A free parameter that binds a model id AND seeds another entity gets a silently-zero gradient column (#530 sibling)

[wshlavacek]

Summary

#530 (ADR-0095) taught the router that a condition target reaches the trajectory through
everything it seeds, carrying each d(entity)/d(target). The bind-by-id path did not get the
same treatment: route_experiment classifies a free parameter with classify_free_param, which
returns one column and never consults the seed map.

When that free parameter is itself only an input to an initialAssignment — it never appears in
the ODE right-hand side — its own sensitivity axis is identically zero, so the assembled column is
silently zero. ADR-0095 listed this as out of scope, but "out of scope" here means a wrong
number rather than a refusal, which is the failure mode that ADR is otherwise built to avoid.

Reproduction

Laske_PLOSComputBiol2019 (Benchmark-Models-PEtab) is a COPASI export in which every rate law reads
a ModelValue_* alias fixed by an initialAssignment, and no source name appears in a rate law:

initialAssignment: ModelValue_79 = k_syn_R_M      # k_syn_R_M is a FREE parameter

The seed map already carries the right term; the route does not:

seed map entry for k_syn_R_M: (SeedTerm(target='param', key='ModelValue_79', node=('num', 1.0)),)

route for k_syn_R_M (a free parameter bound BY ID):
    RouteContribution(target='param', key='k_syn_R_M', factor=1.0, node=None)
is ModelValue_79 in the request? False

Central differences against the assembled gradient at that problem's PEtab nominal point, over all
13 free parameters (the other 12 agree to 1e-3..1e-11; the small-gradient ones wobble with the step
size as expected on a stiff model):

param                            assembled    central diff    rel err
k_syn_R_M                                0        -10.5047   1.00e+00   <-- h=1e-6
k_syn_R_M                                0        -10.4588   1.00e+00   <-- h=1e-5
k_syn_R_M                                0          -10.42   1.00e+00   <-- h=1e-7

Stable under every step size, so it is structural rather than FD noise.

This was masked before #531: the forward model did not track ModelValue_79 either, so a zero
gradient was consistent with an inert parameter. Fixing the forward model exposed the routing gap.

Fix

Give a bind-by-id free parameter the same classification a condition target gets: its own axis
plus one term per entity whose initial value it seeds, each with its own derivative, and no
own-axis term when it is a pure initial-value seed (the existing IC-precedence rule, which is that
same rule as a special case). The seed map and the derivative machinery already exist from #530;
only the by-id branch of route_experiment needs to consult them.

Two behaviours change, both toward correctness:

• a free parameter seeding a non-bare initializer (species <- 2*S0) currently falls through to
  its own parameter axis (a zero column when it is not in the RHS); it should route to the IC axis
  with derivative 2. classify_free_param's "Cut-1" comment names this as a deferred layer — Extend ADR-0076 condition routing to a non-unit seed derivative (d(IC)/d(target) != 1) -- Bertozzi_PNAS2020 #530
  is that layer.
• a free parameter seeding several species currently routes to whichever one matched first; it
  should sum over all of them.

A free parameter that binds a model id and seeds nothing is unaffected, which is nearly all of them.