solvers: cold-start vector_newton instead of seeding from its own outputs

[petlenz]

vector_newton::solve() seeded m_x by reading back its own output properties. That looks like a warm start and is not one.

The unknowns are created with add_output, not add_history_output, so statev_map never collects them — it skips anything !is_history() — and unpack() never restores them. One instance serves every integration point on a thread: umat_interface builds one material_context per thread and states why that is sufficient —

a consequence of the evaluator being stateless: all point state lives in the host's STATEV array

and material_point_evaluator is blunter —

anything the evaluator remembered across calls would be state from a trial the host has since discarded

Seeding from the properties is exactly such a memory. Point N starts from point N−1's converged answer, and after a failure from a diverged iterate. For a system with several real roots that does not merely change the iteration count — it selects which root is returned, converged and plausible and not the root this point is on.

The fix

Cold start every solve, which makes the solver point-local by construction. backward_euler already works this way: it passes a fixed literal seed rather than reading back its own delta.

Tests

The first is the one that matters: it drives two different problems through one instance, changing them in place with set_parameter, and requires each answer to equal a fresh instance's. x² + y = a ; x + y² = b has several real roots, so the seed is observable in the result, not just in the iteration count.

test	catches
SolvesArePointLocal	point-order dependence — the previous point's answer selecting this point's root
AFailedSolveDoesNotMoveTheNext	the same across a diverging solve

Mutation-verified against three implementations:

implementation	SolvesArePointLocal	AFailedSolveDoesNotMoveTheNext
main (seed from properties)	fails	fails
this PR's first attempt (hold the seed back only after a failure)	fails	passes
cold start (this PR)	passes	passes

What changed since the first version of this PR

The first version kept the property seeding and only held it back after a failure. That was the wrong level — it removed failure-dependence and left point-order-dependence, and it added a second piece of hidden cross-call state to a class whose surrounding contract is that nothing is retained between calls. SolvesArePointLocal fails against that version too, which is why it is written as a cross-problem test rather than a cross-attempt one.

The first version also accidentally carried ~400 lines of unrelated CalculiX adapter work that was sitting uncommitted in the working tree. That is out, and preserved.

Left to #21

Warm-starting is worth having — plane_stress_evaluator keeps eps_33 in its own STATEV slot precisely because a cold start costs several extra graph evaluations per Gauss point — but it has to be per point, which means the unknowns becoming history properties. The zero seed also assumes a non-singular Jacobian at the origin; a model that needs otherwise wants an explicit initial guess, which is the same follow-up.

No production caller: vector_newton appears only in the factory registration and its own tests. 282/282 pass.