docs(doxygen): 100% public-API coverage (228 → 0 undocumented)

Completes the work begun in the previous commit on this branch.  Every
public symbol under code/include/ now carries a brief Doxygen comment
(0 undocumented per scripts/doxygen-coverage.sh, with the `detail::`
implementation namespaces excluded as before).

Trajectory on this branch:
  start (after Doxyfile fix):  24.0 %  (165 / 437 in the no-detail set
                                       was 105 / 437 when detail counted)
  after PR #17 base commit  :  42.4 %  (165 / 396)
  this commit               : 100.0 %  (396 / 396)

Files touched (all .hpp / .h headers under code/include/):
  * cgal/Conformal_map_traits.h
  * clausen.hpp, conformal_mesh.hpp, constants.hpp (already docd)
  * cp_euclidean_functional.hpp, cut_graph.hpp, discrete_elliptic_utility.hpp
  * euclidean_functional.hpp, euclidean_geometry.hpp, euclidean_hessian.hpp
  * fundamental_domain.hpp, gauss_bonnet.hpp
  * hyper_ideal_{functional,geometry,hessian,utility,visualization_utility}.hpp
  * inversive_distance_functional.hpp, layout.hpp
  * matrix_utility.hpp, mesh_builder.hpp, mesh_io.hpp
  * newton_solver.hpp, p2_utility.hpp, period_matrix.hpp, projective_math.hpp
  * serialization.hpp, spherical_functional.hpp, spherical_geometry.hpp
  * spherical_hessian.hpp, viewer_utils.h

CI:
.gitea/workflows/doxygen-pages.yml now enforces
`scripts/doxygen-coverage.sh --threshold 100`, so any future regression
(a new public function landed without a `///` brief) fails the build
before the Doxygen HTML is published to Codeberg Pages.

Doxygen warnings remain at 0.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

code/include/newton_solver.hpp

@@ -44,11 +44,12 @@ namespace conformallab {
 
 // ── Result ────────────────────────────────────────────────────────────────────
 
+/// Result of `newton_solve(...)` — converged DOF vector + diagnostics.
 struct NewtonResult {
-    std::vector<double> x;            ///< DOF vector at termination
-    int                 iterations;   ///< Newton steps taken
-    double              grad_inf_norm;///< max |G_i| at termination
-    bool                converged;    ///< true iff grad_inf_norm < tol
+    std::vector<double> x;            ///< DOF vector at termination.
+    int                 iterations;   ///< Newton steps taken.
+    double              grad_inf_norm;///< max |Gᵢ| at termination.
+    bool                converged;    ///< `true` iff `grad_inf_norm < tol`.
 };
 
 // ── Internal helpers ──────────────────────────────────────────────────────────
@@ -96,6 +97,10 @@ inline Eigen::VectorXd solve_with_fallback(
 //
 //   fallback_used  – if non-null, set to true iff SparseQR was invoked
 //   Returns Eigen::VectorXd::Zero(rhs.size()) if both solvers fail.
+/// Solve `A·x = rhs` with the same SimplicialLDLT → SparseQR fallback
+/// strategy used inside all three Newton solvers.  If `fallback_used`
+/// is non-null, it is set to `true` iff the SparseQR fallback ran.
+/// Returns `Eigen::VectorXd::Zero(rhs.size())` if both solvers fail.
 inline Eigen::VectorXd solve_linear_system(
     const Eigen::SparseMatrix<double>& A,
     const Eigen::VectorXd&             rhs,