Two-sided timing diagnostic at saved points
Question
Do the failed stability corrections cross a genuine change of slope in the physical calculation, or are their cost changes explained by other nonlinear calibration directions or inaccurate derivatives?
The saved linear replays identify boundary crossings in both failures and neither matched control. The analytical controls show how a smooth-step check can reject exact nonsmooth minima. Neither result establishes the cause in the physical calculation.
Inputs and unchanged calculation
Use only four already exposed generated-data points from the closed fresh calibration: seeds 281474977010692 and 281474977010693, rate-sample errors, specified-field globe with removal allowed, starts 0 and 1. Preserve original labels, every nuisance column and every failure.
Reconstruct exactly those existing inputs with the frozen generator. Verify all stored array hashes, training observations and error-operator bindings. Use the same compensated mean, noise propagation, numerical environment, gravity anchor, physical bounds and training-only receiver rows. Never call the fitter or produce a new forecast. No new seed families or aircraft reads.
Measurements at each point
- Replay the saved residual, complete 27-column Jacobian and cost, then repeat them to check exact reproducibility.
- Evaluate the saved full correction, timing alone and all other coordinates with timing held fixed. Compare actual and linearized cost changes.
- Locate the nearest common integration boundary from the verified clock. Record its cost, without treating its slope as a smooth derivative.
- At 10, 1 and 0.1 microseconds on each feasible side, compare the analytical
timing column with a centered difference wholly inside that interval. Each
difference uses a quarter of that side's boundary distance. Preserve the
existing comparison scale
1e-8 + 1e-6 * max(column norms).
Both sides are required at the failed interior points. A side beyond a physical
bound is recorded as infeasible, never evaluated. Probe locations may be clamped
to a physical bound only for normalized roundoff within 1e-10; original saved
points and observations are unchanged. Full Jacobians remain in every report.
Separate finite allowance
Four tasks, four workers, one numerical thread each, no competing numerical jobs. Maximum 64 complete residual/Jacobian evaluations per point, 256 total; the declared sequence needs at most 24 per point. Cooperative wall ceiling: one hour. Expected execution is roughly 5–15 minutes, not guaranteed.
The shared reconstruction allowance gives each task at most 23,698 native calls and 119,117,714 packet visits, including reconstruction. Total ceilings: 94,792 calls and 476,470,856 packet visits. Charge before execution; preserve interruption, failure and unused charges. No retries or allowance expansion. Compilation is limited to two source-bound kernels per worker.
Implementation and qualification
Add small lll.timing_boundary_probe, lll.timing_boundary_study and
lll.timing_boundary_report components. Reuse the existing saved-point capture,
compensated kernel provider, journals, lll.studies lifecycle and archive.
Do not copy a worker or change the scientific kernel.
Before execution, qualify independent smooth/kink references, both timing branches, physical bounds, full-column preservation, charging, exact replay, source/environment/selection guards and capture before fitting or forecasting. Freeze the qualified sources, environment, four inputs and this allowance.
Publish all results and derivative curves, including disagreements. This is a diagnostic, not a new convergence decision, solver qualification, uncertainty threshold or Earth-model vote. Calibration and validation remain blocked. Any revised solver or further campaign requires its separately reviewed phase.