Upgrades the cyclic Euclidean Hessian from block-FD to closed-form, satisfying
the novelty-statement §3.2 "analytic Hessians, not finite difference" claim for
the Euclidean path.
- euclidean_hessian.hpp: `euclidean_hessian_analytic` — closed-form cyclic
Hessian from the law-of-cosines angle derivatives
∂α_i/∂s_i = ℓ_i²/4A, ∂α_i/∂s_j = ½cot α_i − ℓ_j²/4A (Σ_j = 0),
chained to (u, λ_e) and sign-mapped to the gradient outputs (−α vertex,
+α_opp edge). Reuses euclidean_cot_weights. Block-FD kept as cross-check.
- newton_solver.hpp: newton_euclidean cyclic path now uses the analytic Hessian.
- tests: CyclicHessian_Analytic_MatchesBlockFD_Tetrahedron — analytic == block-FD
(1e-6), == gradient FD (1e-5), symmetric (1e-9). Existing cyclic convergence
oracle still GREEN with the analytic Hessian routed in.
Tier-2 (Wente) finding: wente_torus02.obj is a QUAD mesh (1240 quads) and the
Java golden comes from cyclic (quad-net) uniformization; the C++ period-matrix
pipeline is triangle-based, so a faithful bit-vs-Java τ comparison needs a
quad/cyclic pipeline (Phase 9f). Deferred and documented; golden τ = ½+i√3/2.
244/244 cgal tests pass.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
822a27da69