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/euclidean_hessian.hpp

@@ -52,8 +52,18 @@ namespace conformallab {
 // cot_k = (t_adj·l123 − t_opp·t_other) / (8·Area)
 //
 // Returns {0,0,0} for degenerate faces (triangle inequality violated or Area=0).
-struct EuclCotWeights { double cot1, cot2, cot3; bool valid; };
+/// Three Euclidean cotangent weights `(cot1, cot2, cot3)` for the
+/// vertices opposite to edges (l₂₃, l₃₁, l₁₂) of a triangle, plus a
+/// `valid` flag that is `false` when the triangle is degenerate.
+struct EuclCotWeights {
+    double cot1; ///< Cotangent at vertex 1 (opposite to l₂₃).
+    double cot2; ///< Cotangent at vertex 2 (opposite to l₃₁).
+    double cot3; ///< Cotangent at vertex 3 (opposite to l₁₂).
+    bool   valid;///< `false` when the triangle is degenerate (triangle inequality violated or area = 0).
+};
 
+/// Compute the three Euclidean cotangent weights from edge lengths.
+/// Returns `{0,0,0,false}` for degenerate triangles.
 inline EuclCotWeights euclidean_cot_weights(double l12, double l23, double l31)
 {
     const double t12 = -l12 + l23 + l31;
@@ -81,15 +91,9 @@ inline EuclCotWeights euclidean_cot_weights(double l12, double l23, double l31)
     };
 }
 
-// ── Analytical Hessian (cotangent Laplacian) ──────────────────────────────────
-//
-// Returns the n×n sparse Hessian matrix H where n = euclidean_dimension(mesh, m).
-//
-// Only vertex DOFs are supported.  Edge DOFs (m.e_idx[e] >= 0) produce
-// additional mixed-derivative entries that are not yet implemented; this
-// function asserts they are absent.
-//
-// x   – current DOF vector (used to compute effective log-lengths Λ̃ij).
+/// Analytical Euclidean Hessian (cotangent Laplacian), sparse.
+/// Only vertex DOFs are supported — the function asserts that no edge
+/// DOF is variable.  `x` is used to compute effective log-lengths Λ̃ᵢⱼ.
 inline Eigen::SparseMatrix<double> euclidean_hessian(
     ConformalMesh&             mesh,
     const std::vector<double>& x,
@@ -168,11 +172,9 @@ inline Eigen::SparseMatrix<double> euclidean_hessian(
 }
 
 // ── Finite-difference Hessian check ──────────────────────────────────────────
-//
-// Compares the analytical Hessian column-by-column against
-//   H_fd[:, j] = (G(x + ε·eⱼ) − G(x − ε·eⱼ)) / (2ε).
-//
-// Returns true if max relative error < tol for every entry.
+/// FD Hessian check for the Euclidean functional.  Compares analytic
+/// `H` column-by-column to `(G(x+εeⱼ) − G(x−εeⱼ)) / (2ε)`; returns
+/// `true` iff max relative error is below `tol`.
 inline bool hessian_check_euclidean(
     ConformalMesh&             mesh,
     const std::vector<double>& x0,