test(euclidean): Tier-1 circular-edge φ cross-validation + cyclic-solve blocker

Build-verified attempt to port the Java EuclideanCyclicConvergenceTest
(cathead, "circular hole edge" φ = π−0.1).

- ✅ GREEN `CyclicCircularEdge_PhiEntersGradient_CatHead`: solver-free
  cross-validation that the circular-edge φ target enters the cyclic edge
  gradient exactly (ΔG_e = −Δφ_e at 1e-12; no other component moves).
- ⏸️ DISABLED `CyclicCircularEdge_CatHead_JavaXVal`: the full Java convergence
  assertion (α_opp+α_opp = π−0.1), kept with golden semantics. Auto-activates
  once the edge-DOF Hessian lands.

Build-verification finding: `newton_euclidean` -> `euclidean_hessian` throws
"edge DOFs are not supported" — the cyclic full solve is blocked by a missing
edge-DOF Euclidean Hessian (gradient supports edge DOFs, analytic Hessian does
not). Spherical convergence (Tier-1 #2) is already covered by test_newton_solver.
Documented in doc/reviewer/java-ignore-crossvalidation.md.

All 13 EuclideanFunctional tests pass (1 disabled).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

code/tests/cgal/test_euclidean_functional.cpp

@@ -27,9 +27,12 @@
 #include "euclidean_functional.hpp"
 #include "euclidean_hessian.hpp"
 #include "clausen.hpp"
+#include "mesh_io.hpp"
+#include "newton_solver.hpp"
 #include <gtest/gtest.h>
 #include <cmath>
 #include <vector>
+#include <string>
 
 using namespace conformallab;
 
