feat(phase4a+4b): Newton solver + CGAL mesh I/O

Phase 4a — newton_solver.hpp:
  - newton_euclidean(): SimplicialLDLT on H (PSD); solves H·Δx = −G
  - newton_spherical(): SimplicialLDLT on −H (NSD→PSD); solves (−H)·Δx = G
  - Backtracking line search (halving α up to 20×) for global convergence
  - NewtonResult struct: x, iterations, grad_inf_norm, converged
  - 7 tests: 4 spherical (convergence, few iters, large perturbation,
    field consistency) + 3 Euclidean (triangle pinned, quad pinned,
    mixed pinned — all with natural-theta equilibrium at x=0)

Phase 4b — mesh_io.hpp:
  - read_mesh() / write_mesh(): CGAL::IO::read/write_polygon_mesh wrappers
  - load_mesh() / save_mesh(): throwing convenience versions
  - Supports OFF, OBJ, PLY (format detected by file extension)
  - 6 tests: OFF round-trip (tet + quad), OBJ round-trip, missing-file throw,
    vertex-position preservation, save/load convenience wrappers

All 75 cgal tests pass (3 skipped as before).

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

code/include/mesh_io.hpp

@@ -0,0 +1,65 @@
+#pragma once
+// mesh_io.hpp
+//
+// Phase 4b — CGAL::IO wrappers for ConformalMesh.
+//
+// Reads and writes ConformalMesh (CGAL::Surface_mesh) in standard polygon-mesh
+// formats using the CGAL Polygon Mesh I/O utilities (CGAL 5.4+).
+//
+// Supported formats (detected by file extension):
+//   .off   — Object File Format   (read + write)
+//   .obj   — Wavefront OBJ        (read + write)
+//   .ply   — Polygon File Format  (read + write)
+//
+// Usage:
+//   ConformalMesh mesh;
+//   if (!read_mesh("input.off", mesh))  throw std::runtime_error("read failed");
+//   // ... process mesh ...
+//   write_mesh("output.off", mesh);
+//
+// Note: property maps (lambda0, v_idx, etc.) are NOT serialised — they must
+// be re-initialised with setup_*_maps() + compute_lambda0_from_mesh() after
+// reading a file.
+
+#include "conformal_mesh.hpp"
+#include <CGAL/IO/polygon_mesh_io.h>
+#include <string>
+#include <stdexcept>
+
+namespace conformallab {
+
+// ── Read ──────────────────────────────────────────────────────────────────────
+//
+// Reads a polygon mesh from file into `mesh` (clears any existing content).
+// Returns true on success, false on failure.
+inline bool read_mesh(const std::string& filename, ConformalMesh& mesh)
+{
+    mesh.clear();
+    return CGAL::IO::read_polygon_mesh(filename, mesh);
+}
+
+// ── Write ─────────────────────────────────────────────────────────────────────
+//
+// Writes `mesh` to `filename`.  Returns true on success.
+inline bool write_mesh(const std::string& filename, const ConformalMesh& mesh)
+{
+    return CGAL::IO::write_polygon_mesh(filename, mesh);
+}
+
+// ── Convenience: throwing wrappers ────────────────────────────────────────────
+
+inline ConformalMesh load_mesh(const std::string& filename)
+{
+    ConformalMesh mesh;
+    if (!read_mesh(filename, mesh))
+        throw std::runtime_error("conformallab: failed to read mesh from " + filename);
+    return mesh;
+}
+
+inline void save_mesh(const std::string& filename, const ConformalMesh& mesh)
+{
+    if (!write_mesh(filename, mesh))
+        throw std::runtime_error("conformallab: failed to write mesh to " + filename);
+}
+
+} // namespace conformallab