Rectangular continuation trial: finite proposal

Repeat the same preselected three failure examples and completed October 5 control under a separate method freeze. Preserve the completed 24-start TRF trial. Start from the original saved first-pass points, not whichever trial point fits best.

• 15 unfinished primary fits, six control fits, three prescribed perturbed repeats.
• At most 600 fitting tangents and two value predictions per start; 24 starts / 14,448 native sweeps total. No retries or replacement starts.
• Rectangular dogbox steps, Jacobian scaling, ftol=None, xtol=1e-11, gtol=1e-14.
• Original gradient threshold 1e-4, relative cost change 1e-8, relative residual change 1e-6; a fresh bounded correction verification is mandatory. Callback stability alone cannot pass. Unchanged callbacks are not accepted improvements.
• Original physical models, parameter bounds, nominal 200 Hz clock, shared h1_v3_tau60 covariance, ±1°/hour offsets and both processing cases.
• Same predetermined normalized 0.01 perturbations and selection as the original recovery proposal, regardless of costs or preferred shape.
• All 24 starts must pass. Control and repeat comparisons require relative objective agreement within 1e-6 and every-axis prediction agreement within 0.01 m RMS.
• Save all evaluated costs/step sizes/fresh flags, callback acceptance markers and the final residual/Jacobian as a hashed compressed artifact. These records require no additional native sweeps beyond the charged final checks. The linear probe retains its original conservative early rejection rule.
• One numerical worker, two total BLAS threads. No other numerical work in parallel.
• Journals charge calls before execution. Interrupted starts remain failed and spent.
• Preserve every original outcome; all new outputs abstain from calibrated decisions.
• Same-recording estimate: approximately 10–14 hours at the ceiling, potentially less with warm starts. The smaller previous runtime is not a guarantee.

Software screen: dogbox passed 30/30 controls versus TRF 29/30. A known-answer near-boundary coupled control reproduces the earlier stopping failure and passes with dogbox without relaxed tolerances. This is not archive qualification or proof of global optima. A separately recorded finite authorization is required before decoding originals or launching observed fits. Success would support preparation of the separately budgeted all-41 recovery study; failure must be reported.