docs: record 2026-05-28 full-library scan findings in roadmap

Cross-referenced all 232 Java classes against the roadmap. New plan
entries for genuinely-useful, previously-unplanned items:
- 9g.1 conformal quality measures (Isothermicity, ConformalEquivalence,
  FlippedTriangles, LengthCrossRatio + ConvergenceUtility metrics)
- 9g.2 optional period-matrix convergence experiment (method only;
  Java harness depends on Mathematica/JLink + jReality, not ported)
- DEC operator layer (heds/dec/) noted as a 10a prerequisite
- HomotopyUtility -> 10a (explicit generator cycles; not covered by
  cut_graph.hpp, which yields only the 2g cut edges)
- SurfaceCurveUtility -> 9c; MercatorTextureProjection -> 9d.3 companion

Documented as deliberately out-of-scope: SpanningTreeUtility (subsumed
by cut_graph.hpp), convergence/* harness, datasource/* (jReality viewer
decoration), *Big arbitrary-precision geometry, jReality GUI, and the
MTJ/Tao/PETSc solver bindings.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

doc/roadmap/java-parity.md

@@ -58,6 +58,7 @@ They are candidates for Phase 9 or Phase 10.
 | `DiscreteHarmonicFormUtility` (657 lines) | Discrete harmonic 1-forms via cotangent Laplacian (Hodge theory) | 10a prerequisite |
 | `DiscreteHolomorphicFormUtility` (285 lines) | Holomorphic differentials via Mercat complex structure | 10a (Bobenko-Springborn 2004 §6) |
 | `CanonicalBasisUtility` (337 lines) | Symplectic homology basis with intersection-form normalisation | 10a prerequisite |
+| `HomotopyUtility` (57 lines) | Reconstructs explicit generator cycles (bridge + tree path) — NOT covered by `cut_graph.hpp` (which gives only the 2g cut edges). Verified 2026-05-28. | 10a |
 | `DiscreteRiemannUtility` (186 lines) | Period matrix τ, Siegel reduction (genus g) | 10b |
 | `DualityUtility` (308 lines), `HomologyUtility` (122 lines) | Primal/dual cohomology, cycle generators | 10a support |
 | `HyperbolicCyclicFunctional` (530 lines) | Discrete hyperbolic conformal energy (analogue of Euclidean) — completes the geometry suite | 10b–c |
@@ -66,10 +67,30 @@ They are candidates for Phase 9 or Phase 10.
 | `StereographicUnwrapper` (266 lines) | Stereographic projection S²→ℂ + Möbius centring — converts the Spherical-DCE output into a 2-D atlas | 10b' (Sphere visualisation) |
 | `CircleDomainUnwrapper` (570 lines) | Conformal map of a multiply-connected planar region onto a disk-with-holes — classical complex-analysis use case | 11+ (new use-case class) |
 | `ElectrostaticSphereFunctional`, `MobiusCenteringFunctional` | Sphere-domain pre-processing functionals | 10c (optional) |
+| `IsothermicityMeasure` (113), `DiscreteConformalEquivalencemMeasure` (82), `FlippedTriangles` (17), `LengthCrossRatio` (12) | Quantitative conformal-quality / embedding-validity measures (math is GUI-independent) | **9g** (added 2026-05-28) |
+| `DEC`, `AbstractDECOperator`, `DECPairing`, `DualChain`, `DualForm` (`heds/dec/`) | Discrete-exterior-calculus operator layer (d / ⋆ / pairing) — foundation the Phase-10a form utilities sit on | **10a prerequisite** (added 2026-05-28) |
+| `SurfaceCurveUtility` (360) | Curve operations on the surface (cut-path tracing) — supports 9c polygon construction | **9c** (added 2026-05-28) |
 
 Note: items marked as *new research* (e.g. Inversive Distance, HyperIdeal Hessian variants)
 are tracked separately in `doc/roadmap/research-track.md`.
 
