fix(transcription): a run whose augmented model goes non-finite reports the certificate it already holds instead of nothing (#581)

[wshlavacek]

Closes #581.

AugmentedLagrangian.run's two non-finite bail-outs returned before any iterate was certified, so a run that hit one reported no fit at all — No simulation completed, so there is no best fit to report — from a point whose reported parameters certify perfectly well.

Why the certificate survives when the model does not

They are different computations. Certification discards every auxiliary state and re-simulates the reported parameters through the fit's ordinary unsegmented path: no continuity block, no auxiliary bounds, and crucially no forward sensitivities. A parameter point whose trajectory integrates fine while its d(state)/d(theta) overflows makes the augmented model non-finite and the certificate perfectly good.

Measured

On Borghans_BiophysChem1997, 1 of 8 oscillating box draws. Rebuilding the m=4 stage at that point:

1. unsegmented simulation: OK, 112 rows
3. objective at the seeded start: value=inf  finite=False
4. segment 0: OK   end_state=[5.8307e+00 1.4589e-03 1.3584e+04] finite=False
   ...                                                       ^ the sensitivities, not the trajectory
5. certificate: accepted=True objective=-150.70078278843627

gntr from the identical start reports -150.70078270720597. ms reported nothing. After this change it reports -150.701, OG 96.0857 — matching gntr to the digits both compute.

Why it was least visible where it mattered most

A multi-start run has other starts to paper over it. Every refine_method = ms is single-start by construction (_resolve_n_starts returns 1 for an injected start), so a refine that landed here contributed nothing while the run still printed the search's own fit — no indication the refine had produced nothing usable.

The inconsistency was already in the suite

Pointing the other way. The stopped branch asserted "the work already done is still reported"; the inner_failed branch two lines below asserted best is None. That assertion is inverted here, and the four steps every accepted iterate goes through — keep, rank, share, notify — are factored into one _record helper, because doing three of the four on one branch is exactly how this arose.

Tests

• the inverted assertion, with the reasoning in its docstring;
• a new offline test of job_type = ms reports no fit at all when its first augmented model is non-finite, although the start point certifies fine (gntr reports it) #581's actual shape — a TranscriptionProblem whose objective_at is non-finite while certify succeeds — asserting the run still reports, that the score is the reconstruction rather than the augmented objective, and that the unavailable quantities are reported as inf rather than invented.

No simulator needed for either. 171 passing across the four shooting/transcription suites.