multiplier_schur_pc: verify or remove — it is read, but no observable responds to it

[lmoresi]

Stokes_Constrained.multiplier_schur_pc is a documented public property. It is read — at one site it swaps the multiplier block's Pmat term to the 1/μ Schur mass:

hh_pc = self._pp_G0 if self._multiplier_schur_pc else self._hh_G0[k]
PetscDSSetJacobianPreconditioner(ds.ds, fid, fid, ext.fns_jacobian[i_jac[hh_pc]], NULL, NULL, NULL)

So it is not dead code. But we could not construct a case where it changes anything.

Measured

Annulus, Stokes_Constrained with add_constraint_bc on both arcs (2 multipliers present, so the loop above is reached), snes_type=ksponly:

configuration	flag=False → flag=True
constant viscosity	|u|, |p|, outer KSP its all identical
η contrast 1e4	identical — including the solve failing identically both ways (DIVERGED_LINEAR_SOLVE, 100 KSP its)
η contrast 1e6	identical, 4 KSP its both
assembled |Pmat| (η contrast 1e3)	identical to 12 digits

The flag reads back correctly (True/False round-trip), so it is recorded.

Also notable in the same runs: |Pmat| equalled |J| exactly in both settings, despite Pmat being a distinct matrix.

Why this is filed as verify-or-remove rather than as a bug

The negative could be honest — two good Schur preconditioners can both converge in four iterations on a problem this easy, and we may simply not have found the discriminating case. The comment at the call site says the point is to reuse pressure's already-compiled 1/μ term "so there is NO extra JIT term", which suggests the motivation was compile cost rather than convergence.

But per the "identical cells are a common defect, never 'this variable does not matter'" rule that found #477, four identical rows across two decades of viscosity contrast is not evidence the flag works.

So: either produce the case where it earns its keep — and add it as a test, so the next audit does not re-open this — or remove the property. A public flag nobody can demonstrate an effect for is the same class as #477 and solver.strategy: accepted, recorded, and invisible if it is doing nothing.

Context worth knowing for whoever picks this up: Stokes_Constrained deliberately rejects saddle_preconditioner ("the Schur preconditioner is built automatically (selfp + the 1/viscosity mass from constitutive_model.K)"), so that class owns its Schur preconditioner by design. multiplier_schur_pc is the one hook left into it.

Found by the property-inertness pass of the solver configuration audit — docs/reviews/2026-07/solver-configuration-reachability-audit.md, Phase 3 (#485). Repro: ~/+Simulations/solver_reachability_audit/property_inertness_fair.py.

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