docs: full Java library scan — new phases 9d/9e/10d–10g + parity table

Complete scan of all de.varylab.discreteconformal packages (functional/,
unwrapper/, unwrapper/circlepattern/, unwrapper/koebe/,
unwrapper/quasiisothermic/, uniformization/, util/) against the
current roadmap.

New items added to java-parity.md:
- ConesUtility: cone detection, BFS cut, auto-placement, quantization (9d)
- MobiusCenteringFunctional: variational Lösung über Lorentz-Geometrie (9d)
- ElectrostaticSphereFunctional: Initialisierungsheuristik auf S² (9d)
- StereographicUnwrapper + SphereUtility: S²→ℂ atlas für genus-0 (9d)
- CirclePatternLayout + CirclePatternUtility + CPEuclideanRotation (9e)
- CutAndGlueUtility, StitchingUtility, PathUtility (9c additions)
- DualityUtility: Hodge-Stern + dual cycles — prerequisite 10a
- HyperellipticUtility + HyperIdealHyperellipticUtility (10b)
- CircleDomainUnwrapper: Koebe-Andreev-Thurston (10d)
- quasiisothermic/ package: QI maps + DBF + sin-condition (10e)
- KoebePolyhedron (10f)
- EuclideanCyclicFunctional + HyperbolicCyclicFunctional (10g)
- "Do not port" table: ColtIterationReporter, PETSc wrappers, etc.

New phases added to phases.md:
- Phase 9d: ConesUtility + StereographicUnwrapper + MobiusCenteringFunctional
- Phase 9e: CirclePatternLayout (complement to already-ported 9a.1)
- Phase 10d: CircleDomainUnwrapper (Koebe-Andreev-Thurston)
- Phase 10e: quasi-isothermic maps
- Phase 10f: Koebe polyhedra
- Phase 10g: cyclic-symmetry functionals

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

doc/roadmap/phases.md

@@ -129,6 +129,89 @@ mesh type.
                  layer, +1 week integration.
 ```
 
+9d — Cone metrics + sphere utilities  (Java port — 2026 library scan)
+────────────────────────────────────────────────────────────────────
+
+```
+9d.1   ConesUtility  (Java port: unwrapper/ConesUtility.java)
+         → cone_singularities.hpp
+         Fills the "⚠️ data structure only" gap in java-parity.md:
+         - Detect interior cone vertices (angle deficit ≠ 0)
+         - BFS path from cone to mesh boundary → cut edge set
+         - Auto-placement: conjugate gradient on Θ-gradient magnitude
+         - Quantization: snap cone angles to π/2, π/3, π/6 for
+           quad / triangle / hexagonal atlas targets
+         Java reference: unwrapper/ConesUtility.java
+
+9d.2   StereographicUnwrapper + SphereUtility  (Java port)
+         → stereographic_layout.hpp
+         Stereographic projection S²→ℂ∪{∞} + Möbius centering for
+         genus-0 surfaces. Converts spherical DCE output to a flat 2-D atlas.
+         Java reference: unwrapper/StereographicUnwrapper.java (266 lines)
+
+9d.3   MobiusCenteringFunctional  (Java port, optional upgrade)
+         → integrate into layout.hpp normalise_hyperbolic()
+         Variational Möbius centering via Lorentz geometry:
+           E = Σ log(-⟨x,p⟩/√(-⟨x,x⟩))
+         Supplies gradient + Hessian — replaces iterative Fréchet mean.
+         Java reference: functional/MobiusCenteringFunctional.java
+```
+
+9e — Circle pattern layout  (Java port — complement to Phase 9a.1)
+────────────────────────────────────────────────────────────────────
+
+```
+9e     CirclePatternLayout + CirclePatternUtility  (Java port)
+         → circle_pattern_layout.hpp
+         Phase 9a.1 ported the CPEuclidean energy + solver; this phase
+         adds the embedding step (ρ values → actual vertex positions in ℝ²).
+         - CirclePatternUtility: compute per-face radii ρ via NTR solver
+         - CirclePatternLayout: embed from ρ values (intersection-angle model)
+         - CPEuclideanRotation: rotation-invariant CP functional variant
+         Java references: unwrapper/circlepattern/CirclePattern{Layout,Utility}.java
+                          unwrapper/circlepattern/CPEuclideanRotation.java
+```
+
+---
+
+## ◼ New research directions — Phases 10d–10g  (2026 library scan)
+
+These were identified by a full scan of the Java source tree in 2026.
+They extend significantly beyond the Java port into new mathematical territory.
+
+```
+10d   CircleDomainUnwrapper  (Koebe–Andreev–Thurston)
+         → circle_domain_unwrapper.hpp
+         Conformal map of a multiply-connected planar region onto a
+         canonical disk-with-holes (classical complex-analysis result).
+         Java reference: unwrapper/CircleDomainUnwrapper.java (570 lines)
+         Mathematical basis: Koebe–Andreev–Thurston + Beardon–Stephenson 1990
+
+10e   Quasi-isothermic maps
+         → quasiisothermic.hpp
+         Generalisation of conformal maps for meshes where exact conformality
+         is unachievable (high Gaussian curvature, coarse triangulation).
+         Includes: Delaunay pre-conditioning, discrete Beltrami field,
+                   sin-condition functional, Lawson-correspondence parameterization.
+         Java references: unwrapper/quasiisothermic/ (~1 200 lines total)
+         Mathematical basis: Lam 2015 + Bohle–Lam–Pinkall–Reitebuch 2015
+
+10f   Koebe polyhedra
+         → koebe_polyhedron.hpp
+         Koebe–Andreev–Thurston theorem: realize every 3-connected planar
+         graph as a convex polyhedron with edges tangent to the unit sphere.
+         Connects circle packing with 3-D convex geometry.
+         Java reference: unwrapper/koebe/KoebePolyhedron.java (321 lines)
+         Mathematical basis: Koebe 1936 + Thurston 1997 (lecture notes)
+
+10g   Cyclic-symmetry functionals
+         → cyclic_functional.hpp
+         Euclidean and hyperbolic DCE functionals reduced to a cyclic-symmetry
+         quotient — dramatically reduces DOFs for ornamental / symmetric surfaces.
+         Java references: functional/EuclideanCyclicFunctional.java
+                          functional/HyperbolicCyclicFunctional.java (~530 lines)
+```
+
 ---
 
 ## ◼ Optional / Hypothetical — geometry-central Cross-Comparison