refactor(api-naming): A1–A3 standardize internal function names across functionals

A1: assign_*_dof_indices → assign_<geom>_<scope>_dof_indices
  - assign_vertex_dof_indices (spherical) → assign_spherical_vertex_dof_indices
  - assign_all_spherical_dof_indices → assign_spherical_all_dof_indices
  - assign_all_dof_indices (hyper_ideal) → assign_hyper_ideal_all_dof_indices
  - euclidean/cp_euclidean/inversive_distance unchanged (already correct)
  - Add [[deprecated]] aliases for backward compatibility

A2: compute_*_from_mesh standardization
  - compute_lambda0_from_mesh (spherical) → compute_spherical_lambda0_from_mesh
  - others unchanged (euclidean, inversive_distance have geometry prefix already)
  - Add [[deprecated]] alias for backward compatibility

A3: gradient_check_<geom> standardization
  - gradient_check (hyper_ideal) → gradient_check_hyper_ideal
  - others already follow the convention
  - Add [[deprecated]] alias for backward compatibility

All call sites updated automatically. 290/290 tests pass.
Compile warnings: expected [[deprecated]] warnings on old names.

Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>

code/include/hyper_ideal_functional.hpp

@@ -105,7 +105,7 @@ inline int hyper_ideal_dimension(const ConformalMesh& mesh, const HyperIdealMaps
 /// rotational mode for an all-hyper-ideal configuration).
 ///
 /// \returns total DOF count = `num_vertices(mesh) + num_edges(mesh)`.
-inline int assign_all_dof_indices(ConformalMesh& mesh, HyperIdealMaps& m)
+inline int assign_hyper_ideal_all_dof_indices(ConformalMesh& mesh, HyperIdealMaps& m)
 {
     int idx = 0;
     for (auto v : mesh.vertices()) m.v_idx[v] = idx++;
@@ -468,7 +468,7 @@ inline HyperIdealResult evaluate_hyper_ideal(
 ///
 /// Returns `true` iff `|G[i] − fd[i]| / max(1, |G[i]|) < tol` for every
 /// DOF.  Defaults `eps = 1e-5`, `tol = 1e-4` match the Java `FunctionalTest`.
-inline bool gradient_check(
+inline bool gradient_check_hyper_ideal(
     ConformalMesh&             mesh,
     const std::vector<double>& x0,
     const HyperIdealMaps&      m,
@@ -501,4 +501,25 @@ inline bool gradient_check(
     return ok;
 }
 
+// ── Deprecated aliases (A1, A3 standardization) ────────────────────────────
+// Use the standardized names assign_<geom>_<scope>_dof_indices and
+// gradient_check_<geom> across all five functionals.
+
+[[deprecated("use assign_hyper_ideal_all_dof_indices instead")]]
+inline int assign_all_dof_indices(ConformalMesh& mesh, HyperIdealMaps& m)
+{
+    return assign_hyper_ideal_all_dof_indices(mesh, m);
+}
+
+[[deprecated("use gradient_check_hyper_ideal instead")]]
+inline bool gradient_check(
+    ConformalMesh&             mesh,
+    const std::vector<double>& x0,
+    const HyperIdealMaps&      m,
+    double                     eps = 1e-5,
+    double                     tol = 1e-4)
+{
+    return gradient_check_hyper_ideal(mesh, x0, m, eps, tol);
+}
+
 } // namespace conformallab