diff --git a/tests/test_vault_recall_rust_parity.py b/tests/test_vault_recall_rust_parity.py
new file mode 100644
index 00000000..8c574ce4
--- /dev/null
+++ b/tests/test_vault_recall_rust_parity.py
@@ -0,0 +1,103 @@
+"""ADR-0020 first-surface parity gate — vault_recall Python ⇔ Rust.
+
+The Rust backend (`CORE_BACKEND=rust`) must produce bit-identical
+results to the Python vectorised path on the same input.  This
+test runs the same fixture under both backends in subprocesses
+(so the backend env var is honoured at module import) and
+asserts:
+
+  - per-versor scores are exactly equal (float32 bit-identity)
+  - top-k ordering matches, including ascending-index tie-break
+
+If this test ever fails, the Rust path has diverged from the
+Python source-of-truth path.  Fix the Rust kernel, not the test.
+The Python path is the canonical implementation per CLAUDE.md
+sequencing rule 5.
+
+Test is skipped at collection time if the `core_rs` extension is
+not importable.
+"""
+
+from __future__ import annotations
+
+import json
+import os
+import subprocess
+import sys
+from pathlib import Path
+
+import pytest
+
+REPO = Path(__file__).resolve().parent.parent
+
+try:
+    import core_rs  # noqa: F401
+
+    _RUST_AVAILABLE = True
+except ImportError:
+    _RUST_AVAILABLE = False
+
+
+SCRIPT = r"""
+import json, os, sys
+import numpy as np
+sys.path.insert(0, "__REPO__")
+from algebra.backend import using_rust, vault_recall
+
+rng = np.random.default_rng(int(os.environ["FIXTURE_SEED"]))
+n = int(os.environ["FIXTURE_N"])
+top_k = int(os.environ["FIXTURE_TOPK"])
+versors = [rng.standard_normal(32).astype(np.float32) for _ in range(n)]
+q = rng.standard_normal(32).astype(np.float32)
+result = vault_recall(versors, q, top_k=top_k)
+
+# Encode scores as raw float32 bytes (hex) to preserve bit-identity
+# through JSON.
+encoded = [(i, np.float32(s).tobytes().hex()) for i, s in result]
+print(json.dumps({"using_rust": using_rust(), "result": encoded}))
+"""
+
+
+def _run_backend(backend: str, seed: int, n: int, top_k: int) -> dict:
+    env = os.environ.copy()
+    if backend == "rust":
+        env["CORE_BACKEND"] = "rust"
+    else:
+        env.pop("CORE_BACKEND", None)
+    env["FIXTURE_SEED"] = str(seed)
+    env["FIXTURE_N"] = str(n)
+    env["FIXTURE_TOPK"] = str(top_k)
+    script = SCRIPT.replace("__REPO__", str(REPO))
+    out = subprocess.check_output(
+        [sys.executable, "-c", script],
+        env=env,
+        cwd=str(REPO),
+        text=True,
+    )
+    return json.loads(out.strip().splitlines()[-1])
+
+
+@pytest.mark.skipif(not _RUST_AVAILABLE, reason="core_rs extension not built")
+@pytest.mark.parametrize("seed,n,top_k", [
+    (0xC07E, 200, 200),
+    (0xBEEF, 137, 50),
+    (0x1234, 500, 10),
+    (0xFACE, 50, 5),
+])
+def test_vault_recall_python_rust_bit_identity(seed: int, n: int, top_k: int) -> None:
+    py = _run_backend("python", seed, n, top_k)
+    rs = _run_backend("rust", seed, n, top_k)
+
+    assert py["using_rust"] is False, "Python subprocess should not load Rust backend"
+    assert rs["using_rust"] is True, "Rust subprocess should load Rust backend"
+
+    assert len(py["result"]) == len(rs["result"]) == min(top_k, n)
+
+    # Bit-identity on scores (hex-encoded f32 bytes) and ordering on
+    # indices (including ascending-index tie-break).
+    for (py_i, py_hex), (rs_i, rs_hex) in zip(py["result"], rs["result"]):
+        assert py_i == rs_i, f"top-k order divergence: python={py_i} rust={rs_i}"
+        assert py_hex == rs_hex, (
+            f"score bit-identity broken at index {py_i}: "
+            f"python={py_hex} rust={rs_hex}"
+        )