Detect local-Newton non-convergence + singular Jacobian (#85)

[petlenz]

Fixes #85.

The in-function local Newton solvers emitted only a max-iteration guard: on non-convergence or a singular Jacobian they silently wrote the last (un-converged) iterate to the state out-params, corrupting the host FE solve with no signal. This closes the gap for both the single-scalar path (Phase 3a-2) and the coupled N×N path (Phase 3b-2b).

Detection

• A per-solve <sv>_converged flag, set true only on a genuine ‖R‖ < tol exit — so max-iter exhaustion is detectable after the loop.
• Scalar path: the update goes through a step local guarded by std::isfinite (a singular/ill-scaled Jacobian makes it non-finite → stop, don't propagate inf/nan).
• Coupled path: the dense solve is guarded — Eigen partialPivLu().solve result checked with .allFinite(); Armadillo switched to arma::solve's bool overload (false on a rank-deficient system). Near-singular-but-finite steps are caught by the outer convergence flag (loop exhausts max_iter).

Failure policy (the issue's design decision)

A new NewtonOptions::on_failure:

• NaN (default) — write a quiet NaN to the failed state variable(s); it propagates into every derived output so the host detects a non-finite result. MOOSE-QP-safe (no throw in a QP loop).
• Throw — throw std::runtime_error from the generated compute function (clean for standalone drivers).

Threaded from NewtonOptions → NewtonSegment/NewtonSystem IR → Rendered* → render_compute_function (as a plain bool, so pass.h needn't depend on recipe.h). Line search / regularization remain a separate future enhancement, as the issue scopes.

Tests

• Structural: NaN-default and Throw emission for the scalar path; NaN emission for the coupled path; the emit_newton_step singular guard + converged flag for both Eigen and Armadillo backends.
• Numerical (end-to-end): a generated recipe driven to a singular Jacobian (K·dt = 1 ⇒ ∂R/∂α = 0) compiles and runs, asserting the output is NaN — proving the runtime signal fires rather than returning bogus-but-finite garbage.

Affected code

• include/numsim_codegen/recipe.h — NewtonOptions::on_failure; scalar-loop emit + detail::emit_newton_failure_policy; coupled-loop frame.
• include/numsim_codegen/code_emit/linear_algebra_emitter.h — emit_newton_step records convergence + guards the solve (Eigen + Armadillo).
• passes/pass.h, recipe_render.h, passes/internal/pass_bodies.h — thread the policy through the IR.
• src/targets/{standalone_cxx,moose_material}.cpp — emit <limits>/<stdexcept>.
• Tests in LocalNewtonTest.cpp, LinearAlgebraEmitterTest.cpp, generated/compile_check_driver.cpp.