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/inversive_distance_functional.hpp

@@ -269,11 +269,18 @@ inline std::vector<double> inversive_distance_gradient(
         double l23sq = id_detail::edge_length_squared(u2, u3, m.I_e[e23]);
         double l31sq = id_detail::edge_length_squared(u3, u1, m.I_e[e31]);
 
+        // A non-real circle configuration (ℓ² ≤ 0) has no limiting angle — skip it.
         if (l12sq <= 0 || l23sq <= 0 || l31sq <= 0) continue;
 
         // euclidean_angles expects 2·log(ℓ) per edge — feed log(ℓ²).
+        // For a triangle-inequality-violating face euclidean_angles returns the
+        // *limiting* angles (π opposite the over-long edge, 0/0 otherwise) with
+        // valid=false.  We deliberately do NOT skip on !fa.valid: using those
+        // limiting angles is the convex C¹ extension onto the infeasible region,
+        // so Newton can pass through a flip instead of stalling (Finding 9 —
+        // mirrors the Euclidean/Spherical fix in Finding 1).  The angles come
+        // from genuine Euclidean side lengths, so the extension is geometric.
         auto fa = euclidean_angles(std::log(l12sq), std::log(l23sq), std::log(l31sq));
-        if (!fa.valid) continue;
 
         h_alpha[id_detail::hidx(h0)] = fa.alpha3;
         h_alpha[id_detail::hidx(h1)] = fa.alpha1;