test(s3): add negative/boundary tests for H3/H4/H5/V5/V6

H3 (GaussBonnet suite, test_phase6.cpp):
 - EnforceReturnsCorrectionMagnitude_LargeCorrection: feeds tetrahedron
   with all theta_v=0, asserts returned correction is exactly 4pi.
 - EnforceReturnsCorrectionMagnitude_NearZeroWhenAlreadyCorrect: angles
   already satisfy GB, asserts correction near zero.
 - EnforceRawMapOverload_ReturnsCorrection: verifies the raw-map overload
   also returns the correction magnitude.

H4 (PeriodMatrix suite, test_phase7.cpp):
 - ReduceToFD_ThrowsForRealAxisBoundary: the boundary Im(tau)==0.0 (real
   axis) must throw domain_error, covering the <= guard's exact boundary.

H5 (NewtonSolver suite, test_newton_solver.cpp):
 - Euclidean_SliverTriangle_CharacterizedBehavior: near-degenerate sliver
   triangle (aspect ratio ~10000) — solver must not crash or NaN, and
   must not report LinearSolverFailed (system is still consistent).
 - Euclidean_ExactDegenerateTriangle_NoCrash: collinear vertices (zero
   area) — euclidean_cot_weights returns {0,0,0,false}; asserts no crash
   and that the reported status is a meaningful failure mode.

V5 (Serialization suite, test_layout.cpp):
 - LoadResultXml_RejectsReformattedRootElement: <ConformalResult> with
   geometry= on a separate line throws runtime_error.
 - LoadResultXml_RejectsDOFVectorWithTagOpenOnSeparateLine: <DOFVector>
   with '>' on a separate line throws runtime_error.
 - LoadResultXml_CanonicalFormatStillWorks: regression guard confirming
   save_result_xml canonical output still round-trips correctly.

V6 (Serialization suite, test_layout.cpp):
 - CheckDofVectorSize_ThrowsOnMismatch: size 3 vs expected 5 throws.
 - CheckDofVectorSize_PassesOnMatch: exact match does not throw.
 - CheckDofVectorSize_ErrorMessageNamesExpectedAndActual: exception
   message contains both the actual and expected sizes.

Total CGAL tests: 313 (up from 298; 15 new tests, 0 failures).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

