diff --git a/.github/workflows/solver-tests.yml b/.github/workflows/solver-tests.yml
new file mode 100644
index 0000000..dbfb0c7
--- /dev/null
+++ b/.github/workflows/solver-tests.yml
@@ -0,0 +1,29 @@
+name: Solver regression tests
+
+on:
+  push:
+    branches: [main]
+  pull_request:
+    branches: [main]
+
+permissions:
+  contents: read
+
+jobs:
+  tests:
+    name: Python ${{ matrix.python-version }}
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.11', '3.12']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+          cache: pip
+      - name: Install dependencies
+        run: python -m pip install -r requirements.txt
+      - name: Run solver regressions
+        run: python -m unittest discover -s tests -v
diff --git a/tests/test_solver.py b/tests/test_solver.py
new file mode 100644
index 0000000..26ef199
--- /dev/null
+++ b/tests/test_solver.py
@@ -0,0 +1,109 @@
+"""Regression tests for the signal-flow graph solver.
+
+Run from the repository root with: python -m unittest discover -s tests -v
+"""
+import unittest
+
+import sympy as sp
+
+from app import Connection, DiagramData, _delta_from_loops, solve_diagram, validate_diagram
+
+
+def diagram(edges, *, nodes=None, input_node="S", output_node="T"):
+    return DiagramData(
+        nodes=nodes if nodes is not None else ["S", "T"],
+        input_node=input_node,
+        output_node=output_node,
+        connections=[
+            Connection(id=f"edge-{index}", from_node=start, to_node=end, gain=gain)
+            for index, (start, end, gain) in enumerate(edges)
+        ],
+    )
+
+
+def assert_equivalent(testcase, actual, expected):
+    testcase.assertEqual(sp.simplify(sp.sympify(actual) - sp.sympify(expected)), 0)
+
+
+class SolverRegressionTests(unittest.TestCase):
+    def test_series_edges_multiply(self):
+        result = solve_diagram(
+            diagram(
+                [("S", "A", "G1"), ("A", "T", "G2")],
+                nodes=["S", "A", "T"],
+            )
+        )
+        self.assertEqual(result["status"], "success")
+        self.assertFalse(result["mason_mismatch"])
+        assert_equivalent(self, result["transfer_function_expr"], "G1*G2")
+        self.assertEqual(len(result["paths"]), 1)
+
+    def test_parallel_edges_add_instead_of_overwriting(self):
+        result = solve_diagram(
+            diagram([("S", "T", "G1"), ("S", "T", "G2")])
+        )
+        self.assertEqual(result["status"], "success")
+        self.assertFalse(result["mason_mismatch"])
+        assert_equivalent(self, result["transfer_function_expr"], "G1 + G2")
+        self.assertEqual(len(result["paths"]), 2)
+
+    def test_single_feedback_loop(self):
+        result = solve_diagram(
+            diagram(
+                [("S", "A", "G"), ("A", "T", "H"), ("A", "A", "K")],
+                nodes=["S", "A", "T"],
+            )
+        )
+        self.assertEqual(result["status"], "success")
+        self.assertFalse(result["mason_mismatch"])
+        assert_equivalent(self, result["transfer_function_expr"], "G*H/(1-K)")
+        self.assertEqual(len(result["loops"]), 1)
+
+    def test_disjoint_loops_produce_second_order_delta_term(self):
+        loops = [
+            {"nodes": {"A"}, "ordered_nodes": ["A"], "gain": sp.Symbol("L1"), "edge_ids": ["a"]},
+            {"nodes": {"B"}, "ordered_nodes": ["B"], "gain": sp.Symbol("L2"), "edge_ids": ["b"]},
+        ]
+        delta, non_touching = _delta_from_loops(loops)
+        assert_equivalent(self, str(delta), "(1-L1)*(1-L2)")
+        self.assertEqual(len(non_touching[2]), 1)
+        self.assertCountEqual(non_touching[2][0]["combo_edge_ids"], ["a", "b"])
+
+    def test_touching_loops_have_no_second_order_term(self):
+        loops = [
+            {"nodes": {"A", "B"}, "ordered_nodes": ["A", "B"], "gain": sp.Symbol("L1")},
+            {"nodes": {"B", "C"}, "ordered_nodes": ["B", "C"], "gain": sp.Symbol("L2")},
+        ]
+        delta, non_touching = _delta_from_loops(loops)
+        assert_equivalent(self, str(delta), "1-L1-L2")
+        self.assertEqual(non_touching, {})
+
+    def test_validate_rejects_duplicate_node_names(self):
+        result = validate_diagram(diagram([], nodes=["S", "T", "S"]))
+        self.assertEqual(result["status"], "error")
+        self.assertIn("duplicate_node_names", {e["type"] for e in result["errors"]})
+
+    def test_validate_rejects_empty_gain(self):
+        result = validate_diagram(diagram([("S", "T", "")]))
+        self.assertEqual(result["status"], "error")
+        self.assertIn("missing_gain", {e["type"] for e in result["errors"]})
+
+    def test_validate_rejects_missing_output_node(self):
+        result = validate_diagram(
+            diagram([("S", "A", "G")], nodes=["S", "A"], output_node="T")
+        )
+        self.assertEqual(result["status"], "error")
+        self.assertIn("missing_output_node", {e["type"] for e in result["errors"]})
+
+    def test_validate_reports_off_path_and_isolated_nodes(self):
+        result = validate_diagram(
+            diagram([("S", "T", "G")], nodes=["S", "T", "Z"])
+        )
+        self.assertEqual(result["status"], "success")
+        warning_types = {w["type"] for w in result["warnings"]}
+        self.assertIn("off_path_nodes", warning_types)
+        self.assertIn("isolated_nodes", warning_types)
+
+
+if __name__ == "__main__":
+    unittest.main()