feat: Problems correlation fingerprint, count, last_seen (d1-2)

- Migration 003; windowed host+type+rule correlation on ingest

- GET /problems filters; GET /problems/{id} with event timeline; ack/resolve 409 guard

- Tests and SAC_PROBLEM_CORRELATION_WINDOW_MINUTES config

Co-authored-by: Cursor <cursoragent@cursor.com>

backend/tests/test_problems.py

@@ -0,0 +1,69 @@
+"""Problems correlation and API smoke tests."""
+
+import uuid
+from datetime import datetime, timezone
+
+from tests.test_ingest import VALID_EVENT
+
+
+def _event_payload(**overrides):
+    now = datetime.now(timezone.utc).astimezone().isoformat(timespec="seconds")
+    base = {
+        **VALID_EVENT,
+        "event_id": str(uuid.uuid4()),
+        "occurred_at": now,
+        "severity": "high",
+        "type": "ssh.ip.banned",
+        "title": "Ban test",
+        "summary": "test problem correlation",
+    }
+    base.update(overrides)
+    return base
+
+
+def test_problem_correlates_two_events(client, auth_headers, jwt_headers):
+    e1 = _event_payload()
+    e2 = _event_payload(title="Ban test 2")
+    assert client.post("/api/v1/events", json=e1, headers=auth_headers).status_code == 201
+    assert client.post("/api/v1/events", json=e2, headers=auth_headers).status_code == 201
+
+    r = client.get("/api/v1/problems?status=open", headers=jwt_headers)
+    assert r.status_code == 200
+    data = r.json()
+    assert data["total"] == 1
+    problem = data["items"][0]
+    assert problem["event_count"] == 2
+    assert problem["fingerprint"].startswith("h")
+    assert ":tssh.ip.banned:" in problem["fingerprint"]
+
+    detail = client.get(f"/api/v1/problems/{problem['id']}", headers=jwt_headers)
+    assert detail.status_code == 200
+    assert len(detail.json()["events"]) == 2
+
+
+def test_problem_ack_and_resolve(client, auth_headers, jwt_headers):
+    payload = _event_payload()
+    client.post("/api/v1/events", json=payload, headers=auth_headers)
+    pid = client.get("/api/v1/problems?status=open", headers=jwt_headers).json()["items"][0]["id"]
+
+    ack = client.post(f"/api/v1/problems/{pid}/ack", headers=jwt_headers)
+    assert ack.status_code == 200
+    assert ack.json()["status"] == "acknowledged"
+
+    res = client.post(f"/api/v1/problems/{pid}/resolve", headers=jwt_headers)
+    assert res.status_code == 200
+    assert res.json()["status"] == "resolved"
+
+
+def test_new_problem_after_resolve(client, auth_headers, jwt_headers):
+    p1 = _event_payload()
+    client.post("/api/v1/events", json=p1, headers=auth_headers)
+    pid = client.get("/api/v1/problems?status=open", headers=jwt_headers).json()["items"][0]["id"]
+    client.post(f"/api/v1/problems/{pid}/resolve", headers=jwt_headers)
+
+    p2 = _event_payload(summary="after resolve")
+    client.post("/api/v1/events", json=p2, headers=auth_headers)
+    open_items = client.get("/api/v1/problems?status=open", headers=jwt_headers).json()["items"]
+    assert len(open_items) == 1
+    assert open_items[0]["event_count"] == 1
+    assert open_items[0]["id"] != pid