feat(phase6): exact hyperbolic layout, Gauss–Bonnet, cut graph, normalisation — 121 tests

New files:
- gauss_bonnet.hpp: euler_characteristic, genus, Σ(2π-Θ_v) sum/rhs/deficit,
  check_gauss_bonnet (throws), enforce_gauss_bonnet (correct sign: Δ=(lhs-rhs)/V)
- cut_graph.hpp: CutGraph struct + compute_cut_graph (tree-cotree, Erickson–Whittlesey
  2005); boundary edges correctly excluded from cut set
- test_phase6.cpp: 26 new tests (GaussBonnet ×8, CutGraph ×6, HyperbolicTrilateration
  ×4, Normalisation ×4 — all pass)

layout.hpp (Phase 6 rewrite):
- detail::trilaterate_hyp: exact Möbius + hyperbolic law of cosines replacing old tanh(d/2)
- detail::center_poincare_disk: Möbius centering for hyperbolic normalisation
- normalise_euclidean: centroid → origin + PCA major-axis rotation
- normalise_hyperbolic: Möbius centering in the Poincaré disk
- normalise_spherical: Rodrigues rotation → north pole
- euclidean_layout / hyper_ideal_layout: optional CutGraph* + HolonomyData* + normalise

Bug fixes caught by new tests:
- gauss_bonnet.hpp: enforce_gauss_bonnet had wrong sign for delta
- cut_graph.hpp: boundary edges were incorrectly marked as cut edges

121 tests pass, 2 skipped (Hessian stubs).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

