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>

CLAUDE.md

@@ -300,6 +300,17 @@ grep -r "ClassName" /Users/tarikmoussa/Desktop/conformallab/src
 
 The 2026-05-21 audit corrected four mis-labels (now fixed): `InversiveDistanceFunctional`, both HyperIdeal Hessians (FD + analytic), and the inversive-distance tutorial were all wrongly tagged "Java port" — they are research (no Java parent; Java declares `hasHessian()==false`).  Details in `research-track.md`.
 
+### Java↔C++ math-correctness audit (2026-05-29)
+
+Full line-by-line audit of all math-critical headers against `de.varylab.discreteconformal.*` lives in **`doc/reviewer/java-port-audit.md`** (read it before re-investigating any of these).  All 11 findings are resolved or noted; the four that needed code changes are now ✅ FIXED and **all CGAL tests pass** (240 after the Euclidean holonomy/τ end-to-end tests + the spherical edge-DOF closed-form oracle landed on top — see `doc/api/tests.md`):
+
+- **Finding 3** (`spherical_functional.hpp`) — spherical edge-DOF now uses Java's *replacement* parameterization (`Λ = λ_e` when the edge is a DOF, via helper `spher_eff_lambda`); edge gradient is `α_opp⁺ + α_opp⁻ − θ_e` (dropped the extra `−(S_f⁺+S_f⁻)/2` term).  Vertex-only path is bit-for-bit unchanged.
+- **Finding 4** (`spherical_hessian.hpp`) — added an always-compiled `throw std::logic_error` edge-DOF guard (mirrors Finding 2 for Euclidean).
+- **Finding 6** (`period_matrix.hpp`) — `compute_period_matrix` now calls the faithful `normalizeModulus` (matches Java oracle: `0 ≤ Re ≤ ½`, `Im ≥ 0`, `|τ| ≥ 1`); `reduce_to_fundamental_domain` retained for the canonical SL(2,ℤ) domain.
+- **Finding 9** (`inversive_distance_functional.hpp`) — degenerate-face gradient now uses limiting angles instead of skipping (mirrors Finding 1); the genuinely-non-real `l*sq <= 0` skip is kept.
+
+**Open follow-ups (tests only, not bugs):** the edge-DOF paths for Findings 3 & 4 are verified for compilation + the unchanged vertex-only case but **not yet against a Java oracle at the solution level** — missing-test items 4, 7, 10 in the audit doc (golden-value oracle tests, period-matrix sign-convention test, inversive-distance degenerate test).  Build/test reminder: the CGAL build dir used for this audit is **`build-cgal`** at the *repo root* (not under `code/`), target `conformallab_cgal_tests`, filter `ctest -R '^cgal\.'`.
+
 ## Documentation map
 
 38 documents across 7 categories. Read the relevant one before reasoning from scratch