docs: citation audit + correct 8 mis-citations; add Phases 12/13

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>

doc/roadmap/research-track.md

@@ -79,7 +79,7 @@ The phase numbers match `doc/roadmap/phases.md`.
 ### CP-Euclidean functional (Phase 9a.1, 🟡 PR #8)
 * **Mathematical source:** Bobenko, Pinkall, Springborn (2010).
   *Discrete conformal maps and ideal hyperbolic polyhedra.*
-  Geometry & Topology 14, 379–426.
+  Geometry & Topology 19(4) (2015), 2155–2215. arXiv:1005.2698.
 * **Java reference:** ✅ `CPEuclideanFunctional.java` (260 lines + 88-line
   `CPEuclideanFunctionalTest.java`).  **This one IS a port.**
 * **Status:** 🟡 PR #8 open, 10 tests including Java-test parity.
@@ -95,11 +95,15 @@ The phase numbers match `doc/roadmap/phases.md`.
     gradient identity Lemma 3.1.
   - **Bowers, P. L. & Stephenson, K.** (2004). *Uniformizing dessins
     and Belyĭ maps via circle packing.* Memoirs of the AMS 170(805).
-    → inversive-distance identity `I_ij = (ℓ²−r_i²−r_j²)/(2 r_i r_j)`.
+    → introduces inversive-distance circle packings. NB: the formula
+    `I_ij = (ℓ²−r_i²−r_j²)/(2 r_i r_j)` is the *classical* inversive
+    distance (= Glickenstein §5.2 η), not a B–S-specific identity.
   - **Glickenstein, D.** (2011). *Discrete conformal variations and
-    scalar curvature on piecewise flat manifolds.* J. Diff. Geom.
-    87(2), 201–238.  → §5 correspondence `I_ij = cos θ_e`, eq. 4.6
-    analytic Hessian (used later by Phase 9b-analytic mirror).
+    scalar curvature on piecewise flat two- and three-dimensional
+    manifolds.* J. Diff. Geom. 87(2), 201–238.  → §5.2 inversive-distance
+    parametrization ℓ²=r_i²+r_j²+2r_ir_jη; correspondence I_ij = cos θ_e
+    holds only up to sign/supplement (intersection at arccos(−η)).
+    The paper does **not** number equations as "(4.6)".
 * **Java reference:** ❌ **none.**  Verified empirically:
   ```bash
   $ find /Users/tarikmoussa/Desktop/conformallab -iname "*nversive*"
@@ -202,7 +206,7 @@ The phase numbers match `doc/roadmap/phases.md`.
 
 ### Inversive-distance Hessian — full analytic (Phase 9a.2-analytic, 🔲 planned)
 
-* **Mathematical source:** Glickenstein, D. (2011) eq. (4.6).
+* **Mathematical source:** Glickenstein, D. (2011) §5.2 (inversive-distance parametrization ℓ²=r_i²+r_j²+2r_ir_jη).
 * **Java reference:** ❌ none.
 * **Chain:** `(uᵢ, uⱼ) → ℓᵢⱼ → αᵢⱼ` with `∂ℓ²/∂u_i = 2(r_i² + I r_i r_j)`.
 * **Effort:** medium (5–7 days, less involved than HyperIdeal because
@@ -219,8 +223,8 @@ The phase numbers match `doc/roadmap/phases.md`.
     → §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.
+  - **Soliman, Slepčev, Crane** (2018). *Optimal Cone Singularities
+    for Conformal Flattening.* ACM Trans. Graph. 37(4), Art. 105. 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.
@@ -260,9 +264,10 @@ The phase numbers match `doc/roadmap/phases.md`.
     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.
+  - **Bunge, Herholz, Kazhdan, Botsch** (2020). *Polygon Laplacian Made Simple.*
+    Computer Graphics Forum 39(2), 303–313. DOI: 10.1111/cgf.13931.
+    → virtual-vertex construction with error analysis. (DEC alternative:
+    de Goes, Butts, Desbrun 2020, ACM TOG 39(4), DOI 10.1145/3386569.3392389.)
 
 * **Java reference:** ❌ **none.**
 
@@ -345,6 +350,72 @@ The phase numbers match `doc/roadmap/phases.md`.
 * **Java reference:** ❌ none — Java has the polygon + period matrix
   pieces but does not assemble them into a Fuchsian group representation.
 * **Status:** **fully new research** — depends on 9c + 10a + 10b.
+* **⚠️ Scope boundary:** 10c delivers the *infrastructure* (Fuchsian-group
+  representation + H²/Γ embedding on the Sechelmann/Bobenko-Springborn path).
+  The Lutz-*specific* algorithms (canonical Delaunay tessellation in Penner
