish global minima.
3. Measure calibration sensitivity. Test assumed constant gyro-offset envelopes of ±0.1 and ±1 degrees/hour while holding other assumptions fixed. Independently test acceleration/gain sensitivity afterward. Smaller envelopes are hypotheses, not established instrument performance or permission to force a preferred result. Report which calibration accuracy would be needed for useful separation.
4. Separate processing hypotheses. Repeat matched candidates with Earth-rate subtraction fixed at zero and with the common subtraction fraction free. Keep the same observations, initialization rules and covariance for every candidate.
5. Use changing geometry and shared calibration carefully. Prefer intervals spanning different speeds/directions according to GPS geometry, before gyro comparisons. Pool calibration only within supported sensor/installation epochs; hardware identity alone does not prove unchanged mounting or independent flights.

The existing six date/configuration representatives remain the initial development set; no replacement is chosen because of a gyro outcome. New empirical runs need a separate finite source/environment/attempt freeze. The preceding corpus study and its original 764-start aggregate limit remain preserved; that completed study must not be resumed.

What is implemented now

The separate ilvis0_refinement module initially provided the constant-bias control, physical scale comparison and a direct globe-family/disc profile summary. The latter refuses to compare unresolved candidate optimizations and always abstains from a calibrated scientific decision. Five focused tests pass, including false-convergence refusal.

The attached refinement snapshot records the six already completed corpus results and their hashes. It starts no new model predictions, fits or campaigns, changes no active source freeze and deletes no data. Further optimization and calibration sweeps were proposed development work at that snapshot's date, not completed results.

Numerical method and run scope

analysis/lll/ilvis0_shape.py and ilvis0_tangent.cpp now implement forward automatic derivatives through every measured IMU packet. Derivatives cover the effective initial orientation, calibration offsets/gains, antenna lever arm, gravity, timing and common Earth-rate removal. Column scaling and a short initial attitude/velocity/position/gain stage precede the final profile with all declared nuisance parameters free. Every native sweep counts; a fresh final derivative must satisfy the stationarity check. Derivatives at exact GPS packet boundaries use the left interval and are flagged. Local convergence still does not prove global minima.

The professional hardware deserves professional-scale sensitivity assumptions. A constant fitted offset is not a measurement of time-varying drift, and observed aircraft motion is not sensor noise. Applanix's POS510 system noise/drift figures do not establish the absolute bias in these logs. Northrop's LN200 family sheet lists gyro bias repeatability of 1–3 degrees/hour for the core variant, 0.5 for enhanced, and 0.15 for high performance, all one-sigma figures. The exact installed variant is unconfirmed; none of those figures is a hard calibration bound for this archive. The new ±0.1 case is an optimistic residual-calibration hypothesis and ±1 a wider sensitivity. They do not cover every family variant or replace per-unit calibration. Other gain/acceleration bounds stay unchanged to isolate this sensitivity; time-varying bias, filtering and transport subtraction remain outside this finite model.

The exact original six recordings and windows are used, with no replacements after gyro outcomes. Each has four matched cases: two constant-offset bounds, crossed with Earth-rate removal fixed at zero or profiled over [0,1]. Both globe members are optimized internally to compare the globe family with the disc without presuming rotation. Rotation diagnostics are withheld unless every case has converged and its signed shape contrast favors the globe. Mixed, tied or unfinished shape results abstain. The result reports which model fits the measurements better. A validated statistical significance level has not been assigned; the separate scientific significance gate abstains.

The worker is analysis/tests/ilvis0_shape_worker.py; output: data/ilvis0-shape-refinement-20261008/. It verifies completion of the preceding v2 corpus and runs deterministic tests before fitting. At most two total numerical threads. Scope: 72 primary starts plus 12 interruption retries, at most two starts per file/case/model identity, and 200 total native evaluations per start, including fresh derivatives and diagnostics. Journals are fsynced; results are hashed and atomic; changed inputs, source or environment refuse resume. Completed work never resumes. Synthetic campaigns, source deletion and scientific promotion are outside this study's scope. The worker produces a compact RESULTS.md on completion.

Fourteen new focused tests pass, including all candidate derivative/value comparisons, known position/velocity recovery, shape-before-rotation withholding, budget enforcement, interrupted-start accounting, corrupt saved results and actual six-file handoff metadata. Five prior refinement tests also pass. Numerical outcomes are reported separately on completion; the worker's saved status and attempt journal provide progress while it runs.

Why the calculation takes hours

An eight-minute recording contains about 96,000 IMU measurement intervals at 200 Hz. Every fit repeatedly integrates the complete measured stream to predict the GPS path. It also calculates how that prediction changes with calibration, orientation, timing and other uncertain quantities, then adjusts them together. The GPS comparison accounts for errors that are correlated over time, rather than treating every position as independent.

There are 12 fits per recording: three Earth models under four matched assumption cases, or 72 fits for the six-recording pilot. Each permits up to 200 complete numerical evaluations, including final convergence checks and diagnostics. This repeated native-packet processing and joint optimization make an individual fit substantially more work than plotting or averaging a gyro channel. Compiled kernels perform the integration and derivatives; the worker uses at most two numerical threads and continues without interactive model calls.

The completed all-stretch extension uses six fits per stretch: three models under two processing cases, with the ±1°/hour offset allowance. The pilot's tighter ±0.1°/hour cases were deferred for that extension.

Automatic completion report

package_results.py --watch waits without fitting or model calls, then audits the finished six-file/four-case grid, every hashed per-file and per-fit artifact, source and input hashes, environment, charged starts and the 200-evaluation ceiling. It recomputes the shape-before-rotation hierarchy before publishing. Four metadata-only tests cover a valid completion, over-budget fits, corrupt results and a forged rotation stage. These controls do not simulate flights or consume observed optimizer starts.

After a successful audit it writes RESULTS.md, per-fit and shape/rotation CSV tables, frozen source copies and an evidence receipt in this documentation directory. Rotation tables include only cases allowed by the shape stage; withheld cases remain explicit. It updates project readiness from the latest metadata so the corpus completion is preserved. Watch mode has a 24-hour waiting limit and leaves workers untouched on error. If the watcher stops, run package_results.py without --watch after completion; do not rerun fits to regenerate a report. The report claims no calibrated detection.