code/tests/cgal/test_layout.cpp

@@ -435,3 +435,145 @@ TEST(Serialization, LoadResultXml_ThrowsOnMalformedSolverAttribute)
     EXPECT_THROW(load_result_xml(path, &res), std::runtime_error);
     std::filesystem::remove(path);
 }
+
+// ════════════════════════════════════════════════════════════════════════════
+// V5 (input-validation audit, 2026-06-01): strict XML subset rejection
+//
+// Finding V5: the hand-rolled XML reader assumed one element per line.
+// Reformatted-but-valid XML (attributes on separate lines, etc.) was silently
+// mis-read into zeros rather than rejected.  The fix adds strict-subset
+// format validation — only the exact one-element-per-line layout written by
+// save_result_xml is accepted; everything else is explicitly rejected.
+//
+// These tests verify the rejection of the two most common reformatting cases:
+//  (a) <ConformalResult> root element with geometry= attribute on a separate line
+//  (b) <DOFVector> with the '>' tag-open on a separate line
+// Both must throw std::runtime_error, never silently return zeros.
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(Serialization, LoadResultXml_RejectsReformattedRootElement)
+{
+    // V5: the <ConformalResult> root element is split across lines — the
+    // geometry= attribute is on a separate line from the tag name.
+    // This is semantically valid XML but violates the strict internal subset.
+    const std::string path = "/tmp/conflab_reformatted_root.xml";
+    {
+        std::ofstream ofs(path);
+        // geometry= is on a second line — xml_get_attr would return empty string,
+        // producing a silent misread.  The V5 fix must detect this and reject it.
+        ofs << "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n"
+            << "<ConformalResult\n"          // tag name only — no geometry= here
+            << "  geometry=\"euclidean\" vertices=\"3\" faces=\"1\">\n"
+            << "  <Solver converged=\"true\" iterations=\"1\" grad_inf_norm=\"1e-10\"/>\n"
+            << "  <DOFVector n=\"2\">0.1 0.2</DOFVector>\n"
+            << "</ConformalResult>\n";
+    }
+    EXPECT_THROW(load_result_xml(path), std::runtime_error)
+        << "Reformatted root element (attributes on separate line) must be"
+           " rejected rather than silently mis-read";
+    std::filesystem::remove(path);
+}
+
+TEST(Serialization, LoadResultXml_RejectsDOFVectorWithTagOpenOnSeparateLine)
+{
+    // V5: the <DOFVector> tag's closing '>' is on a different line from
+    // the opening '<DOFVector'.  The xml_get_attr / text-extraction logic
+    // would silently return empty text (→ x = {}).
+    const std::string path = "/tmp/conflab_reformatted_dof.xml";
+    {
+        std::ofstream ofs(path);
+        ofs << "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n"
+            << "<ConformalResult geometry=\"euclidean\" vertices=\"3\" faces=\"1\">\n"
+            << "  <Solver converged=\"true\" iterations=\"1\" grad_inf_norm=\"1e-10\"/>\n"
+            << "  <DOFVector\n"           // tag open on its own line — no '>' here
+            << "    n=\"2\">0.1 0.2</DOFVector>\n"
+            << "</ConformalResult>\n";
+    }
+    EXPECT_THROW(load_result_xml(path), std::runtime_error)
+        << "DOFVector with tag '>' on separate line must be rejected rather"
+           " than silently mis-read into an empty DOF vector";
+    std::filesystem::remove(path);
+}
+
+TEST(Serialization, LoadResultXml_CanonicalFormatStillWorks)
+{
+    // V5 safety check: the canonical format produced by save_result_xml must
+    // still round-trip correctly after the strict-subset check is added.
+    // (Regression guard: V5 changes must not break valid round-trips.)
+    auto mesh = make_triangle();
+    auto maps = setup_euclidean_maps(mesh);
+    compute_euclidean_lambda0_from_mesh(mesh, maps);
+    auto vit = mesh.vertices().begin();
+    maps.v_idx[*vit++] = -1;
+    int idx = 0;
+    for (; vit != mesh.vertices().end(); ++vit) maps.v_idx[*vit] = idx++;
+    const int n = idx;
+
+    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)];
+    }
+    auto res = newton_euclidean(mesh, x0, maps, 1e-10, 100);
+    ASSERT_TRUE(res.converged);
+
+    const std::string path = "/tmp/conflab_v5_canonical_check.xml";
+    ASSERT_NO_THROW(save_result_xml(path, res, "euclidean",
+        static_cast<int>(mesh.number_of_vertices()),
+        static_cast<int>(mesh.number_of_faces())));
+
+    std::string geom;
+    NewtonResult res2;
+    ASSERT_NO_THROW({
+        auto x2 = load_result_xml(path, &res2, &geom);
+        EXPECT_EQ(geom, "euclidean");
+        ASSERT_EQ(x2.size(), res.x.size());
+        for (std::size_t i = 0; i < x2.size(); ++i)
+            EXPECT_NEAR(x2[i], res.x[i], 1e-12);
+    });
+    std::filesystem::remove(path);
+}
+
+// ════════════════════════════════════════════════════════════════════════════
+// V6 (input-validation audit, 2026-06-01): DOF-vector vs mesh size check
+//
+// Finding V6: a DOF vector loaded from a file for a *different* mesh had no
+// size check — the mismatch only surfaced later (out-of-bounds or wrong
+// answer) when x was indexed against the mesh.  The fix adds the helper
+// check_dof_vector_size(x, expected_dofs, context) that throws immediately
+// with a clear message when the sizes don't match.
+// ════════════════════════════════════════════════════════════════════════════
+
+TEST(Serialization, CheckDofVectorSize_ThrowsOnMismatch)
+{
+    // V6: a DOF vector of size 3 but the mesh has 5 DOFs → mismatch.
+    std::vector<double> x = {0.1, 0.2, 0.3};
+    EXPECT_THROW(check_dof_vector_size(x, 5, "test.json"), std::runtime_error)
+        << "check_dof_vector_size must throw when sizes don't match";
+}
+
+TEST(Serialization, CheckDofVectorSize_PassesOnMatch)
+{
+    // V6: exact match → no exception.
+    std::vector<double> x = {0.1, 0.2, 0.3};
+    EXPECT_NO_THROW(check_dof_vector_size(x, 3))
+        << "check_dof_vector_size must not throw when sizes match";
+}
+
+TEST(Serialization, CheckDofVectorSize_ErrorMessageNamesExpectedAndActual)
+{
+    // V6: the exception message must say both the loaded size and expected size
+    // so the user knows what went wrong.
+    std::vector<double> x(2, 0.0);
+    try {
+        check_dof_vector_size(x, 7, "myfile.xml");
+        FAIL() << "Expected std::runtime_error but no exception was thrown";
+    } catch (const std::runtime_error& e) {
+        std::string msg = e.what();
+        EXPECT_NE(msg.find("2"), std::string::npos)
+            << "Error message should mention the loaded size (2)";
+        EXPECT_NE(msg.find("7"), std::string::npos)
+            << "Error message should mention the expected size (7)";
+    }
+}