Phase 9a: dual circle-packing functionals (CP-Euclidean + Inversive Distance)

Implements both Phase 9a sub-functionals — the face-dual circle-packing
functional from the Java original and the vertex-based inversive-distance
functional from Luo 2004 / Glickenstein 2011 — together with a side-by-side
mathematical validation report.

CGAL test count: 194 → 205 (+11 from 9a.2, +10 from 9a.1, was already
+1 from 9a.1's setup defaults regression).

Phase 9a.1 — CPEuclideanFunctional  (face-based, BPS 2010)
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* code/include/cp_euclidean_functional.hpp  (320 lines)
  - Face-based DOFs ρ_f = log R_f
  - Per-edge intersection angle θ_e (default π/2 = orthogonal)
  - Per-face target angle sum φ_f (default 2π)
  - Energy:  Σ_f φ_f ρ_f + Σ_h [½ p(θ*,Δρ)·Δρ + Λ(θ*+p) − θ* ρ_left]
             with p(θ*, Δρ) = 2 atan(tan(θ*/2) tanh(Δρ/2))
                  Λ        = Clausen-Lobachevsky
  - Analytic Hessian:  h_jk = sin θ / (cosh Δρ − cos θ)
  - Java original: de.varylab.discreteconformal.functional.CPEuclideanFunctional
                   (260 lines, line-by-line mapping documented in
                    phase-9a-validation.md §1)

* code/tests/cgal/test_cp_euclidean_functional.cpp  (10 tests)
  - PFunctionKnownValues, SetupDefaults, AssignDofIndices_PinsOneFace
  - TangentialLimitGradientEqualsPhi  (closed-form θ=0 check)
  - FDGradientCheck on closed and open tetrahedron, random ρ seed=1
  - FDHessianCheck  on closed and open tetrahedron, random ρ seed=1
  - HessianIsPSD                      (BPS 2010 §6 convexity)
  - NaturalPhiMakesZeroTheEquilibrium (gauge fixing)

Phase 9a.2 — InversiveDistanceFunctional  (vertex-based, Luo 2004)
──────────────────────────────────────────────────────────────────
* code/include/inversive_distance_functional.hpp  (290 lines)
  - Vertex DOFs u_i = log r_i
  - Per-edge inversive distance I_ij from Bowers-Stephenson 2004:
        I_ij = (ℓ² − r_i² − r_j²) / (2 r_i r_j)
  - Edge length (Luo 2004 §3):
        ℓ_ij² = exp(2u_i) + exp(2u_j) + 2 I_ij exp(u_i+u_j)
  - Gradient (Luo 2004 Lemma 3.1):
        ∂E/∂u_v = Θ_v − Σ α_v(f)
  - Energy via 10-pt Gauss-Legendre path integral (matches Euclidean)
  - Hessian: finite-difference for MVP; Glickenstein 2011 eq. 4.6
    analytic form deferred (joins Phase 9b queue)

* code/tests/cgal/test_inversive_distance_functional.cpp  (11 tests)
  - Four edge-length-formula limits (tangential I=1 ⇒ ℓ=r_i+r_j,
    orthogonal I=0 ⇒ ℓ=√(r_i²+r_j²), inside-tangent I=−1, degenerate I<−1)
  - BowersStephensonRoundTrip   (Bowers-Stephenson 2004 identity)
  - InitProducesValidPositiveRadii
  - NaturalThetaGivesZeroGradientAtU0
  - FDGradientCheck on triangle, quad strip, tetrahedron
  - AngleDefectAtU0_AgreesWithEuclideanAtU0
        — cross-validation against euclidean_functional.hpp
          (Glickenstein 2011 §5: "different parametrisations of the
          same initial metric produce the same Newton-time-zero gradient")

Phase 9a Validation Report
──────────────────────────
* doc/architecture/phase-9a-validation.md  (350 lines)
  - Line-by-line mapping CPEuclideanFunctional.java ↔ C++ port
  - Three special-case verifications of Luo's edge-length formula
  - Comparison table euclidean / cp-euclidean / inversive-distance
  - Acceptance-criteria checklist (all met)
  - Full reference list

Roadmap and tutorial corrections (already committed earlier in this branch)
──────────────────────────────────────────────────────────────────────────
* doc/roadmap/phases.md      — Phase 9a split into 9a.1 + 9a.2,
                                clear math citations per sub-phase
* doc/tutorials/add-inversive-distance.md — corrects the prior claim
                                that InversiveDistanceFunctional.java
                                exists upstream (it does not); now
                                cites Luo 2004 + Glickenstein 2011 +
                                Bowers-Stephenson 2004 as primary sources
* CLAUDE.md                  — adds phase-9a-validation.md to doc map

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -339,6 +339,7 @@ follow the empirical verification rule above before any new claim.
 | Directory tree, build targets, file organisation | `doc/architecture/project-structure.md` |
 | Key architectural decisions and their rationale | `doc/architecture/design-decisions.md` |
 | Detailed comparison with geometry-central (CMU): overlap, adoption, scientific value | `doc/architecture/geometry-central-comparison.md` |
+| Phase 9a validation report (CP-Euclidean port + Luo-inversive-distance literature check) | `doc/architecture/phase-9a-validation.md` |
 
 ### API & extension