Safeguard steady-state steps during fast transient growth

[jc-macdonald]

steady_state previously accepted every candidate and reduced the next pseudo-time step during fast transient growth. The #209 reproduction either exhausted its iteration budget or diverged after entering negative compartments. Reject non-finite or excessively growing candidates, retain the previous state, and halve the step; accepted transient growth now holds the step.

Adds optional nonnegative=True or a boolean mask. Infeasible candidates, including the final Newton correction, are rejected without clipping conserved totals or evaluating the RHS outside the guarded domain. Singular NumPy solves use the same rejection path, and acceptance remains array-valued under JAX jit/vmap.

With non-negativity enabled, the three reproduction cases reach their analytic endemic equilibria in 66, 30, and 33 attempts, with relative invariant drift below 2e-16. Signs remain unrestricted by default, and rejected attempts count toward the iteration budget.

Algorithm research favored safeguarded pseudo-transient continuation for this coupled, namespace-portable solver. Brent/bisection require a scalar sign-changing bracket, while the existing curvature utilities generate spatial grids. The guide links the primary SciPy documentation, projected PTC research, and PETSc timestep-verification documentation.

Closes #209.

Validation:

• 35 steady-state tests pass on this isolated branch.
• Ruff preview format/lint, strict core mypy, and strict documentation build pass.
• Regressions cover the analytic reproduction, JAX jit/vmap, residual-growth and non-finite rejection, singular-step recovery, selected bound masks, guarded RHS evaluation, and the final Newton correction.
• GitHub CI passes on the final commit against current main: Python 3.11–3.14, CPU Torch, package builds, and documentation.