Accepted meshes: compatibility and accuracy

A frozen accepted mesh is static controller output. Replay invokes its numerical steps and bypasses adaptive error estimates and acceptance decisions. Its AD results are derivatives conditional on that mesh. A compatible mesh may still become inaccurate when model parameters or initial conditions move.

The core contract distinguishes these questions before testing accuracy:

Metadata	Replay treatment
Finite/increasing output grid and positive interval steps summing to each interval	Always validated by AdaptiveStepSchedule
Producing resolved method, state shape/axis order, relevant operator axis, TR-BDF2 gamma, nonlinear stage solver/configuration	Known mismatches reject before stepping
Declared forcing breakpoints	Recorded declarations must match; every accepted step must land at each intervening jump, including legacy/manual meshes
Caller-supplied structural model identity	Compared when recording/replay use an identity; it must describe equations/geometry/layout, not fitted parameter values
Array namespace and dtype	Descriptive; portable meshes may change NumPy/JAX/Torch or precision
Discovery tolerances, controller limits, and reference parameter regime	Descriptive; changing fitted values or requested accuracy requires an external accuracy decision, not an automatic incompatibility
Callback bodies and arbitrary custom solver internals	No automatic semantic identity guarantee; use the structural identity and independently qualify changed implementations

AdaptiveScheduleProvenance is attached to schedules created by live adaptive runs. RunConfig.replay_model_id and replay_reference_regime are optional static labels supplied by the caller. Record concrete nominal values or a stable parameter-set identifier in the reference label at an eager boundary; replay does not inspect or convert dynamic parameter arrays.

Manually constructed meshes and legacy schedules with provenance=None remain accepted by default after mesh/output-grid validation. Their method/model compatibility is unverified and remains the caller's responsibility. Use RunConfig(replay_require_provenance=True) to reject unverified schedules. Adding a provenance record is not an accuracy certificate, and copying labels from another model does not make that model compatible.

Controller settings are recorded to explain discovery. Replay ignores error control even if the supplied configuration requests tighter tolerances. A provider may impose stronger configuration/context checks on its own artifact; these core rules do not remove those provider checks.

For imex-heun-tr, provenance.discovery_settings also records error_estimator="step-doubling: full-step error", error_estimator_partitions="explicit,implicit", and error_estimator_order="3". These describe the producing controller's cubic local estimate. They are descriptive fields, rather than replay compatibility constraints or accuracy certificates. Older meshes discovered using the explicit-only estimator remain replayable with the same accepted full-step formula, but should be rediscovered and checked independently before reuse where implicit error matters. Replay skips the additional half-step solves.

A practical reuse policy is:

1. Discover a live mesh at a documented nominal parameter regime.
2. Reuse it while changing dynamic values, retaining structural model identity.
3. Compare a replay trajectory to a fresh accurate solve or to a refined mesh at representative new parameter values. Check the scientific objective and needed derivatives as well as state error.
4. If the independent discrepancy exceeds the intended accuracy, rediscover the mesh at the new regime, recheck agreement, and freeze that mesh for the next differentiation phase.

The structured example accompanying this guide executes that policy and shows an accuracy failure despite compatible provenance. Discrete refresh decisions remain outside the differentiated numerical solve.

Run the structured refresh example:

uv run python examples/replay_mesh_refresh.py

It transfers mass between two generic pools with A'=-k*A^2, B'=+k*A^2, a shared rate and group-local multipliers. The independent solution is A(t)=A0/(1+k*A0*t), with conserved A+B. A mesh discovered at rate 0.05 remains accurate nearby; rate 3.0 is structurally compatible but exceeds the example's 1e-4 state-error policy on the old mesh. Fresh discovery restores that accuracy. JSON reports both discrepancies and accepted-step counts. This policy checks this fixture's state error; different scientific objectives and derivative accuracy need their own independent checks.