[wshlavacek]

Explains the loose end #1423 left: BIOMD0000000908's reorder row, recorded as a DIFF of 1.09e+134 of the peak with no reason or issue.

What 908 is

Not a bngsim defect. The model's clearance of sunitinib is the reaction Sunitinib_not_working, which consumes S at the rate compartment * (-n * S). A negative rate on a reaction that consumes S makes S' = +0.277·S. With no dose (vs = 0), the model's answer is S = 0 for all time, and an unstable one.

On main 15ba102, at rtol 1e-6 over 0 to 300:

	S at t = 10	outcome
species as written	0 exactly	runs; same at rtol 1e-8 and 1e-10
species reversed	−3.6e-19	grows 16× per 10 days (e^0.277·10); CV_CONV_FAILURE near t = 152

Reversing the species reorders the linear solves, and their rounding leaves S a speck off 0. libRoadRunner from the same nudged start moves 2.6e14, as bngsim does. stable passed the model: no jittered grid or tolerance moves S off 0.

The change (parity_checks/differential/_differential.py)

• check_stable reruns the model once more, from a start nudged by START_NUDGE = 1e-3 of what a step may err by, rtol·|x| + atol. A departure past the bound marks the model contested, as a jittered grid or tolerance does; so does a run that fails from the nudged start.
• Only the species the equations hold still at the start are nudged (held_at_start): a derivative of exactly 0 there, a row of the Jacobian's pattern that can move it, not fixed, and not read by any event trigger. A value held exactly is what rounding alone can break. The others are not a rounding's to move, and the first version of this PR, which nudged every species, flagged 9 models for them:
  • a species already moving at the start, which the nudge only shifts in time;
  • an input nothing in the equations moves: BIOMD0000000265's r31switch and Flag, which only its events write (0.37 nudged; 3.4e-5 without them);
  • a species a trigger reads, carried across its threshold at the start: BIOMD0000000285's PIdeath > 0 and p38death > 0, both true at t = 0, fire neither (a Level 2 trigger is initialValue = true, which bngsim follows and all 494 Level 3 twins of Level 2 events in the SBML test suite say), so the cell they kill at once lives on.
• Only a departure the nudge grew into counts: one already past the bound at the first row after the start is the model's own laws telling the starts apart, as the equality-dwell shape's if(Bobs==0, kb, 0) does (A rate law that branches on an equality the state sits on (if(B==0, ...) with B held at 0) runs on the analytic sensitivity path and returns 0 for the columns that move the switch #1228).

What it flags

A stable-only sweep of the corpus on this branch (macOS, 1,349 models, 600 s a model), extracted with verdicts.py, moves 6 stable rows PASS → DIFF, recorded in baselines/differential.json (those 6 lines and the tally). Each was checked against libRoadRunner from the same nudged start, with a fresh RoadRunner per run:

model	nudged departure	what it is
BIOMD0000000908	2.7e+14	the unstable S = 0 above; RoadRunner 2.6e14
MODEL2003180003	5.0e+148	blows up in both engines, at rtol 1e-6 and 1e-11
MODEL1012110001	71	an unstable balance, M_329 = 7.5: both engines climb to 3,539 from the nudged start, and RoadRunner at rtol 1e-11 leaves the balance unnudged
MODEL1812040005	the run fails	fails in both engines at both tolerances (#1340's model)
MODEL1108260014	1.2e-3 (bound 1e-3)	the rate-rule parameter_3; both engines agree to 9 digits at every tolerance
BIOMD0000000739	1.5e+4 (bound 1.7)	bngsim at the SED-ML tolerances, not the model: see below

BIOMD0000000739 and BIOMD0000000457 (which the first version flagged) are the same thing, and it is not this PR's to fix. At the SED-ML tolerances (rtol 1e-6, atol 1e-9) bngsim's answer for their small species is off by much more than the tolerance: 457's species_42, about 1.6e-7, is 13% off at t = 5 against a run at rtol 1e-10, atol 1e-16, where bngsim and RoadRunner agree to five digits. libRoadRunner's answer at the same nominal tolerances is right because its absolute_tolerance is multiplied by each species' value; bngsim's is absolute. This is #1420's question, for an explicit scalar atol (here the SED-ML file's), which AtolScaleWarning does not second-guess. The RoadRunner parity suite forces rtol 1e-9, atol 1e-12 on both engines, so it does not see it.

The sweep's other differences from the baseline (TIMEOUT → PASS and the like) are its 600 s cap against CI's, and are left as recorded. This PR's own Linux run compares against these rows.

Also

ci/test_floors.env: the full suite's collected floor to 17360. All three legs collected 17370 here, 502 above the floor, past its slack of 500.

Tests (python/tests/test_differential_shapes.py)

• An unstable zero (S → 2S at rate k from S = 0) is contested; its decaying twin passes.
• The nudge moves a held start by its share of a step's allowance, and nothing else.
• Only a species the equations hold still is nudged: not one a trigger reads, not an input, not one already moving.
• A run that fails from the nudged start is contested.
• All 514 shape tests pass, equality-dwell's stable among them.