diff --git a/plugins/spire/skills/gremlins/tests/test_gremlins.py b/plugins/spire/skills/gremlins/tests/test_gremlins.py
index e0dac0d..97c093e 100644
--- a/plugins/spire/skills/gremlins/tests/test_gremlins.py
+++ b/plugins/spire/skills/gremlins/tests/test_gremlins.py
@@ -1521,9 +1521,14 @@ class GateTests(Base):
 
     def test_closed_gate_on_existing_registry(self):
         """A1: a registry made with the gate open; with it closed, nothing launches and no job
-        entry is written; the tick launches no ping (it reads nothing)."""
-        code, out, _ = self.init()
-        self.assertEqual(code, 0, out)
+        entry is written; the tick launches no ping (it reads nothing).
+        The registry is made with the override env set, so the gate is open on any host (on a
+        supported one the env is ignored); the env is gone again before the gate is closed."""
+        with mock.patch.dict(os.environ, {gremlins.UNSUPPORTED_OK_ENV: "1"}):
+            self.assertIsNone(gremlins.platform_gate())
+            code, out, _ = self.init()
+            self.assertEqual(code, 0, out)
+        self.assertNotIn(gremlins.UNSUPPORTED_OK_ENV, os.environ)
         before = gremlins.read_registry(self.state)
         brief = os.path.join(self.tmp, "b.md")
         with open(brief, "w") as f:
@@ -3813,6 +3818,14 @@ class LaunchTests(LaunchBase):
         note = os.path.join(self.tmp, "delta-1.md")
         with open(note, "w", newline="\n") as f:
             f.write("NOTE-MARKER\n" + "d" * 60000 + "\n")
+        # `trained_at` has whole seconds, so a note written in the same second as a training's or
+        # a rebase's end would sit on either side of it by chance: B1's training is moved a minute
+        # back and the note half a minute back, so B1 predates the note and the rebase below
+        # (ending now or later) postdates it, on any host speed.
+        t_note = time.time() - 30
+        os.utime(note, (t_note, t_note))
+        self.set_registry(lambda reg: reg["bases"]["B1"].__setitem__("trained_at", gremlins._iso(t_note - 30)))
+        self.assertLess(gremlins._ts(self.reg()["bases"]["B1"]["trained_at"]), os.path.getmtime(note))
         out = self.fake_spawn("B1", "--delta-note", note, brief=named)
         self.assertEqual(len(out["reasons"]), 1, out)
         self.assertRegex(out["reasons"][0], r"^delta_tokens:\d+$")