code/include/gauss_bonnet.hpp

@@ -0,0 +1,145 @@
+#pragma once
+// gauss_bonnet.hpp
+//
+// Phase 6 — Gauss–Bonnet consistency check for prescribed target angles.
+//
+// Before calling newton_*() with custom target angles, verify that
+// the angle defect sum matches the topology:
+//
+//   Σ_v (2π − Θ_v)  =  2π · χ(M)         (Euclidean / flat)
+//   Σ_v (2π − Θ_v)  >  0                  (spherical, χ > 0)
+//   Σ_v (2π − Θ_v)  <  0                  (hyperbolic, χ < 0)
+//
+// If this fails, no conformal factor can realise the target angles and
+// Newton will silently fail to converge.
+//
+// API:
+//   int    euler_characteristic(mesh)
+//   int    genus(mesh)
+//   double gauss_bonnet_sum(mesh, maps)      — Σ(2π − Θ_v)
+//   double gauss_bonnet_rhs(mesh)            — 2π · χ(M)
+//   double gauss_bonnet_deficit(mesh, maps)  — lhs − rhs  (0 = satisfied)
+//   void   check_gauss_bonnet(mesh, maps [, tol])   — throws if violated
+//   void   enforce_gauss_bonnet(mesh, maps)  — shifts θ_v by uniform Δ
+
+#include "conformal_mesh.hpp"
+#include "euclidean_functional.hpp"
+#include "spherical_functional.hpp"
+#include "hyper_ideal_functional.hpp"
+#include "constants.hpp"
+
+#include <stdexcept>
+#include <sstream>
+#include <cmath>
+#include <string>
+
+namespace conformallab {
+
+// ── Topology helpers ──────────────────────────────────────────────────────────
+
+/// Euler characteristic χ = V − E + F.
+/// For closed orientable surfaces: χ = 2 − 2g.
+inline int euler_characteristic(const ConformalMesh& mesh)
+{
+    return static_cast<int>(mesh.number_of_vertices())
+         - static_cast<int>(mesh.number_of_edges())
+         + static_cast<int>(mesh.number_of_faces());
+}
+
+/// Genus of a closed orientable surface: g = (2 − χ) / 2.
+/// Returns 0 for open meshes (boundary present) — callers should check.
+inline int genus(const ConformalMesh& mesh)
+{
+    int chi = euler_characteristic(mesh);
+    return (2 - chi) / 2;
+}
+
+// ── Left-hand side  Σ(2π − Θ_v) ─────────────────────────────────────────────
+
+inline double gauss_bonnet_sum(
+    const ConformalMesh&                                      mesh,
+    const ConformalMesh::Property_map<Vertex_index, double>&  theta)
+{
+    double s = 0.0;
+    for (auto v : mesh.vertices())
+        s += TWO_PI - theta[v];
+    return s;
+}
+
+inline double gauss_bonnet_sum(const ConformalMesh& m, const EuclideanMaps&   mp)
+    { return gauss_bonnet_sum(m, mp.theta_v); }
+inline double gauss_bonnet_sum(const ConformalMesh& m, const SphericalMaps&   mp)
+    { return gauss_bonnet_sum(m, mp.theta_v); }
+inline double gauss_bonnet_sum(const ConformalMesh& m, const HyperIdealMaps&  mp)
+    { return gauss_bonnet_sum(m, mp.theta_v); }
+
+// ── Right-hand side  2π · χ(M) ───────────────────────────────────────────────
+
+inline double gauss_bonnet_rhs(const ConformalMesh& mesh)
+{
+    return TWO_PI * static_cast<double>(euler_characteristic(mesh));
+}
+
+// ── Deficit: lhs − rhs  (0 = Gauss–Bonnet satisfied) ─────────────────────────
+
+template <typename Maps>
+inline double gauss_bonnet_deficit(const ConformalMesh& mesh, const Maps& maps)
+{
+    return gauss_bonnet_sum(mesh, maps) - gauss_bonnet_rhs(mesh);
+}
+
+// ── check_gauss_bonnet — throws std::runtime_error if |deficit| > tol ─────────
+
+inline void check_gauss_bonnet(const ConformalMesh& mesh,
+                                double lhs,
+                                double tol = 1e-8)
+{
+    double rhs = gauss_bonnet_rhs(mesh);
+    double def = lhs - rhs;
+    if (std::abs(def) > tol) {
+        std::ostringstream msg;
+        msg << "Gauss–Bonnet violated:\n"
+            << "  Σ(2π−Θ_v) = " << lhs
+            << "  expected 2π·χ = " << rhs
+            << "  (χ = " << euler_characteristic(mesh)
+            << ", genus = " << genus(mesh) << ")\n"
+            << "  deficit = " << def;
+        throw std::runtime_error(msg.str());
+    }
+}
+
+template <typename Maps>
+inline void check_gauss_bonnet(const ConformalMesh& mesh,
+                                const Maps& maps,
+                                double tol = 1e-8)
+{
+    check_gauss_bonnet(mesh, gauss_bonnet_sum(mesh, maps), tol);
+}
+
+// ── enforce_gauss_bonnet — adjust θ_v by uniform Δ ───────────────────────────
+//
+// Adds δ = (rhs − lhs) / V to every θ_v so that Gauss–Bonnet holds exactly.
+// After this call, check_gauss_bonnet() will not throw (up to floating-point).
+// Only modifies free vertices (v_idx[v] >= 0 for EuclideanMaps / SphericalMaps;
+// always all vertices for the raw property-map overload).
+
+inline void enforce_gauss_bonnet(
+    ConformalMesh&                                           mesh,
+    ConformalMesh::Property_map<Vertex_index, double>&       theta)
+{
+    double lhs   = gauss_bonnet_sum(mesh, theta);
+    double rhs   = gauss_bonnet_rhs(mesh);
+    // Adding δ to every θ_v decreases the sum Σ(2π−θ_v) by V·δ.
+    // We need lhs − V·δ = rhs, so δ = (lhs − rhs) / V.
+    double delta = (lhs - rhs) / static_cast<double>(mesh.number_of_vertices());
+    for (auto v : mesh.vertices())
+        theta[v] += delta;
+}
+
+template <typename Maps>
+inline void enforce_gauss_bonnet(ConformalMesh& mesh, Maps& maps)
+{
+    enforce_gauss_bonnet(mesh, maps.theta_v);
+}
+
+} // namespace conformallab