@@ -405,3 +408,148 @@ TEST(EuclideanGoldenJava, FullMeshGradientAndEnergy_Tetrahedron)
                     - euclidean_energy(mesh, x0, maps);
     EXPECT_NEAR(dE, 0.15962619236187336, 1e-12);
 }
+
+// ════════════════════════════════════════════════════════════════════════════
+// Java cross-validation (Tier 1, GREEN) — circular-edge φ wiring (no solver)
+//
+// The "circular hole edge" of EuclideanCyclicConvergenceTest works by setting a
+// non-default edge turn angle φ_e. Since the cyclic edge gradient is exactly
+//     G_e = α_opp(f⁺) + α_opp(f⁻) − φ_e,
+// lowering φ_e by 0.1 must raise G_e by exactly 0.1 — independent of geometry —
+// and must leave every other gradient component untouched. This pins the φ
+// wiring without needing the (not-yet-implemented) edge-DOF Hessian, so it runs
+// today and is the evaluation-level prerequisite of the DISABLED convergence
+// test below.
+// ════════════════════════════════════════════════════════════════════════════
+TEST(EuclideanFunctional, CyclicCircularEdge_PhiEntersGradient_CatHead)
+{
+    const std::string path = std::string(CONFORMALLAB_DATA_DIR) + "/obj/cathead.obj";
+    ConformalMesh mesh;
+    ASSERT_NO_THROW(mesh = load_mesh(path)) << "cathead.obj not found: " << path;
+
+    auto maps = setup_euclidean_maps(mesh);
+    compute_euclidean_lambda0_from_mesh(mesh, maps);
+
+    int idx = 0;
+    for (auto v : mesh.vertices())
+        maps.v_idx[v] = mesh.is_border(v) ? -1 : idx++;
+    for (auto e : mesh.edges())
+        maps.e_idx[e] = idx++;
+    const int n = idx;
+    ASSERT_GT(n, 0);
+
+    Edge_index e_circ{};
+    bool found = false;
+    for (auto e : mesh.edges()) {
+        auto h  = mesh.halfedge(e);
+        auto ho = mesh.opposite(h);
+        if (mesh.is_border(h) || mesh.is_border(ho)) continue;
+        e_circ = e; found = true; break;
+    }
+    ASSERT_TRUE(found) << "no interior edge found on cathead";
+    const std::size_t ie = static_cast<std::size_t>(maps.e_idx[e_circ]);
+
+    std::vector<double> x(static_cast<std::size_t>(n), 0.0);
+
+    maps.phi_e[e_circ] = PI;
+    auto G1 = euclidean_gradient(mesh, x, maps);
+    maps.phi_e[e_circ] = PI - 0.1;
+    auto G2 = euclidean_gradient(mesh, x, maps);
+
+    // Lowering φ_e by 0.1 raises exactly this edge's gradient component by 0.1.
+    EXPECT_NEAR(0.1, G2[ie] - G1[ie], 1e-12)
+        << "circular-edge φ target not wired into the cyclic gradient";
+
+    // No other gradient component changes.
+    double max_other = 0.0;
+    for (std::size_t k = 0; k < G1.size(); ++k)
+        if (k != ie) max_other = std::max(max_other, std::abs(G2[k] - G1[k]));
+    EXPECT_LT(max_other, 1e-12)
+        << "changing one φ_e perturbed unrelated gradient components";
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// Java cross-validation (Tier 1) — EuclideanCyclicConvergenceTest
+//
+// Ports de.varylab.discreteconformal.functional.EuclideanCyclicConvergenceTest:
+// prescribe a non-default edge turn angle φ = π − 0.1 on one interior edge of
+// cathead.obj ("circular hole edge"), solve the cyclic Euclidean functional
+// (vertex + edge DOFs), then assert the realised opposite-corner-angle sum
+// across that edge equals π − 0.1.
+//
+// The C++ edge gradient is  G_e = α_opp(f⁺) + α_opp(f⁻) − φ_e, so at the
+// solution (G_e = 0) the geometric angle sum equals φ_e — exactly the Java
+// assertion `circularEdge.getAlpha() + opposite.getAlpha() == π − 0.1`.
+//
