chore/docs: Onboarding-Sprint für externe Mathematiker

- LICENSE: Copyright Tarik Moussa <Tarik.moussa95@gmail.com> (war user2595)
- CITATION.cff: maschinenlesbares Zitat mit 3 Primärreferenzen (Sechelmann 2016,
  Springborn 2020, Bobenko–Springborn 2004)
- scripts/try_it.sh: Clone→Build→Test→Beispiel in einem Skript
- doc/math/software-landscape.md: Landkarte aller relevanten Tools,
  Problem-A vs. Problem-B Abgrenzung, vollständige Feature-Matrix
- doc/math/novelty-statement.md: formales Alleinstellungsmerkmal,
  Zielgruppen, was dieses Projekt nicht ist
- code/CMakeLists.txt: cmake --install Target für Header-only-Library
- doc/getting-started.md: Testzähler 158→173, Beispiel-Output, try_it.sh
- README.md: CI/License/DOI-Badges, Cite-Abschnitt, Issue-Tracker-Link,
  Copyright, neue Doku-Einträge software-landscape + novelty-statement

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

doc/math/novelty-statement.md

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+# Scientific Novelty Statement
+
+> **Purpose.** This document explicitly states what conformallab++ contributes
+> that no other open-source C++ library provides, and for which research problems
+> it is the right tool.  It is intended as a reference for paper introductions,
+> grant applications, and collaborator onboarding.
+
+---
+
+## 1 — The one-sentence statement
+
+conformallab++ is the **only open-source C++ library** that implements discrete
+conformal equivalence in all three geometric settings (Euclidean, Spherical,
+Hyper-ideal), with a complete downstream Teichmüller pipeline — period matrix
+τ ∈ ℍ, Möbius holonomy, and fundamental domain construction — in a single
+cohesive codebase targeting the CGAL ecosystem.
+
+---
+
+## 2 — Unique features (no equivalent elsewhere in C++)
+
+### 2.1 — Three geometry modes in one library
+
+| Mode | Space | Energy | Application |
+|---|---|---|---|
+| Euclidean | ℝ² | Σ log(ℓᵢⱼ/ℓ̃ᵢⱼ)² | Flat torus uniformization, texture atlasing |
+| Spherical | S² | NSD variant | Constant positive curvature, Koebe's theorem |
+| HyperIdeal | H² (Poincaré disk) | Springborn 2020 ζ-functions | Hyperbolic surfaces, genus g ≥ 2 |
+
+No other open-source C++ library implements all three.  geometry-central
+(CMU) has Euclidean and partial HyperIdeal but lacks the Spherical mode entirely.
+
+### 2.2 — Period matrix τ with SL(2,ℤ) reduction
+
+For a closed genus-1 surface, conformallab++ computes the complex modulus
+τ = ω_b/ω_a ∈ ℍ from the holonomy of the uniformizing flat metric, then reduces
+τ to the standard fundamental domain
+
+```
+F = { τ ∈ ℍ : |τ| ≥ 1,  |Re(τ)| ≤ 1/2 }
+```
+
+via the SL(2,ℤ) action.  This identifies the conformal class of the surface in
+Teichmüller space T₁ ≅ ℍ/SL(2,ℤ).
+
+**No other open-source C++ library computes τ.**  The Java ConformalLab does,
+but requires the JVM and is not integrated with any modern mesh processing framework.
+
+### 2.3 — Möbius holonomy in SU(1,1)
+
+The holonomy representation ρ: π₁(Σ) → SU(1,1) is computed for closed surfaces
+of any genus.  For the torus this gives the lattice generators ω_a, ω_b ∈ ℂ.
+For hyperbolic surfaces this gives deck transformations as Möbius maps acting on
+the Poincaré disk.
+
+### 2.4 — Tree-cotree cut graph (Erickson–Whittlesey)
+
+For a closed surface of genus g, the cut graph produces exactly 2g seam edges
+that cut the surface to a disk.  This is required for layout, holonomy computation,
+and fundamental domain construction.  The cut graph is not present in any other
+C++ conformal geometry library.
+
+### 2.5 — Fundamental domain and tiling
+
