feat(euclidean): block-FD edge-DOF Hessian → cyclic Newton + Java convergence oracle
Implements the edge-DOF (cyclic) Euclidean Hessian, unblocking the full cyclic
Newton solve, and enables the Java EuclideanCyclicConvergenceTest cross-validation.
- euclidean_hessian.hpp: `euclidean_hessian_block_fd` / `_sym` — per-face 6×6
block FD over (u1,u2,u3,λ12,λ23,λ31), mirroring hyper_ideal_hessian_block_fd.
Per-face outputs carry the gradient signs (−α vertex, +α_opp edge), so the
result equals ∂G/∂x by construction (locality lemma). Analytic vertex-only
cotangent Hessian unchanged (still used for vertex-only layouts).
- newton_solver.hpp: newton_euclidean routes cyclic layouts (edge DOFs present)
through the block-FD Hessian; vertex-only path unchanged.
- tests:
* CyclicCircularEdge_CatHead_JavaXVal (now GREEN) — prescribe φ=π−0.1 on one
interior edge, solve, assert realised α_opp+α_opp = π−0.1 @1e-9.
* CyclicCircularEdge_PhiEntersGradient_CatHead — solver-free φ-wiring check.
* CyclicHessian_BlockFD_MatchesGradientFD_Tetrahedron — Hessian correctness.
243/243 cgal tests pass; vertex-only Euclidean Newton unaffected.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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