diff --git a/.agents/skills/lib_py/agents/adapters/claude.py b/.agents/skills/lib_py/agents/adapters/claude.py
index 50e092d..bf74770 100644
--- a/.agents/skills/lib_py/agents/adapters/claude.py
+++ b/.agents/skills/lib_py/agents/adapters/claude.py
@@ -78,12 +78,17 @@ def _session_file_live(data: dict, pid) -> bool:
     except OSError:
         pass
     # startedAt is epoch ms: a finite positive number. A bool, a string, NaN
-    # (every comparison with it is false) or an infinity is no time at all.
+    # (every comparison with it is false), an infinity or an int too large
+    # for a float is no time at all.
     started = data.get("startedAt")
-    if isinstance(started, bool) or not isinstance(started, (int, float)) \
-            or not math.isfinite(started) or started <= 0:
+    if isinstance(started, bool) or not isinstance(started, (int, float)):
+        return True
+    try:
+        started = float(started) / 1000.0
+    except OverflowError:
+        return True
+    if not math.isfinite(started) or started <= 0:
         return True
-    started = started / 1000.0
     # lstart in UTC: a local time is ambiguous in the hour a DST change repeats.
     try:
         out = subprocess.run(["ps", "-p", str(pid), "-o", "lstart="], capture_output=True, text=True,
diff --git a/tests/test_issue31_purge_residual.py b/tests/test_issue31_purge_residual.py
index 5e48604..da964b0 100644
--- a/tests/test_issue31_purge_residual.py
+++ b/tests/test_issue31_purge_residual.py
@@ -472,7 +472,8 @@ def test_liveness_reads_lstart_as_utc(tmp_path, monkeypatch, live):
 
 
 @pytest.mark.parametrize("started", ["NaN", float("nan"), float("inf"), float("-inf"), "inf", "1760000000000",
-                                     "soon", True, False, None, [1], "<missing>"])
+                                     "soon", True, False, None, [1], pytest.param(10 ** 400, id="10**400"),
+                                     "<missing>"])
 def test_an_unusable_started_at_means_live(live, started):
     from lib_py.agents.adapters import claude as claude_mod
     data = {} if started == "<missing>" else {"startedAt": started}
@@ -480,10 +481,12 @@ def test_an_unusable_started_at_means_live(live, started):
     assert claude_mod._session_file_live(data, _dead_pid()) is False, "a dead pid holds nothing"
 
 
-@pytest.mark.parametrize("raw", ["NaN", '"NaN"', "Infinity", "true"])
+@pytest.mark.parametrize("raw", ["NaN", '"NaN"', "Infinity", "true",
+                                 pytest.param("1" + "0" * 400, id="10**400")])
 def test_a_live_holder_with_an_unusable_started_at_blocks_the_purge(home, tmp_path, conv, live, raw):
     """json.load turns a bare NaN or Infinity into a float that every
-    comparison fails, which once made a live holder look stale."""
+    comparison fails, which once made a live holder look stale, and a huge
+    integer into an int no float can hold."""
     ws = tmp_path / "ws"
     ws.mkdir()
     sfile, key = _session_file(home / ".claude", live.pid, conv)