+// "Natural targets" first make x = 0 the equilibrium (so the *only* deviation
+// is the prescribed φ); the test therefore FAILS if the solver ignores a
+// non-default φ (the sum would stay at its natural value, not π − 0.1).
+//
+// ⚠️ DISABLED (build-verified 2026-05-29): blocked by a missing feature, not a
+// bug. `newton_euclidean` uses `euclidean_hessian`, which throws
+//     "euclidean_hessian: edge DOFs are not supported
+//      (only the vertex-block cotangent Laplacian is implemented)".
+// The cyclic functional needs vertex+edge DOFs, so the full Newton solve is not
+// yet possible in C++ (the gradient supports edge DOFs; the analytic Hessian
+// does not). PREREQUISITE: edge-DOF Euclidean Hessian — see
+// `doc/roadmap/research-track.md` and `doc/reviewer/java-ignore-crossvalidation.md`.
+// The golden semantics (φ = π−0.1 ⇒ realised α_opp+α_opp = π−0.1) are kept here
+// so this test auto-activates once that Hessian lands; just drop the DISABLED_.
+// ════════════════════════════════════════════════════════════════════════════
+TEST(EuclideanFunctional, DISABLED_CyclicCircularEdge_CatHead_JavaXVal)
+{
+    const std::string path = std::string(CONFORMALLAB_DATA_DIR) + "/obj/cathead.obj";
+    ConformalMesh mesh;
+    ASSERT_NO_THROW(mesh = load_mesh(path)) << "cathead.obj not found: " << path;
+
+    auto maps = setup_euclidean_maps(mesh);
+    compute_euclidean_lambda0_from_mesh(mesh, maps);
+
+    // Cyclic DOFs: interior vertices (border pinned) + all edges.
+    int idx = 0;
+    for (auto v : mesh.vertices())
+        maps.v_idx[v] = mesh.is_border(v) ? -1 : idx++;
+    for (auto e : mesh.edges())
+        maps.e_idx[e] = idx++;
+    const int n = idx;
+    ASSERT_GT(n, 0);
+
+    // Natural targets: set Θ_v / φ_e so that x = 0 is the equilibrium (G(0)=0).
+    std::vector<double> x0(static_cast<std::size_t>(n), 0.0);
+    auto G0 = euclidean_gradient(mesh, x0, maps);
+    for (auto v : mesh.vertices()) {
+        int iv = maps.v_idx[v];
+        if (iv >= 0) maps.theta_v[v] -= G0[static_cast<std::size_t>(iv)];
+    }
+    for (auto e : mesh.edges()) {
+        int ie = maps.e_idx[e];
+        if (ie >= 0) maps.phi_e[e] += G0[static_cast<std::size_t>(ie)];
+    }
+
+    // Pick one interior edge: both incident faces present, both endpoints interior.
+    Edge_index circular{};
+    bool found = false;
+    for (auto e : mesh.edges()) {
+        auto h  = mesh.halfedge(e);
+        auto ho = mesh.opposite(h);
+        if (mesh.is_border(h) || mesh.is_border(ho)) continue;
+        if (mesh.is_border(mesh.source(h)) || mesh.is_border(mesh.target(h))) continue;
+        circular = e; found = true; break;
+    }
+    ASSERT_TRUE(found) << "no interior edge found on cathead";
+    const std::size_t ie = static_cast<std::size_t>(maps.e_idx[circular]);
+
+    // Prescribe the circular edge turn angle φ = π − 0.1 (Java CustomEdgeInfo.phi).
+    const double phi_target = PI - 0.1;
+    maps.phi_e[circular] = phi_target;
+
+    auto res = newton_euclidean(mesh, x0, maps, /*tol=*/1e-11, /*max_iter=*/200);
+    ASSERT_TRUE(res.converged)
+        << "Newton did not converge; ||G||=" << res.grad_inf_norm;
+
+    // Realised geometric opposite-corner-angle sum = φ_e + G_e(x*)  (= α_opp+α_opp).
+    auto Gf = euclidean_gradient(mesh, res.x, maps);
+    const double realised = maps.phi_e[circular] + Gf[ie];
+    EXPECT_NEAR(phi_target, realised, 1e-9)
+        << "prescribed circular edge turn angle π−0.1 not realised at the solution";
+}

