docs: citation audit + correct 8 mis-citations; add Phases 12/13
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External reviewer pass over the literature references. Verified entries against arXiv/DOI/publisher and corrected misattributions that had propagated across the docs. Corrected citations (consistent across all docs): - Bowers-Bowers-Lutz 2026: title was the 2017 paper's -> "Rigidity of Koebe Polyhedra and Inversive Distance Circle Packings" - Liouville theorem: "Springborn 2019" -> Pinkall & Springborn, Geom. Dedicata 214 (2021) - Bobenko-Pinkall-Springborn: "G&T 14 (2010)" -> G&T 19(4) (2015), 2155-2215 - Optimal Cone Singularities: "Crane, Soliman, Ben-Chen, Schroeder" -> Soliman, Slepcev, Crane, ACM TOG 37(4) - Schlaefli formula: "Rivin, Springborn 1999" -> Rivin, Schlenker - Quasiconformal distortion: "Springborn, Veselov" -> Born, Buecking, Springborn (arXiv:1505.01341) - Period matrices: "Bobenko, Buecking 2009" (was Bobenko-Mercat-Schmies' title) -> Bobenko-Mercat-Schmies 2011 + genuine Bobenko-Buecking 2021 - Fabricated entry: "Alexa 2020, DOI 10.1145/3414685.3417840" pointed to an unrelated paper (Pixelor) -> Bunge, Herholz, Kazhdan, Botsch 2020 - Stripe Patterns: "Bonneel et al. 2015" -> Knoeppel, Crane, Pinkall, Schroeder 2015 Equation-number corrections (verified against the PDFs): - Glickenstein 2011 "eq. 4.6" -> "§5.2" (no such equation label exists) - Springborn 2020 "eq. 4.6" -> "§4 variational gradient" - inversive-distance attribution softened to classical inversive distance Other: - DBFEnergy bibliography (separate repo) and convergence half-sentence in novelty-statement.md §3.3 (Bobenko-Buecking 2021) - Status legend (implemented vs planned) at top of references.md - New Phase 12 (decorated DCE & geometric transition, Chain A, near-term) and Phase 13 (canonical tessellations & polyhedral realisation, Chain B capstone) in phases.md + research-track.md; 10c scope-boundary note clarifying infrastructure vs Lutz-specific algorithms Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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@@ -35,7 +35,7 @@ phases whose existence is settled but whose priority is open:
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| **9f** | RESEARCH | Discrete Laplace–Beltrami on **non-triangular** polygonal meshes (virtual-node / generalised cotangent), making DCE work on quad / Voronoi tessellations without re-triangulation | Polygon Laplacians (2011 *SIGGRAPH* + 2020 *TOG*) |
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| **10c + 10c′** | planned | Canonical Delaunay tessellations of decorated hyperbolic surfaces; Koebe polyhedron realisation (KAT) with rigidity-aware Newton | Canonical tessellations of decorated hyperbolic surfaces (2023, *Geom. Dedicata*); rigidity of circle / hyperideal polyhedra (2026, preprint) |
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| **10e** | planned | Quasi-isothermic maps (~800 lines Lawson-correspondence) — generalises conformality to meshes where exact conformality is impossible. Six new classes including a discrete Beltrami-field solver. | Java original `QuasiisothermicUtility` line; no obvious single-paper reference in the existing literature index |
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| **10b** | planned | Hyperelliptic surfaces (genus g ≥ 2 with Z₂ symmetry); period matrices with block-diagonal structure; Penner-coordinate variant via `HyperIdealHyperellipticUtility` | Bobenko–Bücking 2009 *Conformal Structures and Period Matrices of Polyhedral Surfaces* |
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| **10b** | planned | Hyperelliptic surfaces (genus g ≥ 2 with Z₂ symmetry); period matrices with block-diagonal structure; Penner-coordinate variant via `HyperIdealHyperellipticUtility` | Bobenko–Mercat–Schmies 2011 *Period Matrices of Polyhedral Surfaces* / Bobenko–Bücking 2021 *Convergence of discrete period matrices* |
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| **9d.4** | planned | Möbius centring of Poincaré-disk layouts as a *variational* problem (Lorentz energy with full gradient + Hessian), replacing today's iterative Fréchet-mean fallback in `normalise_hyperbolic()` | Java original `MobiusCenteringFunctional`; closest published context: decorated-DCE Möbius normalisation, also used in canonical-tessellation post-processing |
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**Question A:** which of these (if any) would unblock concrete
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@@ -104,7 +104,7 @@ We have:
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[`doc/math/hyperideal-hessian-derivation.md`](../math/hyperideal-hessian-derivation.md)
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(805 lines, all sign pitfalls covered, references Schläfli 1858,
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Milnor 1982, Vinberg 1993, Cho–Kim 1999, Glickenstein 2011,
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Springborn 2020, Rivin–Springborn 1999).
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Springborn 2020, Rivin–Schlenker 1999).
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**Question:**
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