diff --git a/strategy/runner.py b/strategy/runner.py
index 5603ae4..1a4c253 100644
--- a/strategy/runner.py
+++ b/strategy/runner.py
@@ -7,6 +7,8 @@
 
 import os
 import time
+from numbers import Integral
+
 import numpy as np
 
 from .backend import Backend
@@ -51,6 +53,12 @@ def run(n: int, cfg: Config, fill: str = "lowrank", verify: bool = False,
     Default fill is 'lowrank' because that is the regime the strategy targets;
     verify (small n) reports the reconstruction error vs a float64 reference.
     """
+    # Reject a degenerate n before touching the GPU, mirroring matmul.runner.run:
+    # storage's block-size math divides by n, so n=0 raised ZeroDivisionError and
+    # n<0 a numpy "negative dimensions" error -- both only after a Backend (and a
+    # real GPU) had already been demanded.
+    if isinstance(n, bool) or not isinstance(n, Integral) or n < 1:
+        raise ValueError(f"n must be a positive integer, got {n!r}")
     backend = Backend(cfg.device, cfg.verbose)
     dt = cfg.np_dtype
     on_disk = storage.should_use_disk(
@@ -139,6 +147,8 @@ def compare(n: int, cfg: Config, fill: str = "lowrank",
             spectral_alpha: float = 1.0) -> dict:
     """Run the exact baseline and the subspace strategy on the SAME inputs and
     report time, throughput and the smart strategy's reconstruction error."""
+    if isinstance(n, bool) or not isinstance(n, Integral) or n < 1:
+        raise ValueError(f"n must be a positive integer, got {n!r}")
     backend = Backend(cfg.device, cfg.verbose)
     dt = cfg.np_dtype
     on_disk = storage.should_use_disk(
diff --git a/tests/test_runner_n_parity.py b/tests/test_runner_n_parity.py
new file mode 100644
index 0000000..ce5b225
--- /dev/null
+++ b/tests/test_runner_n_parity.py
@@ -0,0 +1,63 @@
+"""matmul and strategy must agree on the runner `n` boundary.
+
+The two packages are deliberately standalone copies of the same orchestration,
+so a boundary check added to one silently drifts out of the other. `matmul`
+rejected a degenerate n up front while `strategy` accepted it and only failed
+later -- after a Backend (a real GPU) had already been demanded, and then with
+a raw ZeroDivisionError from storage's `// (n * 8)` block-size math.
+
+These are parity tests: each public runner entry point is exercised through the
+SAME table, so the two packages cannot drift apart again. A stub Backend that
+raises on construction proves the check runs *before* any device work, which is
+what lets this run on CPU with no GPU/torch.
+"""
+from __future__ import annotations
+
+import pytest
+
+import matmul.runner as matmul_runner
+import strategy.runner as strategy_runner
+from matmul.config import Config as MatmulConfig
+from strategy.config import Config as StrategyConfig
+
+# n values that are not a positive integer. `True` is included because bool is a
+# subclass of int -- matmul.run(True) must not be read as n=1.
+BAD_N = (0, -1, 1.5, True)
+
+# (label, module, callable-name, config-factory) for every runner entry point.
+ENTRY_POINTS = [
+    ("matmul.run", matmul_runner, "run", lambda: MatmulConfig(verbose=False)),
+    ("strategy.run", strategy_runner, "run", lambda: StrategyConfig(verbose=False)),
+    ("strategy.compare", strategy_runner, "compare", lambda: StrategyConfig(verbose=False)),
+]
+
+
+class _ExplodingBackend:
+    """Stands in for Backend so any device work fails loudly instead of being
+    skipped for lack of a GPU."""
+
+    def __init__(self, *args, **kwargs):
+        raise AssertionError("n must be validated before Backend construction")
+
+
+@pytest.mark.parametrize("label,module,fn_name,make_cfg", ENTRY_POINTS,
+                         ids=[e[0] for e in ENTRY_POINTS])
+@pytest.mark.parametrize("n", BAD_N, ids=[repr(v) for v in BAD_N])
+def test_runner_rejects_bad_n_before_backend(monkeypatch, label, module, fn_name, make_cfg, n):
+    monkeypatch.setattr(module, "Backend", _ExplodingBackend)
+    with pytest.raises(ValueError, match="n must be a positive integer"):
+        getattr(module, fn_name)(n, make_cfg())
+
+
+@pytest.mark.parametrize("label,module,fn_name,make_cfg", ENTRY_POINTS,
+                         ids=[e[0] for e in ENTRY_POINTS])
+def test_runner_accepts_smallest_valid_n(monkeypatch, label, module, fn_name, make_cfg):
+    """n=1 is valid, so it must get past the check and reach Backend (our stub),
+    guarding the boundary against an off-by-one."""
+    monkeypatch.setattr(module, "Backend", _ExplodingBackend)
+    with pytest.raises(AssertionError, match="before Backend construction"):
+        getattr(module, fn_name)(1, make_cfg())
+
+
+if __name__ == "__main__":
+    raise SystemExit(pytest.main([__file__, "-q"]))