+### 2026-05-28 scan — valuable items that had been in *no* phase
+
+A class-by-class cross-reference of all 232 Java production classes against the
+roadmap found that the "big math" (Schottky 11a, Koebe 10c′/10f, quasi-isothermic
+10e, circle-pattern layout 9e) is all already planned.  Three genuinely useful
+items were unrecorded and have now been added above:
+1. **Conformal-quality measures** → new **Phase 9g** (small, no dependencies; raises
+   validation coverage for the already-shipped pipeline).
+2. **DEC operator layer** (`heds/dec/`) → noted as a **Phase 10a prerequisite** (the
+   form utilities assume these primitives exist).
+3. **`SurfaceCurveUtility`** → folded into the **Phase 9c** source list.
+
+Everything else unmentioned is intentionally out of scope: the `plugin/*` jReality
+Swing GUI, the `MTJ*`/`Tao*`/`*PETSc` solver bindings (replaced by Eigen), the
+convergence/`*Series` test harness, and the `*Big` arbitrary-precision geometry
+(`P2Big`/`PnBig`/`RnBig` — deliberately dropped in favour of `Simple_cartesian<double>`).
+
 ---
 
 ## Java packages not yet in the roadmap — 2026 full-library scan
@@ -154,6 +175,9 @@ Entirely absent from the current roadmap.
 | `EuclideanUnwrapperPETSc` / `SphericalNormalizerPETSc` | PETSc solver binding — replaced by Eigen |
 | `Search` | CoHDS-specific graph search — replaced by CGAL halfedge iteration |
 | `SparseUtility` | Colt sparse matrix utils — replaced by Eigen |
+| `SpanningTreeUtility` | Primal + dual spanning tree — already implemented inline in `cut_graph.hpp` (tree-cotree Steps 1+2). Verified 2026-05-28. |
+| `convergence/*` harness (CLI driver, ~1400 lines) | The driver depends on Mathematica (JLink) + jReality OBJ reader + LoopLinear. Do not port the harness — only its math: quality measures → 9g.1, study method → 9g.2 (optional). Verified 2026-05-28. |
+| `datasource/*` (`ConicalEdgesDataSource`, `CylinderEdgesDataSource`) | jReality SceneGraph viewer decoration (draws cone/cylinder edge arcs) — NOT example geometry; nothing to harvest. Verified 2026-05-28. |
 
 ---
 

doc/roadmap/phases.md

@@ -124,6 +124,10 @@ mesh type.
          Java sources: FundamentalPolygonUtility.java (698 lines)
                      + CanonicalFormUtility.java (532 lines)
                      + CuttingUtility / SurgeryUtility (~800 lines)
+                     + SurfaceCurveUtility.java (360 lines, 2026-05-28
+                       scan) — curve operations on the surface (cut-path
+                       tracing / fundamental-domain boundary); supporting
+                       infrastructure for the polygon construction.
          Mathematical source: Poincaré 1882 + Sechelmann 2016 §5
          Research component: bridging to conformallab++ cut_graph.hpp
                              + holonomy infrastructure.
@@ -164,6 +168,15 @@ mesh type.
          Stereographic projection S²→ℂ∪{∞} + Möbius centering for
          genus-0 surfaces. Converts spherical DCE output to a flat 2-D atlas.
          Java reference: unwrapper/StereographicUnwrapper.java (266 lines)
+         Note (2026-05-28 visualisation scan): plugin/algorithm/
+           StereographicTextureProjection.java (88 lines) is the texture
+           front-end of this same math — no separate item.  The supporting
+           math/CP1 + ComplexUtility.stereographic are deliberately NOT
+           ported (redundant with std::complex + the existing MobiusMap,
+           see porting-status.md).
+         Optional companion: MercatorTextureProjection.java (47 lines) —
+           a distinct cylindrical conformal display projection; small
+           nice-to-have for the sphere-visualisation bucket, not required.
 
