diff --git a/apps/api/src/services/governance_agent.py b/apps/api/src/services/governance_agent.py
index 24ea676e..9e2596bf 100644
--- a/apps/api/src/services/governance_agent.py
+++ b/apps/api/src/services/governance_agent.py
@@ -399,6 +399,7 @@ class GovernanceAgent:
         2026-04-27 P3.4 by Claude — AI SLO（ADR-100）
         """
         import httpx
+        import math
 
         from src.core.config import settings
 
@@ -457,6 +458,21 @@ class GovernanceAgent:
                             )
                             continue
                         value = float(result_list[0]["value"][1])
+                        if not math.isfinite(value):
+                            results[name] = {
+                                "name": name,
+                                "status": "skipped",
+                                "error": "non_finite_value",
+                                "reason": "prometheus_nan_or_inf",
+                                "hint": "SLO 分母目前沒有足夠事件，等待下一個有效樣本再評估",
+                            }
+                            logger.warning(
+                                "governance_slo_non_finite",
+                                slo=name,
+                                query=query,
+                                value=str(result_list[0]["value"][1]),
+                            )
+                            continue
                         threshold = hard_red_lines[name]
                         target = slo_targets[name]
                         violated = value < threshold
diff --git a/apps/api/tests/test_governance_agent.py b/apps/api/tests/test_governance_agent.py
index e84c0fdb..d345a402 100644
--- a/apps/api/tests/test_governance_agent.py
+++ b/apps/api/tests/test_governance_agent.py
@@ -23,13 +23,6 @@ import pytest
 
 from src.services.governance_agent import (
     GovernanceAgent,
-    get_governance_agent,
-    reset_governance_agent,
-    run_governance_loop,
-    EXECUTION_FAIL_RATE_THRESHOLD,
-    HALLUCINATION_RATE_THRESHOLD,
-    KM_STALE_RATIO,
-    TRUST_DRIFT_THRESHOLD,
 )
 
 
@@ -645,3 +638,48 @@ class TestRunSelfCheckGlobalFailureAlert:
 
         calls = [c[0][0] for c in alerter.alert_governance.call_args_list]
         assert "governance_self_failure" not in calls
+
+
+class _FakePrometheusResponse:
+    def __init__(self, value: str) -> None:
+        self._value = value
+
+    def json(self) -> dict[str, Any]:
+        return {
+            "status": "success",
+            "data": {"result": [{"value": [1778756604, self._value]}]},
+        }
+
+
+class _FakePrometheusClient:
+    def __init__(self, value: str) -> None:
+        self._value = value
+
+    async def __aenter__(self):
+        return self
+
+    async def __aexit__(self, exc_type, exc, tb):
+        return False
+
+    async def get(self, *args, **kwargs):  # noqa: ANN002, ANN003
+        return _FakePrometheusResponse(self._value)
+
+
+class TestCheckSloCompliance:
+    @pytest.mark.asyncio
+    async def test_non_finite_prometheus_value_is_skipped_not_ok(self):
+        """Prometheus NaN 代表分母暫無有效事件，不可被治理層誤判為 ok."""
+        agent = _make_agent()
+
+        with patch("httpx.AsyncClient", return_value=_FakePrometheusClient("NaN")):
+            result = await agent.check_slo_compliance()
+
+        for name in (
+            "autonomy_rate",
+            "decision_accuracy",
+            "confidence_calibration",
+            "km_growth_rate",
+        ):
+            assert result[name]["status"] == "skipped"
+            assert result[name]["reason"] == "prometheus_nan_or_inf"
+        assert result["_meta"]["status"] == "no_data"