fix(coverage+validation): C2/C3 script gate, V1/V2/V4 JSON/XML errors, I2/I3/I4 tests

C2: Fix coverage.sh — remove || true from lcov capture/extract steps so real
    lcov failures are visible; empty coverage.info now exits with code 3.
C3: Add coverage gate to quality-gates CI job (SKIP_COVERAGE_GATE=1 ramp-up
    mode until I5 is resolved — fast suite covers ~9.6% not 80%). Thresholds:
    80% line / 70% branch / 90% function (agreed 2026-05-31).

V1: Wrap JSON parse + field extraction in try/catch — nlohmann parse_error and
    type_error now surface as std::runtime_error with the file path.
V2: Wrap stoi/stod in XML Solver parser — missing/non-numeric attributes throw
    std::runtime_error instead of leaking std::invalid_argument.
V4: Validate required JSON keys (dof_vector, solver, solver.*) before access —
    missing field produces a clear named-field error message.

I2: 6 serialization negative tests (missing file, malformed JSON, missing
    dof_vector, missing solver block, missing XML file, non-numeric XML attr).
I3: load_mesh throws on non-triangulated (quad) mesh — covers the
    is_triangle_mesh guard that was previously untested.
I4: spherical_hessian throws on edge DOFs — covers the logic_error guard.

290/290 tests pass (+8 new).

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

.gitea/workflows/cpp-tests.yml

@@ -160,9 +160,18 @@ jobs:
       - name: shellcheck (scripts/**/*.sh, severity=warning, strict)
         run: bash scripts/quality/shellcheck.sh --strict
 
+      - name: Install lcov (coverage gate)
+        run: apt-get install -y --no-install-recommends lcov
+
+      - name: Coverage gate (fast-test suite, ramp-up mode)
+        # SKIP_COVERAGE_GATE=1: reports numbers but does not fail on threshold.
+        # Remove once I5 is resolved (coverage is wired to the full CGAL suite,
+        # not just the 26 fast tests).  Threshold: 80% line / 70% branch / 90% func.
+        run: SKIP_COVERAGE_GATE=1 bash scripts/quality/coverage.sh
+
       - name: Summary
         if: always()
         run: |
-          echo "QUALITY ▸ all four gates passed."
+          echo "QUALITY ▸ all gates passed."
           echo "  see scripts/quality/README.md for the full catalogue"
-          echo "  (sanitizers, clang-tidy, coverage, etc. are local-only)"
+          echo "  (sanitizers, clang-tidy, coverage report in build-coverage/)"