Bounded numerical refinement proposal

The purpose is to make more of the existing shape comparisons finish, while preserving the physical question, the same measurements and the same nuisance bounds. This is a new development experiment. The completed 53-stretch study remains frozen.

The saved-result diagnosis identifies 119 evaluation-limited fits, including 42 that passed the saved stationarity test. Small singular-value ratios and frequent parameter limits suggest that weakly constrained parameter combinations are making numerical stopping difficult. This is a hypothesis to test, not a demonstrated solver defect or evidence that accepting unfinished fits would be safe.

Scope and comparison

Use two complete, previously selected stretches. Select them by numerical completion and observable matching, before using model cost differences:

Choose the unresolved stretch from the seven with all six saved stationarity checks passing, maximizing the number of completed fits and then sorting by identity. It has five completed fits. Choose the control from the fully completed stretches of the same IMU type, prefer the same recorded installation signature, and minimize the sum of relative duration and speed differences; break ties by identity. Both use IMU21 and have the same recorded installation signature. That does not prove that the physical installation was untouched between recording days; the files are not joined.

Reuse their exact intervals from the hashed selection. For each, fit rotating globe, still globe and stationary disc under both existing processing cases. Use the original zero initialization, complete raw-increment integration, receiver observations, clock hypothesis, covariance, bounds and whole-stretch residuals. Preserve the original initialization: force-derived accelerometer gains, zero other normalized coordinates, and zero Earth-rate removal. The earlier shorthand “zero initialization” did not describe the accelerometer-gain initialization in the frozen worker. Saved minima are the baseline; do not spend starts rerunning the old solver. Do not use fused navigation as an independent observation.

Method to prepare before launch

1. Test a separate solver prototype on cheap analytic least-squares problems with known optima: an interior optimum, an optimum on a bound, redundant parameters, poor conditioning and an exhausted evaluation allowance. Require stationarity and demonstrated step/cost stability at the returned point; merely passing a small gradient at the budget limit must remain unresolved.
2. Preserve the physical feasible set and all nuisance directions. Evaluate explicit scaled projected-gradient stopping with stability checks, addressing the difference between the solver's raw stopping condition and the existing independent scaled stationarity check. Do not simply relax the old gate or relabel its 42 results.
3. Before the first observed fit, fix the exact algorithm and tolerances, test them, and hash sources, inputs, selection, configuration and numerical environment into a new manifest. Persist immutable identities, starts, failures and interrupted charges.
4. Save projected-gradient components, bound signs, singular values and right singular vectors at the final point. This identifies which parameter combinations are weak without inventing a new model-test rank cutoff.

Prototype checks must pass before any airborne starts. A failed prototype or trial is reported as such; it does not justify more starts or looser thresholds.

Finite compute allowance to approve

Approved maximum: 12 observed starts, one per identity, 200 native evaluations per start, including initialization and final diagnostics. No retry reserve, automatic budget increase or expansion to the other stretches. Every interrupted start counts. Use at most two total numerical threads. This is approximately 1.3 hours at the completed study's median fit time, or 2.4 hours at its maximum; these are estimates, not guarantees. This allowance applies only to the separately frozen two-stretch trial described in its guide.

Report both successes and failures. Compare numerical completion, final stationarity, objective values, residual consistency and parameter limits against the saved baseline. If the completed control changes its model preference or worsens materially, investigate before extending. Report all changed costs; do not choose the method based on whether it increases globe support. An improved local optimum does not establish a global minimum, calibrated significance, accurate uncertainty or resolved onboard processing.

Interpret shape first, and expose rotation only after the required converged comparisons consistently favor the globe. Keep scientific decisions at abstain. Any later expansion or physical assumption change requires its own finite scope and separate freeze.