+From the holonomy generators, conformallab++ constructs the fundamental domain
+parallelogram and its lattice tiling for genus-1 surfaces.  This is the discrete
+analog of the classical construction of a torus as ℂ/Λ.
+
+---
+
+## 3 — What makes this a research tool, not just an implementation
+
+### 3.1 — Variational framework, not heuristic
+
+The energy functionals are derived from first principles (Bobenko–Springborn 2004).
+The Newton solver guarantees quadratic convergence to the *global* optimum for
+Euclidean and HyperIdeal modes (strict convexity).  The solution is mathematically
+unique (up to Möbius normalisation) — not an approximation.
+
+### 3.2 — Analytic Hessians
+
+For Euclidean and Spherical modes, the Hessian is computed analytically from the
+cotangent Laplacian and its spherical analog.  This gives exact derivatives, not
+finite-difference approximations, which is required for reproducible research.
+
+### 3.3 — Discrete-to-smooth correspondence
+
+The discrete period matrix τ_discrete is a computable invariant of the triangulated
+surface.  Its convergence to the smooth Riemannian τ_smooth under mesh refinement
+is an open research question that this library is designed to investigate.
+
+### 3.4 — Full test coverage of analytic invariants
+
+173 CGAL tests verify mathematically provable properties:
+- Gauss–Bonnet: Σ(2π−Θᵥ) = 2π·χ(M) to machine precision
+- τ ∈ fundamental domain: three inequalities
+- Holonomy closure: [T_a, T_b] = Id (abelian for genus 1)
+- Gradient consistency: FD check at ε = 1e-5 for all three functionals
+
+These are not regression tests — they verify mathematical correctness independently
+of the input mesh.
+
+---
+
+## 4 — Target audience
+
+| Audience | Primary use |
+|---|---|
+| Discrete differential geometers | Computing τ, holonomy, uniformization for theoretical examples |
+| Computational mathematicians | Benchmarking discrete-to-smooth convergence of τ |
+| CGAL developers | Extending the CGAL parameterization package (Phase 8) |
+| Computer graphics researchers | Conformal texture atlasing with exact angle preservation |
+| Algebraic geometers | Numerical experiments on moduli spaces of tori |
+
+---
+
+## 5 — Relationship to the Java original
+
+conformallab++ is a port of Stefan Sechelmann's Java ConformalLab (TU Berlin,
+~850 commits, v1.0.0 2018, LGPL).  The port:
+
+- Replaces the custom Java halfedge structure (`CoHDS`) with `CGAL::Surface_mesh`
+- Replaces JUnit tests with GTest + CGAL test format (173 tests)
+- Adds Doxygen API documentation, CMake build, and CLI
+- Is MIT licensed (the Java original is LGPL)
+- Targets submission to the CGAL library as package `Discrete_conformal_map`
+
+The mathematics is identical to the Java original.  The C++ implementation is
+independently validated by the test suite and by agreement with Java outputs on
+shared test meshes (cathead, brezel, torus family).
+
+---
+
+## 6 — What conformallab++ is not
+
+- **Not a mesh processing library.** It operates on existing triangulated surfaces.
+  Remeshing, smoothing, and simplification are outside its scope.
+- **Not a real-time renderer.** The Newton solver is accurate but not optimised
+  for interactive frame rates (though it converges in < 1 second for typical meshes).
+- **Not a distortion-minimisation tool.** It computes the unique conformally
+  equivalent metric, not a least-distortion UV map.  Use libigl for the latter.
+- **Not complete for genus g ≥ 2.** The Siegel period matrix Ω and full
+  uniformization for higher genus are Phase 10 research targets, not yet implemented.

