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>
2026-05-29 19:17:17 +02:00
parent 18b9c61492
commit 26f4f0637d
11 changed files with 274 additions and 70 deletions
--- a/doc/roadmap/phases.md
+++ b/doc/roadmap/phases.md
@@ -109,8 +109,8 @@ mesh type.
 9b-analytic   Full analytic HyperIdeal Hessian via Schläfli identity
         → planned, see research-track.md
         Mathematical source: Springborn 2020 §4 + Schläfli 1858/60
-                              + Rivin, Springborn 1999 "The Schläfli formula in
-                                Einstein manifolds with boundary" (ERA-AMS 5)
+                              + Rivin, Schlenker 1999 "The Schläfli formula in
+                                Einstein manifolds with boundary" (ERA-AMS 5, 18–23)
                              + Cho-Kim 1999 + Glickenstein 2011 §4
         Algorithm: explicit chain rule through (bᵢ,aₑ) → ℓᵢⱼ → ζ₁₃/ζ₁₄/ζ₁₅ → αᵢⱼ/βᵢ
         Includes: short LaTeX correctness note in doc/math/.
@@ -165,8 +165,8 @@ mesh type.
             Non-Euclidean Geometries" (Discrete & Comput. Geom. 2025,
             arXiv:2310.17529) §3 — decorated DCE framework unifying cone
             singularities and cusps in hyperbolic + spherical geometry.
-           Crane, Soliman, Ben-Chen, Schröder 2018 "Optimal Cone Singularities
-             for Conformal Flattening" (ACM SIGGRAPH 2018) — L¹-optimal
+           Soliman, Slepčev, Crane 2018 "Optimal Cone Singularities
+             for Conformal Flattening" (ACM TOG 37(4), Art. 105) — L¹-optimal
             automatic cone placement; directly applicable to 9d.2 algorithm.
         Status: 🔲 planned

@@ -223,8 +223,10 @@ mesh type.
           Alexa, Wardetzky 2011 "Discrete Laplacians on General Polygonal
             Meshes" (ACM SIGGRAPH 2011) — virtual-node construction,
             polygon cotangent weights extending the Pinkall-Polthier formula.
-           Alexa 2020 "Discrete Laplacians on General Polygonal Meshes"
-             (ACM TOG 39, 2020) — extended journal treatment, error bounds.
+           Bunge, Herholz, Kazhdan, Botsch 2020 "Polygon Laplacian Made
+             Simple" (Computer Graphics Forum 39(2), 303–313) — virtual-vertex
+             construction with error analysis. (DEC alternative: de Goes,
+             Butts, Desbrun 2020, ACM TOG 39(4).)
         Enables: DCE energy evaluation on quad-dominant / Voronoi /
                  polygon meshes without forced triangulation.
                  Replaces euclidean_hessian.hpp for non-triangular inputs.
@@ -425,15 +427,19 @@ Phase 10   Global uniformization for genus g ≥ 2
       → Ωᵢⱼ = ∫_{bⱼ} ωᵢ
       → Reduction to Siegel fundamental domain via Sp(2g,ℤ).
       Mathematical reference: Bobenko-Springborn 2004 + Gottschling 1959.
-                               Bobenko, Bücking 2009 "Conformal Structures and
-                               Period Matrices of Polyhedral Surfaces" — discrete
-                               period matrix Ωᵢⱼ on polyhedral surfaces.
+                               Bobenko, Mercat, Schmies 2009/2011 "Conformal
+                               Structures / Period Matrices of Polyhedral
+                               Surfaces" (arXiv:0909.1305) + Bobenko, Bücking 2021
+                               "Convergence of discrete period matrices ..."
+                               (Math. Phys. Anal. Geom. 24, Art. 23) — discrete
+                               period matrix Ωᵢⱼ on polyhedral surfaces + convergence.
                               Bobenko, Lutz 2024 IMRN "Decorated Discrete Conformal
                               Maps and Convex Polyhedral Cusps" — uniformization
                               theorem connecting cusps ↔ hyperideal vertices
                               (bridges Phase 2/3 HyperIdeal geometry to 10b).
