Qualify compensated arithmetic during fitting

Question: Does the corrected arithmetic pass the unchanged optimizer checks when fitting generated measurements, rather than only evaluating saved points?

The complete saved-point diagnostic passes all 315 derivative comparisons and four stopping probes. This permits optimizer qualification, not a restart of the stopped calibration campaign.

Fixed experiment

Use the two already exposed simulated seed families, 281474976810725 and 281474976810726. For each, retain all three generating physical candidates, both processing assumptions, both declared input-error formats and both original starts: 48 fits. These are development examples selected to include the previous failure, not independent confirmation or a calibration sample.

Preserve the two-minute trajectories, 300 Hz input, 119 receiver epochs, earlier-only initialization, original calibration bounds, gravity treatment, noise settings, covariance anchor and full 26/27-column problems. Change only the mean integration arithmetic to the qualified compensated implementation. Keep the original noise propagation. Reconstruct the four earlier saved-point input bindings and error operators exactly; never relabel the original fits.

Each fit has at most 200 evaluations, one continuous forecast, no retries and no alternative starts. Use four workers with one thread each and a two-hour cooperative ceiling. Prepay the existing per-case construction and native caps: 2,877,792 native operations and 18,072,612,144 conservative packet-query visits overall. Allow two compiler builds per worker: original noise bridge and compensated tangent. No aircraft or protected inputs are read. Unused allowance remains charged; a failed or interrupted task is preserved.

Qualification gates

Before freezing, test the optional native-provider interface with its unchanged default path; reject altered tasks, sources, environments and failed parent checks before work. Exercise the real compensated full protocol in all twelve model/processing/error-format combinations on short generated examples. Their small evaluation cap tests integration and accounting, not convergence.

For the full experiment, report separately:

• Every original numerical stopping decision and physical prediction screen.
• Objective agreement between the two prescribed starts, using the original relative-cost tolerance of 1e-8.
• Agreement of the two reconstructed training tracks, using the original 1 mm per-axis RMS and 10 mm maximum position-stability limits.
• All parameter boundaries and unavailable outcomes. Parameter agreement is not required where parameters are unidentifiable.

The method qualifies on this matrix only if all 48 fits pass numerical and physical checks, all 24 start pairs pass objective/track agreement, and the four saved input/error bindings reproduce exactly. A failure blocks calibration; do not expand this experiment, change its gates or retry a failure.

Shared implementation and verification

1. Add an optional kernel-provider argument to lll.structured_noisy_study.run_case; preserve its default, prepayment, construction, forecasts and failure records.
2. Add lll.coordinate_optimizer_study as a small definition/evaluator using that shared runner, the existing generated-truth implementation and shared lifecycle. Freeze the qualified arithmetic, environment, original points and finite matrix.
3. Add lll.coordinate_optimizer_report to audit saved results and start pairs. Reporting must never fit, generate inputs or reclassify old failures.
4. Verify focused deterministic tests, prepare the source-bound qualification, then launch only its frozen matrix. Audit and publish every outcome, update the public overview and status registry, and retain reproducible archives.

Fresh calibration, independent validation and observed fitting require their own subsequent finite release. The 53-stretch findings remain unchanged.

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