 9d.4   MobiusCenteringFunctional  (Java port, optional upgrade)
          → integrate into layout.hpp normalise_hyperbolic()
@@ -210,6 +223,59 @@ mesh type.
                   Replaces euclidean_hessian.hpp for non-triangular inputs.
          Status: 🔲 planned (pure research, no Java source)
          Effort: medium (~2 weeks core + tests; +1 week Newton integration).
+
+9g — Conformal quality measures  (Java port — 2026-05-28 scan)
+──────────────────────────────────────────────────────────────────
+
+9g.1   Quantitative correctness metrics for a computed conformal map
+         → conformal_quality.hpp
+         Lifts the measure math out of the jReality plugin + convergence
+         layers (the math is GUI-independent).  High value / low effort:
+         these directly strengthen the validation story for the already-
+         shipped genus-0/1 pipeline (doc/math/validation.md).
+         - IsothermicityMeasure        (113 lines) — pointwise deviation
+           from conformality (anisotropy of the induced metric).
+         - DiscreteConformalEquivalencemMeasure (82 lines) — per-edge
+           length-cross-ratio residual vs. the conformal-equivalence
+           condition.
+         - FlippedTriangles            (17 lines)  — detects inverted /
+           degenerate triangles in a 2-D layout (embedding-validity check).
+         - LengthCrossRatio            (12 lines)  — the discrete conformal
+           invariant itself (per-edge), shared input for the two measures.
+         - ConvergenceUtility measures (~110 lines, math/float only — no
+           Mathematica/jReality deps): getMaxMeanSumCrossRatio
+           (q=(a·c)/(b·d), qfun=(q+1/q)/2−1), getMaxMeanSumMultiRatio
+           (per-face product, =1 iff conformal), and
+           getMaxMeanSumScaleInvariantCircumRadius (R/√A, scale-invariant
+           mesh-quality).  The operational counterpart of LengthCrossRatio.
+         Java references:
+           plugin/visualizer/IsothermicityMeasure.java
+           plugin/visualizer/DiscreteConformalEquivalencemMeasure.java
+           plugin/visualizer/FlippedTriangles.java
+           heds/adapter/types/LengthCrossRatio.java
+           convergence/ConvergenceUtility.java
+         Mathematical reference: Springborn-Schröder-Pinkall 2008
+           (length cross-ratio = discrete conformal invariant).
+         Status: 🔲 planned (Java port; no new theory).
+         Effort: small (~3 days incl. gradient-free tests).  No
+                 dependencies — can land before 9a–9f.
+
+9g.2   Period-matrix convergence study  (validation experiment — optional)
+         → tests/cgal/test_period_matrix_convergence.cpp (experiment, not
+           a library feature)
+         Empirical validation for the already-shipped period_matrix.hpp +
+         discrete_elliptic_utility.hpp: generate a genus-1 elliptic mesh
+         with a known analytic τ, then refine / subdivide / add Gaussian
+         vertex noise and plot |τ_computed − τ_expected| → 0.
+         Java reference: convergence/* (~1400 lines) — a CLI harness
+           (joptsimple) that drives the same study.  Do NOT port the
+           harness: it depends on Mathematica via JLink and on jReality's
+           OBJ reader + LoopLinear subdivision.  Port only the *method*:
+           - subdivision  → igl::loop (libigl already available)
+           - noise        → trivial (vᵢ += σ·N(0,1))
+           - error metric → the 9g.1 quality measures + τ residual
+         Status: 🔲 optional (raises empirical confidence in genus-1 τ;
+           no new library surface).  Effort: small (~2–3 days).
 ```
 
 ---
@@ -332,10 +398,21 @@ Phase 10   Global uniformization for genus g ≥ 2
        Java sources (partial, port-with-research):
          CanonicalBasisUtility.java        337 lines  (homology basis)
          HomologyUtility.java              122 lines
+         HomotopyUtility.java               57 lines  (2026-05-28 scan) —
+           reconstructs the explicit generator *cycles* (bridge edge +
+           tree path via HomologyUtility.findCycle).  NOT covered by
+           cut_graph.hpp, which yields only the 2g cut *edges*; the closed
+           loops are needed to integrate 1-forms along b-cycles.
          DualityUtility.java               308 lines
          DiscreteHarmonicFormUtility.java  657 lines
          DiscreteHolomorphicFormUtility.java 285 lines
-       Effort: ~6 weeks net (4 utility ports + 1 integration).
+       Prerequisite — DEC operator layer (2026-05-28 scan, previously
+         unrecorded): the four utilities above are built on the discrete-
+         exterior-calculus primitives in heds/dec/ (DEC.java 76 lines,
+         AbstractDECOperator, DECPairing, DualChain, DualForm — the d / ⋆ /
+         primal-dual pairing operators).  Port this thin operator layer
+         first; the form utilities assume it exists.  Effort: ~3 days.
+       Effort: ~6 weeks net (1 DEC layer + 4 utility ports + 1 integration).
 
 10b  Siegel period matrix Ω ∈ H_g  (g×g complex symmetric, Im(Ω) > 0)
        → Ωᵢⱼ = ∫_{bⱼ} ωᵢ