Builds on the newton_core refactor; all three findings live in exactly that code.
I1 (test-coverage): add NewtonStatus { Converged, MaxIterations,
LinearSolverFailed, LineSearchStalled } and a `status` field to NewtonResult, so
the three non-convergent exits that `converged == false` previously conflated are
now distinguishable. `converged` is kept (== status==Converged) for back-compat;
+ to_string(NewtonStatus) for logs/tests. newton_core sets the status at each
exit point (centralised by the H2 refactor).
H1 (test-coverage): set res.iterations explicitly at the LinearSolverFailed and
LineSearchStalled breaks (= completed steps), instead of relying on the last
successful iteration's stale value.
N7 (numerical-stability): surface linear-algebra conditioning in the result —
`sparse_qr_fallback_used` (any iteration fell back to SparseQR) and
`min_ldlt_pivot` (smallest |Dᵢᵢ| of the last LDLT, a cheap near-singularity
proxy). This catches the silent case the audit flagged: on a gauge-singular
Hessian SimplicialLDLT "succeeds" with a ~0 pivot and no fallback fires — now
min_ldlt_pivot is tiny and observable.
Tests (+3 synthetic newton_core status/diagnostic tests; +1 assertion on the
closed-mesh-no-pin fallback test). All purely additive — no control-flow or
convergence behaviour changes; 301/301 CGAL tests pass incl. Java parity.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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