fix+test: Euclidean holonomy/τ end-to-end + spherical edge-DOF oracle (2026-05-29 audit)

Bundles the 2026-05-29 Java↔C++ math-correctness audit (doc/reviewer/
java-port-audit.md, 11 findings) with two follow-up fixes.

Audit code changes:
- Finding 3 (spherical_functional): edge-DOF replacement parameterization via
  spher_eff_lambda; edge gradient α_opp⁺+α_opp⁻−θ_e (drops additive −(S⁺+S⁻)/2)
- Finding 4 (spherical_hessian): always-compiled edge-DOF throw guard
- Finding 6 (period_matrix): faithful normalizeModulus (0≤Re≤½, Im≥0, |τ|≥1)
- Finding 9 (inversive_distance): degenerate-face limiting angles, no skip
- Findings 1/2 (euclidean): degenerate gradient limiting angles + Hessian guard

Euclidean holonomy/τ fix: develop the cut surface across the dual spanning tree
only (cut_graph now exposes is_dual_tree), so genus-1 cut edges yield
non-degenerate lattice generators. Previously τ came out 0 / NaN / 1e13 on the
bundled tori; now matches the analytic revolution modulus i·√(R²−r²)/r. Re-enabled
τ reporting in the Euclidean CLI; rewrote validation.md §3/§4 accordingly.

Tests (240 CGAL, 0 skipped):
- HolonomyEndToEnd ×3 — tori of revolution (4×4, hex 6×6, 8×8) vs analytic modulus
- SphericalFunctional.EdgeGradient_RegularTetClosedForm — independent closed-form
  π/3 oracle locking the Finding-3 edge formula (the path-integral FD check cannot
  detect a wrong-but-conservative gradient)

Also documents the latent spherical/hyperbolic holonomy-extraction bug (same
single-development pattern, dead code today) in research-track.md (Phase 9c/10),
and adds favour/normalisations to the codespell ignore list.

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

code/include/mesh_io.hpp

@@ -26,6 +26,7 @@
 
 #include "conformal_mesh.hpp"
 #include <CGAL/IO/polygon_mesh_io.h>
+#include <CGAL/boost/graph/helpers.h>
 #include <string>
 #include <stdexcept>
 
@@ -47,11 +48,20 @@ inline bool write_mesh(const std::string& filename, const ConformalMesh& mesh)
 
 /// Throwing wrapper around `read_mesh`: returns the mesh by value
 /// or throws `std::runtime_error` on read failure.
+///
+/// Also enforces that the mesh is triangulated, because every functional
+/// in this library assumes triangle faces — a quad/polygon mesh would be
+/// read in silently and then mis-handled by the angle/length formulas.
+/// Fail loudly here at the I/O boundary instead.
 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);
+    if (!CGAL::is_triangle_mesh(mesh))
+        throw std::runtime_error(
+            "conformallab: mesh from " + filename +
+            " is not triangulated (functionals require triangle faces)");
     return mesh;
 }