+  coordinates, Epstein-Penner hull, Weeks-flip, polyhedral realisation) are
+  **not** auto-delivered by reaching 10c — they are split out as **Phase 13**
+  (Chain B capstone), which sits on top of this runway.
+
+---
+
+### Decorated DCE & geometric transition (Phase 12, 🔲 planned — near-term, Chain A)
+* **Mathematical sources:**
+  - **Bobenko, Lutz** (2025). *Decorated Discrete Conformal Equivalence in
+    Non-Euclidean Geometries.* Discrete & Comput. Geom. arXiv:2310.17529. §3
+    — Penner-coordinate decoration unifying Euclidean/spherical/hyperbolic
+    DCE; continuous deformation at fixed discrete conformal invariant.
+  - **Lutz** (2024). *PhD thesis, TU Berlin.* DOI: 10.14279/depositonce-20357.
+* **Java reference:** ❌ none.
+* **Builds on (✅ landed):** `inversive_distance_functional.hpp` (9a.2),
+  `hyper_ideal_functional.hpp` (Springborn 2020), `spherical_functional.hpp`
+  — the decoration is a re-parametrisation of these, not a new solver.
+* **Does NOT require:** 9c / 10a / 10b / holonomy-bug fix. This is the
+  **short path**: the earliest Lutz-adjacent result, independent of Chain B.
+* **Scope:** (1) Penner-coordinate decoration layer ↔ classical inversive
+  distance `ℓ²=r_i²+r_j²+2r_ir_jη`; (2) curvature-transition driver κ∈{+,0,−}
+  at fixed invariant; (3) validation harness + example gallery.
+* **Acceptance criteria:**
+  - Decoration round-trip `I_ij ↔ (r_i,r_j,ℓ)` at machine precision.
+  - At κ=0 bit-for-bit match with the existing Euclidean/inversive path.
+  - Gauss-Bonnet per geometry; invariant constant across the κ-transition
+    to tol (numerical witness of the Bobenko-Lutz master theorem).
+  - Cross-geometry agreement of the invariant on one test surface.
+* **Effort:** medium (functionals exist; reparametrisation + driver + tests).
+
+---
+
+### Decorated canonical tessellations & polyhedral realisation (Phase 13, 🔲 planned — Chain B capstone)
+* **Mathematical sources:**
+  - **Lutz** (2023). *Canonical Tessellations of Decorated Hyperbolic
+    Surfaces.* Geom. Dedicata 217. arXiv:2206.13461 — canonical (weighted-
+    Delaunay-analogue) tessellation + dual; Epstein-Penner convex hull in
+    Minkowski space; Weeks-flip extension.
+  - **Bobenko, Lutz** (2024). IMRN 2024(12), 9505–9534. arXiv:2305.10988 —
+    discrete uniformization theorem for decorated surfaces.
+  - **Lutz** (2024). *PhD thesis* (depositonce-20357) — polyhedral realisation.
+  - Rigidity backing: **Bowers, Bowers, Lutz** (2026), arXiv:2601.22903.
+* **Java reference:** ❌ none.
+* **Prerequisites (the "given Voraussetzungen", all must be in place):**
+  ✅ `cut_graph.hpp` (2g seams) · 🔲 Phase 9c (fundamental domain) ·
+  🔲 Phase 10a (1-forms) · 🔲 Phase 10b (period matrix Ω) ·
+  🔲 Phase 10c (Fuchsian group / H²/Γ) ·
+  🔲 holonomy-bug fix (`detail::spherical_holonomy` /
+  `detail::hyperbolic_holonomy` + `cpp_dec_float_50`; see Phase 9c block) ·
+  🟡 Phase 12 (Penner-coordinate decoration layer — reused here; land first).
+* **Scope:** (1) Penner-coordinate canonical tessellation + dual on the
+  H²/Γ embedding from 10c; (2) Epstein-Penner hull + Weeks-flip to reach the
+  canonical decomposition; (3) polyhedral realisation of the uniformised
+  genus-g surface.
+* **Acceptance criteria:**
+  - Canonical tessellation unique & flip-stable (Weeks-flip terminates,
+    start-triangulation-independent).
+  - Penner-coordinate consistency with the Phase 12 decoration layer.
+  - Gauss-Bonnet + holonomy closure `∏[a_i,b_i] = Id` (high precision).
+  - Rigidity witness: Newton finds the unique realisation on the
+    tangency-case test set (Bowers-Bowers-Lutz 2026).
+* **Effort:** very large — gated on the full 9c/10a/10b/10c chain; the Lutz
+  algorithms themselves ≈ several weeks on top.
 
 ---