diff --git a/src/kitchenbench/embodiment.py b/src/kitchenbench/embodiment.py
index a19e7c5..6f168f8 100644
--- a/src/kitchenbench/embodiment.py
+++ b/src/kitchenbench/embodiment.py
@@ -19,6 +19,8 @@
 
 from __future__ import annotations
 
+from typing import Any
+
 import numpy as np
 from inspect_robots import (
     Action,
@@ -149,7 +151,7 @@ def _observe(self) -> Observation:
             instruction=self._instruction,
         )
 
-    def _render(self) -> np.ndarray:
+    def _render(self) -> np.ndarray[Any, Any]:
         img = np.zeros((_IMG, _IMG, 3), dtype=np.uint8)
         filled = round(self._progress * _IMG)
         img[_IMG - filled :, :, 1] = 200  # a green progress bar rising from the bottom
diff --git a/src/kitchenbench/instances.py b/src/kitchenbench/instances.py
index 05fb15b..90fdcc5 100644
--- a/src/kitchenbench/instances.py
+++ b/src/kitchenbench/instances.py
@@ -15,7 +15,6 @@
 from __future__ import annotations
 
 from dataclasses import dataclass, field
-from typing import Any
 
 import numpy as np
 
@@ -206,7 +205,7 @@ class TaskInstance:
     setup: dict[str, Distribution]
     target_kind: str
     language_vars: tuple[str, ...] = ()
-    static: dict[str, Any] = field(default_factory=dict)
+    static: dict[str, Scalar] = field(default_factory=dict)  # hashable scalars only
     validation: Validation = field(default_factory=Validation)
     sim: SimSpec | None = None
 
diff --git a/tests/test_instances.py b/tests/test_instances.py
index fa34587..a01e79f 100644
--- a/tests/test_instances.py
+++ b/tests/test_instances.py
@@ -101,20 +101,28 @@ def test_validation_rejects_too_few_experts() -> None:
 def test_instances_and_realizations_are_hashable() -> None:
     from kitchenbench.specs import SPECS
 
-    inst = _instance()
-    # TaskInstance should be hashable
-    assert hash(inst) is not None
-    s_inst = {inst}
-    assert inst in s_inst
-
-    # Realization should be hashable
-    real = inst.realize(0)
-    assert hash(real) is not None
-    s_real = {real}
-    assert real in s_real
-
-    # TaskSpec should also be hashable
-    spec = SPECS[0]
-    assert hash(spec) is not None
-    s_spec = {spec}
-    assert spec in s_spec
+    # TaskInstance: equal objects must hash equal and support dict lookup
+    inst_a = _instance()
+    inst_b = _instance()
+    assert inst_a == inst_b
+    assert hash(inst_a) == hash(inst_b)
+    assert {inst_a: "x"}[inst_b] == "x"
+
+    # Realization: equal objects must hash equal and support dict lookup
+    real_a = inst_a.realize(0)
+    real_b = inst_b.realize(0)
+    assert real_a == real_b
+    assert hash(real_a) == hash(real_b)
+    assert {real_a: "y"}[real_b] == "y"
+
+    # TaskSpec: equal objects must hash equal and support dict lookup
+    spec_a = SPECS[0]
+    spec_b = SPECS[0]
+    assert spec_a == spec_b
+    assert hash(spec_a) == hash(spec_b)
+    assert {spec_a: "z"}[spec_b] == "z"
+
+    # Spec-wide invariant: every instance across SPECS must be hashable
+    for spec in SPECS:
+        for instance in spec.instances:
+            assert hash(instance) is not None