-                               Springborn 2019 "A discrete version of Liouville's
-                               theorem on conformal maps" (arXiv:1911.00966) —
+                               Pinkall, Springborn 2021 "A discrete version of
+                               Liouville's theorem on conformal maps"
+                               (Geom. Dedicata 214, 389–398; arXiv:1911.00966) —
                               proves uniqueness/rigidity of the discrete conformal
                               structure; justifies that Ω is a conformal invariant.
       Java partial reference: DiscreteRiemannUtility.java (186 lines).
@@ -467,9 +473,9 @@ Phase 10   Global uniformization for genus g ≥ 2
                               Bobenko, Lutz 2024 IMRN (arXiv:2305.10988) —
                               discrete uniformization theorem for decorated
                               piecewise Euclidean surfaces.
-                               Springborn, Veselov 2015 "Quasiconformal distortion
-                               of projective transformations and discrete conformal
-                               maps" (Int. Math. Res. Not.) — error estimates for
+                               Born, Bücking, Springborn 2015 "Quasiconformal
+                               distortion of projective transformations and discrete
+                               conformal maps" (arXiv:1505.01341) — error estimates for
                               the discrete-to-smooth conformal approximation;
                               quantifies how well H²/Γ approximates the smooth
                               hyperbolic metric.
@@ -479,11 +485,22 @@ Phase 10   Global uniformization for genus g ≥ 2
       Status: **fully new research.**
       Requires: 10a + 10b + Phase 9c.

+       ⚠️ SCOPE BOUNDARY (was 10c delivers vs. was offen bleibt):
+         10c as scoped here builds the *infrastructure* — Fuchsian-group
+         representation + H²/Γ embedding on the Sechelmann/Bobenko-Springborn
+         uniformisation path.  The Lutz-SPECIFIC algorithms it references
+         (canonical Delaunay tessellation in Penner coordinates, Epstein-Penner
+         convex-hull construction, Weeks-flip extension, polyhedral realisation)
+         are NOT delivered automatically by reaching 10c — they sit ON TOP of
+         this infrastructure and are their own implementation effort.
+         → that effort is split out as **Phase 13** (Chain B capstone).
+         10c = runway;  Phase 13 = the Lutz algorithms that land on it.
+
 10c'  Optional Java-port additions (low priority)
       → KoebePolyhedron.java (321 lines) — Koebe-Andreev-Thurston
         circle packings.  Adds a fifth DCE method.
-         Rigidity: Bowers, Bowers, Lutz 2026 "Rigidity of circle polyhedra
-         and hyperideal polyhedra: the tangency case" (arXiv:2601.22903)
+         Rigidity: Bowers, Bowers, Lutz 2026 "Rigidity of Koebe Polyhedra
+         and Inversive Distance Circle Packings" (arXiv:2601.22903)
         — theoretical uniqueness backing the KAT construction.
       → ElectrostaticSphereFunctional (127 lines) — sphere
         distribution baseline.
@@ -560,3 +577,102 @@ All three items are tracked here so the project memory is preserved;
 none of them are roadmap commitments.  See `research-track.md` for the
 formal research-versus-port classification before starting any.
 ```
+
+---
+
+## ◼ Phase 12 — Decorated DCE & geometric transition  (RESEARCH, near-term)
+
+> **Note on ordering:** despite the higher number, Phase 12 is *near-term
+> and independent* of Phases 9c–11.  It builds ONLY on already-landed code
+> and is the **short path (Chain A)** to a first Lutz-adjacent scientific
+> result.  It does **not** require the genus-g≥2 chain (9c/10a/10b/10c) or
+> the holonomy-bug fix — those gate Phase 13 (Chain B), not this.
+
+```
+12   Decorated DCE & geometric transition  (no Java parent)
+       → Numerical demonstration of the Bobenko-Lutz "master theory":
+         one discrete conformal invariant, continuously deformable across
+         Euclidean / spherical / hyperbolic background geometry.
+       Mathematical reference:
+         Bobenko, Lutz 2025 "Decorated Discrete Conformal Equivalence in
+           Non-Euclidean Geometries" (Discrete & Comput. Geom.;
+           arXiv:2310.17529) §3 — Penner-coordinate decoration unifying the
+           three background geometries; continuous deformation at fixed
+           discrete conformal invariant.
+         Lutz 2024 PhD thesis (depositonce-20357) — full proofs.