doc/reviewer/java-ignore-crossvalidation.md

@@ -93,6 +93,69 @@ Assertion strategy: because the values are symmetric per DOF-class, assert
 
 ---
 
+## 3b — Effort-adjusted tiering (2026-05-29 inventory)
+
+> A broader scan (not just `@Ignore`d tests) revealed that the §3 ranking was
+> **effort-blind**: cheaper, equally-valuable oracles exist than the Lawson
+> generator. Re-tiered by **value / cost**:
+
+| Tier | Oracle | Mesh / asset | Solver | Golden | C++ status | Cost |
+|---|---|---|---|---|---|---|
+| **1** | `EuclideanCyclicConvergenceTest` | `cathead.obj` *(already in C++)* | MTJ BiCGstab (no PETSc) | `α_opp+α_opp = π−0.1` @1e-12 (per-edge φ target) | `euclidean_functional` ✅, `phi_e` ✅, cathead ✅ | **near-zero** |
+| **1** | `SphericalConvergenceTest` | octahedron | MTJ Newton (no PETSc) | self-consistency (const. curvature) | spherical ✅, `make_octahedron_face` ✅ | low |
+| **2** | Wente genus-1 uniformization | `wente_torus02.obj` + `wente_uniformization.xml` | — (stored result) | exact `IsometryPSL2R` uniformizing-group generators | holonomy/`MobiusMap` ✅; **needs XML reader** | medium |
+| **2** | `regular_uniformization.xml` | (stored) | — | uniformization data | needs XML reader | medium |
+| **3** | HyperIdeal Lawson convergence (3 golden vectors) | combinatorial `createLawsonSquareTiled` | — (hard-coded u\*) | symmetric u\* | needs **low-level half-edge generator** (§5) | high |
+| **4** | genus-2 (`genus2.xml`/`lawson2498.obj`), holomorphic forms (`HolomorphicEuclideanUniformization_*.xml`), Schottky (`genus2.xml`), hyperelliptic | assets present in Java | — | various | Phases 10a/10c/11/13 | future |
+
+**Key correction:** the Lawson generator (originally flagged HIGH) is actually
+**Tier 3** — higher effort than Tier 1/2. Cheapest first wins:
+
+1. **Tier 1 — `EuclideanCyclicConvergenceTest` on cathead** (asset already
+   present; the C++ edge gradient `G_e = α_opp(f⁺)+α_opp(f⁻) − φ_e` makes the
+   Java assertion `α_opp+α_opp = π−0.1` exactly the converged `G_e = 0`
+   condition with `phi_e = π−0.1`). Fails if the solver ignores a non-default
+   `φ`, so it is a genuine check, not a tautology.
+2. **Tier 1 — `SphericalConvergenceTest`** on the octahedron.
+3. **Tier 2 — Wente genus-1 uniformization** (needs a small `UniformizationData`
+   XML reader; strongest deterministic pipeline oracle that maps to landed C++).
+4. **Tier 3 — Lawson generator** (only after Tiers 1–2).
+
+### Build-verification finding (2026-05-29) — Tier 1 cyclic is blocked
+
+Attempting the Tier-1 `EuclideanCyclicConvergenceTest` port **build-verified** a
+blocker: `newton_euclidean` calls `euclidean_hessian`, which throws
+*"edge DOFs are not supported (only the vertex-block cotangent Laplacian is
+implemented)"*. The cyclic functional needs **vertex + edge** DOFs, so the full
+Newton solve is **not yet possible** in C++ — the *gradient* supports edge DOFs,
+the *analytic Hessian* does not. (This is also why PR #27 cross-validated only
+the cyclic *evaluation*, never a solve.)
+
+**Landed in this PR instead** (`test_euclidean_functional.cpp`):
+- ✅ `CyclicCircularEdge_PhiEntersGradient_CatHead` (**GREEN**) — solver-free
+  cross-validation that the circular-edge φ target enters the cyclic gradient
+  exactly (`ΔG_e = −Δφ_e` at 1e-12, no other component moves). This is the
+  evaluation-level prerequisite of the convergence oracle.
+- ⏸️ `DISABLED_CyclicCircularEdge_CatHead_JavaXVal` — the full Java convergence
+  assertion (`α_opp+α_opp = π−0.1`), kept in-code with the golden semantics; it
+  auto-activates (drop `DISABLED_`) once the edge-DOF Hessian lands.
+
+**New prerequisite for Tier-1 cyclic:** an **edge-DOF Euclidean Hessian** (the
+cyclic Hessian over vertex + edge variables, cf. Java `getNonZeroPattern`). Spherical
+convergence (Tier-1 #2) turned out to be **already covered** by
+`test_newton_solver` (`Spherical_ConvergesFromPerturbation` et al. on the
+spherical tetrahedron), and `make_octahedron_face()` is a single face, not a
+closed octahedron — so Tier-1 #2 adds little. → the next genuinely-new
+cross-validation target is **Tier 2 (Wente uniformization XML)** or implementing
+the edge-DOF Hessian to unblock the cyclic convergence oracle.
+
+### Other generators in the Java tree
+`HyperellipticCurveGenerator` (→ Phase 13), `SchottkyGenerator` (→ Phase 11a),
+`FunctionalTest.createOctahedron/createTetrahedron` (trivial — C++ has
+`make_octahedron_face` / `make_tetrahedron`).
+
+---
+
 ## 4 — Recommended order of work
 
 1. **Port `make_lawson_square_tiled()`** (low-level half-edge; see §5) →