[Montana]

Fixes #1311.

Stacked on #1321. This PR's first nightly failed Path-agreement on TIMEOUTs only: models at the edge of the 900 s cap (MODEL1006230049, 0053, 0077) lost every row once a check was added to every model. #1321 bounds each check by the model's cap and keeps a killed worker's finished rows. It is merged in here, and this PR's new checks run after every check main runs. Until #1321 merges, this PR also shows its commits.

Builds on #1291 (merged). It adds two rows to CHECKS (steady_vs_run, newton_vs_run), as #1315, #1316, #1318 and #1319 each add theirs, so whichever lands second keeps both. I'll resolve it.

What it adds

steady_state() has its own routes: the CVODE march, the KINSOL polish, the scaled criterion's run test (#1001), the stability certificate (#78). None of them was compared with the plain integrator's answer. Two checks now do it, one per method, against the same run:

check	path	reference
steady_vs_run	steady_state() (integration)	a run() to t = 1e6 (steady_state()'s own max_time) from the same initial state
newton_vs_run	steady_state(method="newton")	the same run

Both are passed the job's rtol/atol. Write-only accumulators (Model.is_pure_sink()) are masked from the solve and left out of the comparison, since they settle nowhere (#74).

Judged only where both have arrived, as the issue asks:

• the solve's converged;
• the run's last quarter of the horizon moving it by no more than 1e3·rtol on its own scale.

Otherwise the row is SKIP, saying why. The bound is max(1e3·rtol, 10·max(settle, drift)), where drift is the run's end at a tenfold tighter tolerance, the harness's usual rule.

Where the two differ, a run from the solve's state, and its spectrum, say which case it is:

the solve's state	verdict
a run from it leaves it	DIFF: a converged that is not
off the initial state's conserved totals (conservation_laws), which the run keeps	DIFF: another system's root
an unstable root (eigvals(model.jacobian(x)), independent of the certificate) that the solve moved to	DIFF
the initial state itself, an unstable root a run leaves on rounding alone	SKIP, said why
another state a run rests at	SKIP, both states named (the species that differs most, with both values), for the baseline to hold: the model's multistability, or a tail slower than the horizon

A refusal by name (an event, time(), a conservation law the RHS breaks: #710, #758) is UNSUPPORTED. A reference run that fails is SKIP ("no reference"): the parity suites own run failures.

 CHECKS = (
     ...
     "grid",
+    "steady_vs_run",
+    "newton_vs_run",
     "sparsity_covers_jacobian",
     "backend_as_asked",
 )

Over the corpus

Local run, --checks steady_vs_run,newton_vs_run, fd_sens's 53 .net models and 1,300 BioModels (2,706 rows):

	PASS	SKIP	UNSUPPORTED	DIFF	EXCEPTION	TIMEOUT
fd_sens	68	36	2	0	0	0
BioModels	1,049	829	722	0	0	0

No finding. The first full run read 2 DIFF and 6 EXCEPTION. All eight were the reference's, and the second commit reclassifies them. I reran those 5 models on the final code; the rest of the corpus is unchanged by it:

• BIOMD0000000518 (DIFF on both methods): the initial state is itself a root (RHS ~1e-14), unstable along one mode (+5.6e-4). The solve stays on it, as the trajectory does in exact arithmetic. The run leaves it on rounding (e^558 over the horizon) and comes to rest at N2 = 15.5; a run started 1e-6 away rests at a third state, 46.4. This is steady_state()'s documented contract, not a bug.
• BIOMD0000000609, BIOMD0000001041, MODEL1112050000, MODEL2003040001 (EXCEPTION): the run to 1e6, or its tenfold tighter twin, fails in CVODE (non-finite RHS, or no progress) far past the model's own window.

Two states, recorded as SKIP: BIOMD0000000072, BIOMD0000000546, MODEL1911120001 (Newton). On 72 Newton returns L = 0 while the run holds L at 6.02e17. L is not conserved (RL degrades), so L = 0 is the true limit, about 1e14/k away. The run settles only relative to its own size, and integration rightly reports unconverged. Hence the note's "or a tail slower than the horizon".

Cost: 1,663 s of CPU over the 1,300 BioModels (median 0.43 s per model, worst 155 s, MODEL1006230053), base run included. That is about 7 minutes on the nightly's 4 workers, against the job's 52 of 180.

Tests (python/tests/test_differential_shapes.py, appended)

New models, each called through check_steady directly rather than added to SHAPES, so they don't pay for every other check's compiles:

• steady_state() accepts a state by an absolute residual: a model in small units, or a slow one, is returned far from its steady state with converged=True (x = 0.89 for 1 at 1e-9; BIOMD0000000407 one step from where it starts) #1001's cubic at a scale of 1e-9 (stable roots 0 and 1, unstable 0.3);
• a logistic (0 unstable);
• A <-> B (one conservation law);
• an accumulator counting a flux;
• the Brusselator (a limit cycle).

test	expects
both methods on the cubic from x0 = 0.5	PASS
negative control: criterion="residual", #1001's defect	DIFF: integration's state a run leaves (5.0e-10), Newton's unstable root 0.3 (a run from it stays, so the spectrum is what sees it)
the same wrong state, reported unconverged	SKIP
a solve resting on the cubic's other stable root, 0	SKIP, "two stable states", X() at 0 against 1e-09
a stable root of A <-> B with the total off (2 for 1)	DIFF, conservation law 0
the logistic's 0, which no run from it leaves	DIFF, unstable root
the cubic started on 0.3, the run leaving it on rounding	SKIP, initial state
the run to equilibrium raising	SKIP, no reference
the Brusselator, converged planted	SKIP, "has not settled"
the accumulator	PASS (mask and comparison both leave it out)
x0 = 0.2	PASS (both reach 0)

The four event and time-reading shapes are declared refused by name in REFUSED.

Mutations, each caught:

• no settle gate;
• no eigenvalue guard;
• no rest test;
• no converged gate;
• method ignored;
• refusals not recognised;
• the rest test run from the initial state;
• no mask;
• the run reading every species;
• a 1e9·rtol bound;
• no conservation guard;
• no initial-root SKIP;
• a failed reference raising.

Suites: parity_checks/tests and the shapes give 1,127 passed, 28 skipped, 1 xfailed. ruff 0.14.0 is clean. The branch merges cleanly with lanl main.

Still to do

The baseline (parity_checks/nightly/baselines/differential.json) gains these rows from this PR's own nightly run. I'll record them from its nightly-differential artifact, as #1291 did.

[wshlavacek]

Landed through #1384 (merge commit 29bfc85), which merged this pull request at 4dbccf1. GitHub did not mark it merged because the branch moved afterwards to 3f03ec8, a merge of main (e425546) pushed after #1384 was cut. That merge adds nothing main lacks: its conflict resolution keeps both sides, in the order main now runs the checks (jacobian_values, then this pull request's), and differs from main only in one comment line. Closing as landed; #1311 was closed by #1384.