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/gauss_bonnet.hpp

@@ -16,6 +16,13 @@
 // If this fails, no conformal factor can realise the target angles and
 // Newton will silently fail to converge.
 //
+// PRECONDITION — closed meshes only.  Every function here sums (2π − Θ_v)
+// over ALL vertices.  On a mesh with boundary the boundary vertices carry a
+// (π − Θ_v) term instead, so the identity Σ(2π−Θ_v) = 2π·χ does NOT hold and
+// `check_gauss_bonnet` will (correctly) throw.  For open meshes pin the
+// boundary directly and skip the Gauss–Bonnet check (see the CLI's
+// flattening path).
+//
 // API:
 //   int    euler_characteristic(mesh)
 //   int    genus(mesh)
@@ -128,10 +135,10 @@ inline void check_gauss_bonnet(const ConformalMesh& mesh,
 
 // ── enforce_gauss_bonnet — adjust θ_v by uniform Δ ───────────────────────────
 //
-// Adds δ = (rhs − lhs) / V to every θ_v so that Gauss–Bonnet holds exactly.
+// Adds δ = (lhs − rhs) / V to every θ_v so that Gauss–Bonnet holds exactly.
 // After this call, check_gauss_bonnet() will not throw (up to floating-point).
-// Only modifies free vertices (v_idx[v] >= 0 for EuclideanMaps / SphericalMaps;
-// always all vertices for the raw property-map overload).
+// Modifies ALL vertices' θ_v (no v_idx filtering) — the shift is a property
+// of the target angles, independent of which vertices are free DOFs.
 
 /// Distribute the Gauss-Bonnet deficit uniformly across all `Θ_v`:
 /// add `δ = (lhs − rhs) / V` to every entry so that the identity holds