diff --git a/src/torchsim/model/_signal.py b/src/torchsim/model/_signal.py
index 023014ad..45a275a8 100644
--- a/src/torchsim/model/_signal.py
+++ b/src/torchsim/model/_signal.py
@@ -36,6 +36,7 @@
 
 __all__ = ["_SignalModel"]
 
+import numbers
 from abc import ABC, abstractmethod
 from collections.abc import Mapping, Sequence
 from copy import copy as shallow_copy
@@ -298,8 +299,22 @@ def _shaped(self, signal: torch.Tensor, batch: tuple[int, ...]) -> torch.Tensor:
 
 
 def _moved(values: Mapping[str, Any], device: torch.device) -> dict[str, Any]:
-    """The mapping with every tensor in it on ``device``, the rest untouched."""
-    return {
-        name: value.to(device) if torch.is_tensor(value) else value
-        for name, value in values.items()
-    }
+    """The mapping with every array in it on ``device``, the rest untouched.
+
+    Off the host, a list or tuple of numbers arrives as the tensor
+    :func:`as_torch` makes of it; on the host it stays as the caller wrote it.
+    """
+    return {name: _on(value, device) for name, value in values.items()}
+
+
+def _on(value: Any, device: torch.device) -> Any:
+    if torch.is_tensor(value):
+        return value.to(device)
+    numbers_given = (
+        isinstance(value, (list, tuple))
+        and len(value) > 0
+        and all(isinstance(entry, numbers.Real) for entry in value)
+    )
+    if numbers_given and device.type != "cpu":
+        return as_torch(value).to(device)
+    return value
diff --git a/tests/recon/test_operator.py b/tests/recon/test_operator.py
index bb36521d..0c42ffa5 100644
--- a/tests/recon/test_operator.py
+++ b/tests/recon/test_operator.py
@@ -283,6 +283,20 @@ def test_a_policy_changes_where_the_work_runs_and_nothing_else(
         torch.testing.assert_close(theirs, ours, atol=1e-5, rtol=1e-5)
 
 
+@pytest.mark.parametrize("echo_times", [TE_MS.tolist(), tuple(TE_MS.tolist())])
+def test_maps_on_a_card_meet_echo_times_written_as_numbers_there(echo_times) -> None:
+    """A protocol given as plain numbers travels to the card with the maps."""
+    if not torch.cuda.is_available():
+        pytest.skip("CUDA is unavailable")
+    operator = ModelOperator(MultiEchoSimulator(TE=echo_times), "T2", bounds=BOUND)
+    x = operator.initial((7,), T2=80.0)
+
+    there = operator.A(x.cuda())
+
+    assert there.device.type == "cuda"
+    torch.testing.assert_close(there.cpu(), operator.A(x), atol=1e-5, rtol=1e-5)
+
+
 def test_streaming_a_volume_too_big_for_the_budget(operator) -> None:
     """The chunking is the policy's, and the seams do not show."""
     x = operator.initial((20_000,), T2=80.0)