Polish web demo tests and refresh notebooks

- add README live-demo badge
- tighten engine validation for jump grids and detector indices
- replace flaky FastAPI TestClient web tests with direct handler tests
- remove unused httpx dev dependency
- clean stale frontend comments
- re-execute notebooks with clean sequential outputs

tests/test_webapp.py

@@ -1,36 +1,30 @@
-from fastapi.testclient import TestClient
+import pytest
+from pydantic import ValidationError
 
-from webapp.app import app
-
-
-client = TestClient(app)
+from webapp.app import SimulateRequest, app, health, simulate
 
 
 def test_health_endpoint():
-    response = client.get("/api/health")
-    assert response.status_code == 200
-    payload = response.json()
+    payload = health()
     assert payload["ok"] is True
     assert payload["version"] == "0.4.7"
 
 
 def test_simulation_endpoint_preserves_equal_budget():
-    response = client.post(
-        "/api/simulate",
-        json={
-            "rng_seed": 3,
-            "n_paths": 5,
-            "n_steps": 100,
-            "drop_fraction": 0.05,
-            "rise_fraction": 0.08,
-            "max_detection_lag_steps": 3,
-        },
+    payload = simulate(
+        SimulateRequest(
+            rng_seed=3,
+            n_paths=5,
+            n_steps=100,
+            drop_fraction=0.05,
+            rise_fraction=0.08,
+            max_detection_lag_steps=3,
+        )
     )
-    assert response.status_code == 200
-    payload = response.json()
     assert payload["adaptive_total_samples"] == payload["fixed_total_samples"]
     assert payload["max_detection_lag_steps"] == 3
 
+
 def test_webapp_imports_from_source_checkout_without_installed_package(tmp_path):
     """The documented direct uvicorn command must resolve the src-layout package."""
     import os
@@ -53,30 +47,32 @@ def test_webapp_imports_from_source_checkout_without_installed_package(tmp_path)
     assert "Adaptive Barrier Monitor" in completed.stdout
 
 
-
 def test_simulation_endpoint_supports_fixed_cadence():
-    response = client.post(
-        "/api/simulate",
-        json={
-            "rng_seed": 3,
-            "n_paths": 5,
-            "n_steps": 200,
-            "window_minutes": 200.0,
-            "dt_cap_minutes": 2.0,
-            "comparison_mode": "fixed_cadence",
-            "fixed_cadence_minutes": 20.0,
-        },
+    payload = simulate(
+        SimulateRequest(
+            rng_seed=3,
+            n_paths=5,
+            n_steps=200,
+            window_minutes=200.0,
+            dt_cap_minutes=2.0,
+            comparison_mode="fixed_cadence",
+            fixed_cadence_minutes=20.0,
+        )
     )
-    assert response.status_code == 200
-    payload = response.json()
     assert payload["comparison_mode"] == "fixed_cadence"
     assert payload["fixed_cadence_minutes"] == 20.0
     assert payload["adaptive_total_samples"] != payload["fixed_total_samples"]
 
 
 def test_simulation_endpoint_rejects_unknown_comparison_mode():
-    response = client.post(
-        "/api/simulate",
-        json={"comparison_mode": "unknown"},
-    )
-    assert response.status_code == 422
+    with pytest.raises(ValidationError):
+        SimulateRequest.model_validate({"comparison_mode": "unknown"})
+
+
+def test_app_registers_expected_routes():
+    route_methods = {
+        route.path: getattr(route, "methods", set())
+        for route in app.routes
+    }
+    assert "GET" in route_methods["/api/health"]
+    assert "POST" in route_methods["/api/simulate"]