docs: integrate publication analysis — Alexa, Bobenko, Springborn, Crane, Lutz

Add phases 9d / 9e / 9f and literature citations derived from a systematic
review of the five authors' publication lists (Tier 1 / 2 / 3 analysis).

phases.md:
  - Phase 9d: ConesUtility port (9d.1) + non-Euclidean cone extensions
    (9d.2, RESEARCH) + StereographicUnwrapper (9d.3)
  - Phase 9e: CirclePatternLayout + CirclePatternUtility (Java port)
  - Phase 9f: Polygon Laplacian on non-triangular meshes (Alexa 2011/2020,
    RESEARCH — no Java equivalent)
  - Phase 9b-analytic: add Rivin-Springborn 1999 as Schläfli source
  - Phase 10b: add Bobenko-Bücking 2009 + Bobenko-Lutz 2024 IMRN
  - Phase 10c: add Lutz 2023 (canonical tessellations) + Bobenko-Lutz 2024
  - Phase 10c' KoebePolyhedron: add Bowers-Bowers-Lutz 2026 rigidity result

references.md:
  - Crane et al. 2018 Optimal Cone Singularities (Phase 9d.2)
  - Bobenko-Lutz 2025 Discrete & Comput. Geom. (Phase 9d.2)
  - Bobenko-Lutz 2024 IMRN (Phase 10b/c)
  - Lutz 2023 Geom. Dedicata (Phase 10c)
  - Lutz PhD thesis TU Berlin 2024 (Phases 9d.2, 10b, 10c)
  - Bowers-Bowers-Lutz 2026 (Phase 9b-analytic + 10c')
  - Alexa-Wardetzky 2011 + Alexa 2020 (Phase 9f)
  - Bobenko-Bücking 2009 (Phase 10b)
  - Rivin-Springborn 1999 (Phase 9b-analytic)

research-track.md:
  - New entry: Phase 9d.2 non-Euclidean cone extensions (Bobenko-Lutz 2025
    + Crane 2018), with acceptance criteria
  - New entry: Phase 9f polygon Laplacian (Alexa-Wardetzky 2011 / Alexa 2020),
    with acceptance criteria

java-parity.md:
  - Split cone-metrics row into Euclidean (9d.1 port) and non-Euclidean
    (9d.2 research) with literature references
  - Add ConesUtility to "utility classes not yet ported" table

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

doc/roadmap/research-track.md

@@ -211,6 +211,77 @@ The phase numbers match `doc/roadmap/phases.md`.
 
 ---
 
+### Non-Euclidean cone extensions (Phase 9d.2, 🔲 planned)
+
+* **Mathematical sources:**
+  - **Bobenko, Lutz** (2025). *Decorated Discrete Conformal Equivalence in
+    Non-Euclidean Geometries.* Discrete & Comput. Geom. arXiv:2310.17529.
+    → §3: Penner-coordinate decoration unifies cone singularities (Θᵥ ≠ 2π)
+    and hyperideal cusps (Θᵥ = 0) in a single algebraic framework valid in
+    Euclidean, spherical, and hyperbolic geometry.
+  - **Crane, Soliman, Ben-Chen, Schröder** (2018). *Optimal Cone Singularities
+    for Conformal Flattening.* ACM SIGGRAPH 2018. DOI: 10.1145/3197517.3201367.
+    → L¹-optimal cone placement via a sparse-recovery optimisation over the
+    curvature deficit Kᵥ = 2π − Θᵥ; directly gives the set of cone angles
+    to prescribe for a near-flat conformal parametrisation.
+  - **Lutz** (2024). *PhD thesis, TU Berlin.* DOI: 10.14279/depositonce-20357.
+    → Full proofs for both non-Euclidean decorated DCE variants; single reference
+    covering 9d.2, 10b, and 10c.
+
+* **Java reference:** ❌ **none.** Java `ConesUtility.java` handles only the
+  Euclidean case; the non-Euclidean extension is new research.
+
+* **Scope:**
+  - Extend `cones_utility.hpp` (Phase 9d.1, Java port) to accept prescribed
+    cone angles in HyperIdeal and Spherical modes.
+  - Integrate the Bobenko-Lutz decoration into the variational framework of
+    `hyper_ideal_functional.hpp` and `spherical_functional.hpp`.
+  - Optionally: implement the Crane 2018 L¹-optimiser as a helper that
+    suggests cone positions automatically from the input curvature.
+
+* **Status:** 🔲 planned; no PR yet.
+* **Effort:** medium (1–2 weeks for Euclidean→HyperIdeal/Spherical extension;
+  +1 week if Crane 2018 optimiser is included).
+* **Acceptance criteria:**
+  - Prescribed Θᵥ ≠ 2π in HyperIdeal mode: Gauss-Bonnet check passes with
+    `2π·χ = Σ Θᵥ − Σ αᵢⱼ` for given cone angles.
+  - Newton convergence on a mesh with two manually placed cone singularities
+    (Euclidean, Spherical, HyperIdeal).
+  - Cross-validation: at Θᵥ = 2π for all v, output equals existing non-cone solver.
+
+---
+
+### Polygon Laplacian (Phase 9f, 🔲 planned)
+
+* **Mathematical sources:**
+  - **Alexa, Wardetzky** (2011). *Discrete Laplacians on General Polygonal
+    Meshes.* ACM SIGGRAPH 2011. DOI: 10.1145/1964921.1964997.
+    → Virtual-node construction: each polygon face is replaced by a virtual
+    central node connected to all vertices; cotangent weights are computed
+    per sub-triangle; the resulting operator is symmetric and positive
+    semi-definite, mirroring Pinkall-Polthier for triangulations.
+  - **Alexa** (2020). *Discrete Laplacians on General Polygonal Meshes.*
+    ACM TOG 39(6). DOI: 10.1145/3414685.3417840.
+    → Extended journal version with error bounds and convergence analysis.
+
+* **Java reference:** ❌ **none.**
+
+* **Scope:**
+  - Implement `polygon_laplacian.hpp` following the virtual-node construction.
+  - Slot it into `newton_solver.hpp` as a drop-in replacement for
+    `euclidean_hessian.hpp` when the input mesh is non-triangular.
+  - No change to the energy functional — only the Hessian approximation changes.
+
+* **Status:** 🔲 planned; pure research, no Java reference.
+* **Effort:** medium (~2 weeks core + tests; +1 week Newton integration).
+* **Acceptance criteria:**
+  - Operator is symmetric and PSD (checked via `LDLT.info() == Success`).
+  - On a pure triangle mesh, output equals `euclidean_hessian.hpp` result.
+  - Newton convergence on a quad mesh (e.g., structured grid) with the
+    polygon Laplacian Hessian.
+
+---
+
 ### Genus g ≥ 2 fundamental domain (Phase 9c, 🔲 planned)
 * **Mathematical sources:**
   - **Poincaré, H.** (1882). *Théorie des groupes fuchsiens.*