Journey 06 — Limits

# One IVP per call — orchestrate sweeps yourself:
for params in grid:
    result = solvsrk.run(cfg, ndim, t0, t_end, y0, make_rhs(params))
 
# Blow-up refusal (branch on failure_mode):
blow = solvsrk.run(cfg, 1, 0, 10, (1,), lambda t,y: y*y)
assert not blow['survived'] and blow['failure_mode'] == 'blowup'

What SolvSRK is for — and what it will not do for you

-- Act 1 - What SolvSRK is for --
  -> One stiff, possibly nonlinear, initial-value ODE integrated forward in time to a final state — reactors, kinetics, thermal transients, control plants. You give it rhs(t, y); it gives you y(t_end) with a receipt.

-- Act 2 - Robertson vs explicit RK45 --
  -> Same stiff Robertson problem, same rtol/atol on both sides. SciPy's RK45 is excellent on non-stiff problems; here we compare finished_ok, wall time, RHS evaluations, and y_final — apples to apples. Install SciPy with pip install solvsrk[scipy] if you want the comparison locally.
  log: rtol=1e-08, atol=1e-12
  _section: SolvSRK (SolvScout tuned (solvsrk, high))
  finished_ok: True
  failure_mode: ok
  wall_s: 0.002527
  nfev: 795
  y_final: [0.715827, 9.18553e-06, 0.284164]
  _section: SciPy RK45
  finished_ok: True
  failure_mode: ok
  wall_s: 1.34
  nfev: 238148
  y_final: [0.715827, 9.18553e-06, 0.284164]
  -> RK45 used 300× more RHS evaluations (238,148 vs 795) and 530× more wall time (1.34s vs 0.002527s) to reach the same endpoint.

-- Act 3 - Linear systems ride the same token path --
  -> Constant affine IVPs (y' = A y + b with fixed A) are not a separate product limit. SolvScout compares mode 0 (time stepping) vs mode 1 (Talbot contour) and encodes the winner in the profile token. run_profile(token, ...) dispatches mode 1 to the bundled Talbot solver inside libsolvsrk — same wheel, same SolvSRK seat. The standalone solvlrde package is only for when you already hold the matrix A and want solvlrde.solve(A, y0, T) without an rhs callback.
  solvscout_solver: solvsrk
  profile_mode: 0
  confidence: high
  _section: Linear IVP via run_profile — time stepping (mode 0)
  finished_ok: True
  failure_mode: ok
  wall_s: 0.001704
  nfev: 795
  y_final: [-4.97331e-29, 0.368248]

-- Act 4 - Limit 1 - one IVP per call --
  -> SolvSRK integrates ONE problem per run() call. Parameter studies, Monte Carlo sweeps, and design-of-experiments loops belong in your orchestration layer — call run() in a for-loop (or your job scheduler) and aggregate the receipts yourself.

-- Act 5 - Limit 2 - it will refuse rather than lie --
  -> Ask for something impossible — here, integrate a system that blows up — and SolvSRK returns survived=False with a failure_mode string instead of a plausible-looking wrong number. A refusal you can branch on beats a silent bad answer every time.
  survived: False
  failure_mode: blowup
  t_reached: 1.03
  failure_msg: ek blowup

-- Act 6 - The stack --
  -> SolvScout classifies your rhs and emits one profile token. SolvSRK run_profile integrates it — mode 0 for stiff nonlinear stepping, mode 1 for bundled Talbot on constant affine linear plants. Use the standalone solvlrde package only when you already have matrix A and want a direct solve API.

-- Run complete --
  suite: complete
  see: examples/PROGRESSION.md

cd python
# Guided tour — narrated scenario walkthrough (recommended first run):
python examples/journeys/06_limits.py
 
# Production one-liner — same API call you ship:
python examples/journeys/06_limits.py