+       Builds on (✅ already landed):
+         inversive_distance functional (9a.2), hyper_ideal (Springborn 2020),
+         spherical functional — the decoration is a RE-PARAMETRISATION of
+         these, not a new solver.
+       Does NOT require: 9c / 10a / 10b / holonomy-bug fix.
+       Scope:
+         1. Decoration layer: per-vertex circle/horocycle radius as Penner
+            coordinate; map ↔ existing inversive distance I_ij (classical
+            formula ℓ²=r_i²+r_j²+2r_ir_jη).
+         2. Transition driver: deform background curvature κ ∈ {+,0,−} while
+            holding the discrete conformal invariant fixed; solve per geometry.
+         3. Validation harness producing example galleries.
+       Acceptance criteria:
+         - Decoration round-trip I_ij ↔ (r_i,r_j,ℓ) at machine precision.
+         - At κ=0: bit-for-bit match with 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: one test surface solved in all three backgrounds
+           shares the invariant.
+       Effort: medium (functionals exist; reparametrisation + driver + tests).
+       Status: 🔲 planned (proposed 2026-05-29).
+```
+
+---
+
+## ◼ Phase 13 — Decorated canonical tessellations & polyhedral realisation  (Chain B capstone)
+
+> **This is the genus-g≥2 Lutz contribution.**  It sits ON TOP of the
+> infrastructure built by Phases 9c + 10a + 10b + 10c (see the 10c SCOPE
+> BOUNDARY note above) and implements Lutz's *specific* algorithms that the
+> 10c "runway" does not deliver by itself.
+
+```
+13   Decorated canonical tessellations + polyhedral realisation  (no Java parent)
+       → Canonical Delaunay tessellation of a decorated hyperbolic surface
+         in Penner coordinates, its dual decomposition, and the polyhedral
+         realisation of the uniformised genus-g≥2 surface.
+       Mathematical reference:
+         Lutz 2023 "Canonical Tessellations of Decorated Hyperbolic Surfaces"
+           (Geom. Dedicata 217; arXiv:2206.13461) — canonical (weighted-
+           Delaunay-analogue) tessellation + dual; Epstein-Penner convex-hull
+           construction in Minkowski space; Weeks-flip extension.
+         Bobenko, Lutz 2024 IMRN (arXiv:2305.10988) — discrete uniformization
+           theorem for decorated surfaces (cusps ↔ hyperideal vertices).
+         Lutz 2024 PhD thesis (depositonce-20357) — polyhedral realisation +
+           complete proofs for 9d.2 / 10b / 10c / 13.
+         Rigidity backing: Bowers, Bowers, Lutz 2026 (arXiv:2601.22903).
+       PREREQUISITES (the "given Voraussetzungen" — all must be in place):
+         ✅ cut_graph.hpp (2g seams)                — landed
+         🔲 Phase 9c  — 4g-gon fundamental domain
+         🔲 Phase 10a — holomorphic/harmonic 1-forms
+         🔲 Phase 10b — Siegel period matrix Ω ∈ H_g
+         🔲 Phase 10c — Fuchsian-group representation / H²/Γ embedding
+         🔲 holonomy-bug fix — detail::spherical_holonomy /
+              detail::hyperbolic_holonomy (+ cpp_dec_float_50 for the
+              group-relation product ∏gᵢ = Id); see research-track.md §9c.
+         🟡 Phase 12  — decoration layer (Penner coords) is reused here;
+              strongly recommended to land Phase 12 first so the Penner-
+              coordinate machinery already exists.
+       Scope:
+         1. Penner-coordinate weighted-Delaunay (canonical) tessellation +
+            dual decomposition on the H²/Γ embedding from 10c.
+         2. Epstein-Penner convex-hull construction (Minkowski space) to
+            obtain the canonical decomposition; Weeks-flip to reach it.
+         3. Polyhedral realisation of the uniformised surface.
+       Acceptance criteria:
+         - Canonical tessellation is unique & flip-stable (Weeks-flip
+           terminates; result independent of start triangulation).
+         - Decoration / Penner-coordinate consistency with Phase 12 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 (depends on the full 9c/10a/10b/10c chain landing
+         first; the Lutz algorithms themselves ≈ several weeks on top).
+       Status: 🔲 planned (Chain B capstone; gated on prerequisites above).
+```
--- a/doc/roadmap/research-track.md
+++ b/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.

 ---