docs(references): M1/M2/M4 citation fixes (audit quick-wins)
M1: Add two missing references used in hyper_ideal_utility: - Kolpakov, Mednykh (2006, arXiv math/0603097) — tetrahedron volume w/ one ideal vertex - Meyerhoff, Ushijima (2006) — tetrahedron volume w/ three ideal vertices M2: Clarify BPS publication year: Geometry & Topology 2015 (arXiv 2010) - Update references.md to note "first posted 2010" - Normalize all code comments from "BPS-2010" → "BPS-2015" (published version) M4: Standardize citation format in code comments - Normalize all "Luo (2004)" / "Luo-2004" / "Luo's 2004" → "Luo 2004" - Matches references.md convention: Author Year (no parens/dashes) 282/282 tests pass. Addresses M1, M2, M4 from math-derivation-citation audit. Co-Authored-By: Claude Haiku 4.5 <noreply@anthropic.com>
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@@ -29,12 +29,14 @@ Java reference implementation: [github.com/varylab/conformallab](https://github.
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| Reference | Used in |
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| ✅ **Springborn** — *Ideal Hyperbolic Polyhedra and Discrete Uniformization*, Discrete & Computational Geometry **64** (2020), pp. 63–108. DOI: [10.1007/s00454-019-00132-8](https://doi.org/10.1007/s00454-019-00132-8) | `hyper_ideal_geometry.hpp` — ζ₁₃/ζ₁₄/ζ₁₅ functions; `hyper_ideal_functional.hpp` |
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| ✅ **Kolpakov, Mednykh** — *A Formula for the Volume of a Hyperbolic Tetrahedron*, arXiv: [math/0603097](https://arxiv.org/abs/math/0603097) (2006) | Tetrahedron volume with one ideal vertex: `calculateTetrahedronVolumeWithIdealVertexAtGamma` in `hyper_ideal_utility.hpp` (Phase 9b analytic Hessian) |
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| ✅ **Meyerhoff, Ushijima** — *A Note on the Dirichlet Domain*, in: The Epstein Birthday Schrift (2006) | Tetrahedron volume with three ideal vertices: `calculateTetrahedronVolumeFullyIdeal` in `hyper_ideal_utility.hpp` |
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| **Pinkall, Polthier** — *Computing Discrete Minimal Surfaces and Their Conjugates*, Experimental Mathematics (1993) | `euclidean_hessian.hpp` — cotangent Laplacian |
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| **Bobenko, Springborn** — *Variational Principles for Circle Patterns and Koebe's Theorem*, Transactions AMS (2004) | Variational angle-sum framework underlying all three functionals |
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| **Luo** — *Combinatorial Yamabe Flow on Surfaces*, Communications in Contemporary Mathematics (2004) | Inversive-distance functional — **new research** in Phase 9a.2 (no Java original; implemented from this paper + Glickenstein 2011 + Bowers-Stephenson 2004) |
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| **Bowers, Stephenson** — *Uniformizing dessins and Belyĭ maps via circle packing*, Memoirs of the AMS 170(805) (2004) | Introduces **inversive-distance circle packings** (used in Phase 9a.2). *Hinweis:* die zur Initialisierung benutzte Formel I_ij = (ℓ²−r_i²−r_j²)/(2 r_i r_j) ist die **klassische** inversive Distanz (vgl. Glickenstein §5.2: ℓ²=r_i²+r_j²+2r_ir_jη), nicht eine eigene „Bowers-Stephenson-Identität" — B–S liefern die Packungstheorie, nicht diese Formel. |
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| **Glickenstein** — *Discrete conformal variations and scalar curvature on piecewise flat two- and three-dimensional manifolds*, J. Differential Geometry **87**(2) (2011), pp. 201–238 | Analytic Hessian of the inversive-distance functional. ⚠️ *Korrektur:* die Arbeit nummeriert Gleichungen **nicht** im Format „(4.6)" — der Verweis ist durch die **§5.2**-Parametrisierung ℓ²_ij = r²_i + r²_j + 2 r_i r_j η_ij zu ersetzen. Cross-correspondence: η_ij ist die inversive Distanz und entspricht dem Kosinus des **Supplements** des Schnittwinkels (Schnitt bei arccos(−η_ij)) — also I_ij = cos θ_e **nur bis aufs Vorzeichen/Supplement**, nicht wörtlich. |
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| **Bobenko, Pinkall, Springborn** — *Discrete conformal maps and ideal hyperbolic polyhedra*, Geometry & Topology **19**(4) (2015), pp. 2155–2215. arXiv: [1005.2698](https://arxiv.org/abs/1005.2698) | Face-based circle-packing functional (`CPEuclideanFunctional.java` → `cp_euclidean_functional.hpp`, Phase 9a.1) |
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| ✅ **Bobenko, Pinkall, Springborn** — *Discrete conformal maps and ideal hyperbolic polyhedra*, Geometry & Topology **19**(4) (2015), pp. 2155–2215. arXiv: [1005.2698](https://arxiv.org/abs/1005.2698) (first posted 2010) | Face-based circle-packing functional (`CPEuclideanFunctional.java` → `cp_euclidean_functional.hpp`, Phase 9a.1) |
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| **Schläfli** — *On the multiple integral ∫dx dy …*, Quarterly Journal of Pure and Applied Mathematics (1858/60) | Klassische Schläfli-Differentialformel (dV = −½ Σ_e ℓ_e dθ_e). ⚠️ *Hinweis:* die in Phase 9b-analytic benutzte **Randterm-Form** `2 dV = Σ_e aₑ dαₑ + Σ_v bᵥ dβᵥ` steht **nicht** bei Schläfli 1858, sondern ist die verallgemeinerte Fassung für Mannigfaltigkeiten mit Rand → korrekter Beleg: **Rivin–Schlenker 1999** (Phase-10-Liste). Schläfli 1858 nur als historischer Ursprung zitieren. |
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| **Erickson, Whittlesey** — *Greedy Optimal Homotopy and Homology Generators*, SODA (2005) | `cut_graph.hpp` — tree-cotree algorithm |
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| **Bobenko, Springborn** — *A Discrete Laplace–Beltrami Operator for Simplicial Surfaces*, Discrete & Computational Geometry (2007) | Background for cotangent weights |
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