fix(agents): a session file whose startedAt is no finite time is live (Issue #31, Mac review)

float("NaN") and a JSON NaN passed the old check, and every comparison with
NaN is false, so a live holder looked like a reused pid: the in-use gate let
the purge through and the session file was taken as stale. startedAt must
now be an int or float (not bool), finite and positive; anything else cannot
be told and counts as live. A dead pid is still stale whatever it says.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/test_issue31_purge_residual.py

@@ -447,6 +447,33 @@ def test_session_file_liveness_fails_safe(monkeypatch, live):
     assert claude_mod._session_file_live({"startedAt": hour_ago}, live.pid) is True, "ps unavailable: live"
 
 
+@pytest.mark.parametrize("started", ["NaN", float("nan"), float("inf"), float("-inf"), "inf", "1760000000000",
+                                     "soon", True, False, None, [1], "<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}
+    assert claude_mod._session_file_live(data, live.pid) is True
+    assert claude_mod._session_file_live(data, _dead_pid()) is False, "a dead pid holds nothing"
+
+
+@pytest.mark.parametrize("raw", ["NaN", '"NaN"', "Infinity", "true"])
+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."""
+    ws = tmp_path / "ws"
+    ws.mkdir()
+    sfile, key = _session_file(home / ".claude", live.pid, conv)
+    sfile.write_text(f'{{"pid": {live.pid}, "sessionId": "{conv}", "cwd": "/x", "startedAt": {raw}}}')
+    adapter = get_adapter("claude")
+    ctx = _ctx(ws, home)
+
+    assert adapter.conversation_in_use(conv, ctx) is True
+    res = _agents_cli(["in-use", "claude", conv, str(ws)], ws)
+    assert res.returncode == 4, res.stdout + res.stderr
+    assert adapter.purge_artifacts(conv, ctx) == []
+    assert sfile.exists() and key.exists()
+
+
 def test_claude_purge_takes_the_stale_key_with_its_session_file(home, tmp_path, conv, other, live):
     ws = tmp_path / "ws"
     ws.mkdir()