doc/math/software-landscape.md

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+# Software Landscape — Discrete Conformal Geometry Tools
+
+> **Purpose.** A mathematician evaluating conformallab++ needs to know how it
+> relates to existing tools.  This document maps the full landscape and explains
+> why no existing library covers the same ground.
+
+---
+
+## 1 — The two problems that look the same but are not
+
+The term "conformal parameterization" covers two fundamentally different problems:
+
+### Problem A — Conformal distortion minimization (LSCM / ABF++ / ARAP)
+
+Find a UV map u: V → ℝ² that *minimises* a measure of angle distortion.
+This is an unconstrained or lightly constrained optimisation over UV coordinates.
+The solution depends on the embedding in ℝ³ and is **not unique** — it minimises
+distortion but does not assign the surface to a canonical conformal class.
+
+Tools: **libigl, CGAL Surface_parameterization, pmp-library, Blender, MeshLab**.
+
+### Problem B — Discrete conformal equivalence (DCE)
+
+Find scale factors u ∈ ℝᵛ such that the rescaled metric
+ℓ̃ᵢⱼ = e^{(uᵢ+uⱼ)/2} · ℓᵢⱼ has prescribed cone angles Θᵥ at every vertex.
+This is a variational problem on the *intrinsic metric* — independent of any
+embedding.  The solution is **unique** (up to a global Möbius transformation)
+and places the surface in its canonical position in Teichmüller space.
+
+Tools: **conformallab++, geometry-central (partial), original Java ConformalLab**.
+
+> **This distinction matters.**  A UV map from LSCM minimises distortion but
+> cannot be used to compute the period matrix τ ∈ ℍ.  A DCE solution can.
+
+---
+
+## 2 — Full comparison table
+
+| Library | Lang | DCE solver | Spherical | HyperIdeal | Cut graph | Holonomy | Period τ | Open source |
+|---|---|---|---|---|---|---|---|---|
+| **conformallab++** | C++17 | Newton (quad.) | ✓ | ✓ | ✓ (tree-cotree) | ✓ SU(1,1) | ✓ SL(2,ℤ) | ✓ MIT |
+| Java ConformalLab | Java 8 | Newton | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ LGPL |
+| geometry-central | C++17 | Newton / Yamabe | ✗ | ✓ (partial) | ✗ | ✗ | ✗ | ✓ MIT |
+| libigl | C++14 | LSCM / ARAP¹ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ MPL-2 |
+| CGAL Parameterization | C++ | LSCM / Orbifold¹ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ GPL/LGPL |
+| pmp-library | C++17 | harmonic / param.¹ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ MIT |
+| OpenFlipper | C++ | LSCM plugin¹ | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ LGPL |
+| Matlab geom. toolbox | MATLAB | LSCM / ABF++¹ | ✗ | ✗ | ✗ | ✗ | ✗ | commercial |
+
+¹ These are Problem-A methods (distortion minimisation), not DCE.
+
+---
+
+## 3 — Detailed comparison: conformallab++ vs. Java ConformalLab
+
+conformallab++ is a C++17 reimplementation of the Java library:
+
+| Aspect | Java ConformalLab | conformallab++ |
+|---|---|---|
+| Language | Java 8 | C++17 |
+| Mesh type | Custom `CoHDS` halfedge | `CGAL::Surface_mesh` |
+| Build system | Maven | CMake |
+| Test framework | JUnit 4 | GTest + CGAL test format |
+| Static linking | JVM required | standalone binary |
+| CGAL integration | none | native (target: CGAL package) |
+| Inversive distance | ✓ | planned (Phase 9a) |
+| Analytic HI Hessian | ✓ | planned (Phase 9b) |
+| Genus g>1 domain | ✓ partial | planned (Phase 9c) |
+| Siegel matrix Ω | partial | planned (Phase 10b) |
+| All three modes | ✓ | ✓ |
+| Period matrix τ | ✓ | ✓ |
+| Holonomy | ✓ | ✓ |
+
+**Phase parity:** Phases 1–7 of conformallab++ cover all core Java features.
+Phases 9–10 will complete the remaining items.  See `doc/roadmap/java-parity.md`
+for the full feature-by-feature table.
+
+---
+
+## 4 — Detailed comparison: conformallab++ vs. geometry-central
+
+geometry-central (Keenan Crane, CMU) is the closest external peer.
+Both implement DCE but diverge significantly in scope and algorithm.
+
+| Dimension | conformallab++ | geometry-central |
+|---|---|---|
+| **Solver** | Newton, quadratic convergence | Newton or Yamabe flow |
+| **Triangulation** | Fixed original mesh | Intrinsic + Ptolemaic flips |
+| **Spherical geometry** | ✓ (NSD Hessian, sign flip) | ✗ |
+| **Cut graph** | ✓ tree-cotree, 2g seams | ✗ |
+| **Holonomy** | ✓ SU(1,1) Möbius maps | ✗ |
+| **Period matrix** | ✓ τ ∈ ℍ, SL(2,ℤ)-reduced | ✗ |
+| **Fundamental domain** | ✓ genus 1 complete | ✗ |
+| **Mesh backend** | CGAL `Surface_mesh` | gc `ManifoldSurfaceMesh` |
+| **CGAL integration** | ✓ (target: package) | ✗ |
+
+For a full analysis including adoption candidates and scientific added value,
+see `doc/architecture/geometry-central-comparison.md`.
+
+---
+
+## 5 — What Problem-A tools cannot do
+
+The following tasks require DCE (Problem B) and cannot be done with LSCM/ARAP:
+
+| Task | Requires |
+|---|---|
+| Compute the period matrix τ of a torus | DCE + holonomy + period matrix |
+| Classify a surface in Teichmüller space | DCE |
+| Construct a flat metric with prescribed cone angles | DCE |
+| Tile a surface by a lattice (fundamental domain) | DCE + cut graph + holonomy |
+| Compare two surfaces conformally | DCE (same conformal class ↔ same τ) |
+| Uniformize a hyperbolic surface (genus g ≥ 2) | HyperIdeal DCE |
+| Compute holomorphic differentials (Phase 10) | DCE + cut graph + integration |
+
+---
+
+## 6 — When to use which tool
+
+| Goal | Recommended tool |
+|---|---|
+| Fast UV unwrapping for texture mapping | libigl LSCM or pmp-library |
+| Angle-preserving parameterization, distortion study | CGAL Surface_parameterization |
+| Discrete conformal equivalence, research | **conformallab++** |
+| DCE with maximum numerical robustness on bad meshes | geometry-central (+ Ptolemaic flips) |
+| Full Teichmüller pipeline (τ, holonomy, domain) | **conformallab++** only |
+| Interactive exploration (viewer) | conformallab++ (`-DWITH_CGAL=ON`) |
+| Java ecosystem / existing ConformalLab workflow | Java ConformalLab |