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>

doc/api/tests.md

@@ -29,7 +29,7 @@ All tests have CTest prefix `cgal.` (set via `TEST_PREFIX "cgal."` in CMakeLists
 | `ConformalMeshProperties` | `test_conformal_mesh.cpp` | 5 | Property maps (λ, θ, idx, α, geometry type) |
 | `ConformalMeshValidity` | `test_conformal_mesh.cpp` | 1 | CGAL validity for all factory meshes |
 | `HyperIdealFunctional` | `test_hyper_ideal_functional.cpp` | 7 | FD gradient checks + Hessian symmetry |
-| `SphericalFunctional` | `test_spherical_functional.cpp` | 12 | Angle formula + gradient + gauge-fix + cross-module Hessian check |
+| `SphericalFunctional` | `test_spherical_functional.cpp` | 13 | Angle formula + gradient + gauge-fix + cross-module Hessian check + closed-form edge-DOF oracle |
 | `EuclideanFunctional` | `test_euclidean_functional.cpp` | 12 | Angle formula + gradient + cross-module Hessian check |
 | `EuclideanHessian` | `test_euclidean_hessian.cpp` | 9 | Cotangent Laplacian structure, FD agreement, PSD, null space |
 | `SphericalHessian` | `test_spherical_hessian.cpp` | 8 | Derivative correctness, NSD at equilibrium |
@@ -51,6 +51,7 @@ All tests have CTest prefix `cgal.` (set via `TEST_PREFIX "cgal."` in CMakeLists
 | `PeriodMatrix` | `test_phase7.cpp` | 7 | τ ∈ ℍ, SL(2,ℤ) reduction, exception outside ℍ |
 | `FundamentalDomain` | `test_phase7.cpp` | 7 | Genus-1 parallelogram CCW, generators, g > 1 empty |
 | `TilingCopy/Neighbourhood` | `test_phase7.cpp` | 4 | Translation correct, tile count |
+| `HolonomyEndToEnd` | `test_phase7.cpp` | 3 | Full pipeline τ on tori of revolution (4×4, hex 6×6, 8×8) vs analytic modulus i·√(R²−r²)/r |
 | `CuttingUtility` | `test_geometry_utils.cpp` | 3 | `point_in_triangle_2d`: false, true, unit triangle (Java CuttingUtilityTest) |
 | `UnwrapUtility` | `test_geometry_utils.cpp` | 2 | Corner angle: collinear → π, equilateral → π/3 (Java UnwrapUtilityTest) |
 | `ConvergenceUtility` | `test_geometry_utils.cpp` | 6 | Circumradius + scale-invariant R_f/√A (Java ConvergenceUtilityTests) |
@@ -66,7 +67,7 @@ All tests have CTest prefix `cgal.` (set via `TEST_PREFIX "cgal."` in CMakeLists
 | `NewtonPhase9a` | `test_newton_phase9a.cpp` | 7 | Phase 9a-Newton — convergence for the two new circle-packing solvers |
 | `CGALPhase8bLite` | `test_cgal_phase8b_lite.cpp` | 17 | Phase 8b-Lite — CGAL entries for all 5 DCE models + `output_uv_map` (Euclidean, Spherical, HyperIdeal, Inversive-Distance) + CP-Euclidean throws-clearly + pipe-operator chaining |
 
-**Total: 236 tests, 0 skipped.**
+**Total: 240 tests, 0 skipped.**
 
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