B — Gradient plumbing: route free params to sensitivity_params/sensitivity_ic (bind-by-id + condition chain-rule)

[wshlavacek]

Part of #385 (cut 1, step 2 of A→B→C). Depends on #447. Pure mapping — no objective math.

What

Given an edition-2 fit, compute, per experiment, the bngsim sensitivity request and the
per-free-parameter chain-rule factor that converts a native sensitivity column into the derivative
w.r.t. the free parameter.

The mapping (edition-2)

• Bind by id (ADR-0034). A parameter: free parameter (ADR-0043) binds to the model entity of
  the same id, the same contract set_param already uses (net_model.py:203-218). A free parameter
  that matches no model id (e.g. a free σ) is not a sensitivity request — it carries no model
  column (its gradient is assembled in C — Gradient plumbing: Gaussian gradient + residual-Jacobian assembly, convention pin, native→sampling transform, FD-check #449 / layer D). This is the existing unmatched-param path
  (warning, not error — ADR-0034).

• Param vs IC. Route a free parameter that binds to a kinetic/global parameter to
  sensitivity_params; one that binds to a species initial value (_parse_net_species_initializers,
  net_model.py:159) to sensitivity_ic. Cut-1 must-have is sensitivity_params; IC routing is the
  secondary branch.

• Per-condition perturbation = local derivative. A condition: is a MutationSet on the base
  model (ADR-0028, config.py:1198); each Mutation carries operation ∈ {=,+,-,*,/}
  (pset.py:1714, ops at pset.py:1741-1749). For free parameter p perturbed in an experiment's
  condition:

  • p = c → p is pinned to a constant in that experiment ⇒ factor 0 (drop p's column).
  • p * c → factor c; p / c → factor 1/c; p + c / p - c → factor 1.

  An unperturbed free parameter has factor 1. The factor multiplies that parameter's native
  sensitivity column when C — Gradient plumbing: Gaussian gradient + residual-Jacobian assembly, convention pin, native→sampling transform, FD-check #449 assembles the per-experiment Jacobian.

Deliverables

• A per-experiment routing object: {free_param → (request_target ∈ {param, ic} | none, factor)}.
• sensitivity_params / sensitivity_ic lists handed to A — Gradient plumbing: capability gate + preserve the output-sensitivity tensor through net execution #447's request at each experiment's Simulator.
• Unit tests (no simulation needed): correct request lists and per-condition factors for
  wildtype, =-pinned, *//-scaled, and unmatched (σ-style) free parameters; IC vs param routing.

Out of scope

Consuming the factors / building the objective Jacobian → #449. Pre-equilibration conditions
(layer J). Comparison-difference constraints (layer I).

[wshlavacek]

Done in f464e41 (feat(gradient): route free params to sensitivity_params/sensitivity_ic), pushed to main.

Step B of the #385 cut-1 chain — a pure mapping, no objective math:

• pybnf/gradient/routing.py (new package). classify_free_param binds by id (ADR-0034): a species' bare initial-value expression → sensitivity_ic keyed by the species (an IC parameter is absent from the ODE RHS, so the parameter axis is identically zero — checked first since it's also a begin parameters id); a model parameter → sensitivity_params; no model id (a free σ) → none (no model column). condition_factor is the local derivative of the condition's MutationSet (ADR-0028): =→0 (pinned, column dropped), *c→c, /c→1/c, +/-→1; multiple mutations on one id compose multiplicatively.
• route_experiment → the per-experiment {free_param → ParamRoute(target, key, factor)} object plus derived sensitivity_params/sensitivity_ic request lists (zero-factor columns dropped, declaration order preserved). route_for_model + apply_routing hand the lists to A — Gradient plumbing: capability gate + preserve the output-sensitivity tensor through net execution #447's capability-gated enable_output_sensitivities.
• net_model.py: BngsimModel.sensitivity_entity_namespace() exposes (param ids, species initializers) — the only model coupling, keeping the routing core backend-agnostic.

Tests (tests/test_gradient_routing.py, 27, no simulation): classification (param/ic/none, IC precedence, literal & non-bare initializers), per-condition factors (wildtype, =-pinned, *//-scaled, +/- shift, compose), full routing request-lists, and a bngsim tier on e2e_ode_decay.net checking the namespace seam, condition-name resolution, and that the lists reach #447's Simulator kwargs (incl. the capability gate). Added to the pre-push bngsim gate. Full gate green (2580 passed, 9 skipped).

Consuming the factors / building the objective Jacobian → #449.