[#385 layer J] Gradient through pre-equilibration / steady-state (blocked: bngsim sensitivities)

[wshlavacek]

Part of #385. The last coverage layer.

What

A pre-equilibrated fit (ADR-0052) runs the model to steady state, then perturbs and scores the
transient. The gradient must propagate parameter sensitivities through the steady-state
solve — ∂(steady state)/∂θ via the implicit-function theorem on f(x*,θ)=0, i.e.
∂x*/∂θ = -(∂f/∂x)⁻¹ (∂f/∂θ) — and use that as the initial-sensitivity seed for the
post-perturbation trajectory's forward sensitivities.

Dependency

Per the #385 epic notes this is blocked on bngsim providing sensitivities through a
steady-state / pre-equilibration solve (bngsim #210 — confirm the bngsim-side capability and
its issue number before starting). PyBNF cannot assemble what the backend does not emit.

Deliverables (once unblocked)

• Seed forward sensitivities from the steady-state sensitivity; thread through the
  pre-equilibration → perturbation → score chain.
• FD oracle: a pre-equilibrated fit on a small net, central differences vs the assembled
  gradient.

[wshlavacek]

Done in d768417 (pushed to main).

Unblocked: bngsim 0.11.7 implements GH #210 — Simulator.run(carry_sensitivities=True) continues the forward-sensitivity state across the pre-equilibration boundary, seeding the measurement phase's yS(0) from the equilibration phase's steady-state sensitivity dx_ss/dθ (the implicit-function-theorem seed, computed backend-side). The backend enforces the contract bidirectionally: it raises if sensitivities are requested on a carried-over state without the flag, and if the flag is set on a fresh run.

PyBNF side: net_model tracks a carried_state flag on the shared action-execution state (True once a simulate has run on the current persistent simulator; cleared by resetConcentrations()/model.reset() or a simulator (re)creation — exactly bngsim's 'advanced since last reset' rule). On the gradient path the measurement-phase simulate passes carry_sensitivities=True. The scalar path never sets it, so pre-equilibration is byte-identical there. An IC-only free parameter is washed out by a stable steady state (∂x*/∂x(0)=0) and the backend refuses it; the parameter axis gates the flag.

FD oracle: test_fd_acceptance_gate_preequilibration — a two-phase fit on a switchable birth-death net (A_ss = k_prod/k_deg, then production OFF → decay). ∂A/∂k_prod flows entirely through the steady-state seed (k_prod is switched out of the measurement-phase RHS), so a missing seed would read identically zero — the sharpest probe of the seam. Central differences of PyBNF's own loss match the assembled gradient to ~1e-6 (linear + log-scaled native→sampling variants).

Docs: docs/gradient_fitting.rst gains a Pre-equilibration / steady state section and the capability gate no longer lists it as unsupported.

This was the last coverage layer (J) of #385.