test: Java golden-value oracles for the five DCE math cores + P1-2/P1-3 fixes

Add bit-for-bit (1e-12) golden-value oracle tests pinning the C++ pure-math
and functional cores against the compiled upstream Java library (openjdk 17):

- HyperIdealGoldenJava: Clausen/Л/ImLi2, ζ13/14/15/ζ, both tetrahedron-volume
  formulas (real de.varylab…Clausen / HyperIdealUtility).
- EuclideanGoldenJava / SphericalGoldenJava: angle formulas + β relations + Л
  energy terms, plus FULL-MESH oracles driving the real EuclideanCyclicFunctional
  / SphericalFunctional on a shared tetrahedron — per-vertex gradient (Θ−Σα) and
  ΔE = E(x)−E(0) (C++ Gauss-Legendre path integral vs Java closed form).
- SphericalGoldenJava.FullMeshEdgeDofGradient: edge-DOF gradient (vertex + edge
  components, α_opp⁺+α_opp⁻−θ_e) vs raw conformalEnergyAndGradient — locks
  Finding 3 at the solution level (audit items 4 & 5).
- PeriodMatrix.NormalizeModulus_GoldenJava: τ-reduction fold convention vs the
  real DiscreteEllipticUtility.normalizeModulus (audit items 7 & 8).

Subtlety documented: the spherical oracles call Java's raw
conformalEnergyAndGradient, not evaluate() (which pre-runs a Brent gauge
maximization that C++ factors into the Newton solver's spherical_gauge_shift).

Also:
- P1-2 (layout.hpp): Euclidean holonomy now uses a per-cut-edge rigid-motion fit
  g(z)=a·z+b, exposing residual_rotation = |arg(a)| as a diagnostic; non-
  regressive (flat case a=1 reduces to the old midpoint formula).
- P1-3 (period_matrix.hpp): is_in_fundamental_domain fixed to the correct
  half-open SL(2,ℤ) domain (−½ ≤ Re < ½). Updated the now-exposed
  ComputePeriodMatrix_ReducedTau_InFD to assert the normalizeModulus domain
  (closed +½ edge) instead.

Test counts (single source of truth = doc/api/tests.md): 272/272 pass, 0
skipped (26 non-CGAL + 246 CGAL).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

doc/api/tests.md

@@ -7,14 +7,14 @@ Pure-math tests, only Eigen required. Covers Java utilities ported in Phase 1–
 | File | What it tests |
 |---|---|
 | `test_clausen.cpp` | Clausen Cl₂, Lobachevsky Л, ImLi₂ — values at known points |
-| `test_hyper_ideal_utility.cpp` | Tetrahedron volumes (Meyerhoff / Kolpakov–Mednykh) |
+| `test_hyper_ideal_utility.cpp` | Tetrahedron volumes (Meyerhoff / Kolpakov–Mednykh) + Java golden-value oracle (Clausen/Л/ImLi₂, ζ₁₃/₁₄/₁₅/ζ, both volume formulas) |
 | `test_matrix_utility.cpp` | Matrix helpers |
 | `test_surface_curve_utility.cpp` | Surface curve utilities |
 | `test_discrete_elliptic_utility.cpp` | Discrete elliptic functions |
 | `test_p2_utility.cpp` | P2 projective utilities |
 | `test_hyper_ideal_visualization_utility.cpp` | Poincaré disk projection, circumcircle |
 
-**Total: 23 tests, 0 skipped.**
+**Total: 26 tests, 0 skipped.**
 
 ---
 
@@ -30,7 +30,9 @@ All tests have CTest prefix `cgal.` (set via `TEST_PREFIX "cgal."` in CMakeLists
 | `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` | 13 | Angle formula + gradient + gauge-fix + cross-module Hessian check + closed-form edge-DOF oracle |
+| `SphericalGoldenJava` | `test_spherical_functional.cpp` | 3 | Java golden oracles: (1) law-of-cosines angles + β relations + Л energy term; (2) full-mesh tetrahedron — per-vertex gradient + ΔE; (3) full-mesh **edge-DOF** gradient (vertex + edge components, Finding 3) vs raw `conformalEnergyAndGradient` |
 | `EuclideanFunctional` | `test_euclidean_functional.cpp` | 12 | Angle formula + gradient + cross-module Hessian check |
+| `EuclideanGoldenJava` | `test_euclidean_functional.cpp` | 2 | Java golden oracles: (1) angle formula + 2·Л(α) energy term; (2) full-mesh tetrahedron — per-vertex gradient + ΔE vs real `EuclideanCyclicFunctional` |
 | `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 |
 | `NewtonSolver` | `test_newton_solver.cpp` | 11 | Convergence: Euclidean ×3, Spherical ×4, HyperIdeal ×4 |
@@ -48,7 +50,7 @@ All tests have CTest prefix `cgal.` (set via `TEST_PREFIX "cgal."` in CMakeLists
 | `HalfedgeUV` | `test_phase7.cpp` | 4 | Size = number of half-edges, seam consistency, boundary half-edges = 0 |
 | `PriorityBFS` | `test_phase7.cpp` | 3 | Success, no seam on open meshes, all vertices placed |
 | `NormaliseEuclidean` | `test_phase7.cpp` | 2 | UV centroid = 0, halfedge_uv centroid = 0 |
-| `PeriodMatrix` | `test_phase7.cpp` | 7 | τ ∈ ℍ, SL(2,ℤ) reduction, exception outside ℍ |
+| `PeriodMatrix` | `test_phase7.cpp` | 8 | τ ∈ ℍ, SL(2,ℤ) reduction, exception outside ℍ, Java `normalizeModulus` golden oracle |
 | `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 |
@@ -67,7 +69,7 @@ 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: 240 tests, 0 skipped.**
+**Total: 246 tests, 0 skipped.**
 
 ---