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

@@ -0,0 +1,143 @@
+# 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.