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/spherical_geometry.hpp

@@ -57,9 +57,19 @@ inline SphericalFaceAngles spherical_angles(double l12, double l23, double l31)
     double s23 = s - l23;
     double s31 = s - l31;
 
-    // Spherical triangle inequalities: all s-deficiencies > 0 and s < π.
-    if (s12 <= 0.0 || s23 <= 0.0 || s31 <= 0.0 || s >= PI_SPHER)
-        return {0.0, 0.0, 0.0, false};
+    // Degenerate spherical triangle: return the *limiting* angles, matching the
+    // Java reference (SphericalFunctional.triangleEnergyAndAlphas).  a1 is the
+    // angle opposite l23, a2 opposite l31, a3 opposite l12.  `valid` stays false
+    // so the Hessian still skips the face, but the gradient uses these angles
+    // (convex C¹ extension onto the infeasible region).
+    //   s12<=0 (Δij<=0) → corner opposite l12 = π  → a3 = π
+    //   s23<=0 (Δjk<=0) → corner opposite l23 = π  → a1 = π
+    //   s31<=0 (Δki<=0) → corner opposite l31 = π  → a2 = π
+    //   s>=π  (Δijk>=2π) → all three corners = π
+    if (s12 <= 0.0) return {0.0, 0.0, PI_SPHER, false};
+    if (s23 <= 0.0) return {PI_SPHER, 0.0, 0.0, false};
+    if (s31 <= 0.0) return {0.0, PI_SPHER, 0.0, false};
+    if (s >= PI_SPHER) return {PI_SPHER, PI_SPHER, PI_SPHER, false};
 
     const double ss   = std::sin(s);
     const double ss12 = std::sin(s12);