diff --git a/src/interscript/equivalence.py b/src/interscript/equivalence.py
new file mode 100644
index 0000000..d422ab8
--- /dev/null
+++ b/src/interscript/equivalence.py
@@ -0,0 +1,34 @@
+"""A3 (WO59): mechanical equivalence checking between two systems.
+
+Mirrors the ruby Interscript::Equivalence contract: probe a sample set
+through both systems, report the agreement ratio plus the distinguishing
+samples.
+"""
+
+from __future__ import annotations
+
+from .engine import Engine
+from .isc import isc_to_tree
+
+
+def check(first_source: str, second_source: str, samples: list[str]) -> dict:
+    first = Engine(isc_to_tree(first_source))
+    second = Engine(isc_to_tree(second_source))
+    distinguishing = []
+    tested = 0
+    matched = 0
+    for sample in samples:
+        tested += 1
+        a = first.transliterate(sample)
+        b = second.transliterate(sample)
+        if a == b:
+            matched += 1
+        else:
+            distinguishing.append({"sample": sample, "first": a, "second": b})
+    ratio = 1.0 if tested == 0 else matched / tested
+    return {
+        "tested": tested,
+        "matched": matched,
+        "ratio": ratio,
+        "distinguishing": distinguishing,
+    }
diff --git a/tests/test_equivalence.py b/tests/test_equivalence.py
new file mode 100644
index 0000000..6ce6ccf
--- /dev/null
+++ b/tests/test_equivalence.py
@@ -0,0 +1,48 @@
+import pytest
+
+from interscript.engine import Engine
+from interscript.equivalence import check
+from interscript.isc import isc_to_tree
+
+A = (
+    'system "TSTA:xx-Latn:Latn:1" {\n'
+    '  stage main { parallel {\n    sub "a" "x"\n  } }\n'
+    "}\n"
+)
+B = (
+    'system "TSTB:xx-Latn:Latn:2" {\n'
+    '  stage main { parallel {\n    sub "a" "y"\n  } }\n'
+    "}\n"
+)
+B_EQUIV = (
+    'system "TSTB2:xx-Latn:Latn:3" {\n'
+    '  stage main { parallel {\n    sub "a" "x"\n  } }\n'
+    "}\n"
+)
+
+
+def test_equivalent_systems_report_ratio_one():
+    r = check(A, B_EQUIV, ["ba", "a", "zzz"])
+    assert r["tested"] == 3
+    assert r["matched"] == 3
+    assert r["ratio"] == 1.0
+    assert r["distinguishing"] == []
+
+
+def test_distinguishing_samples_are_collected():
+    r = check(A, B, ["zzz", "ba"])
+    assert r["tested"] == 2
+    assert r["matched"] == 1
+    assert r["ratio"] == 0.5
+    assert r["distinguishing"] == [
+        {"sample": "ba", "first": "bx", "second": "by"}
+    ]
+
+
+def test_empty_sample_set_is_vacuously_equivalent():
+    assert check(A, B, [])["ratio"] == 1.0
+
+
+@pytest.mark.parametrize("src", [A, B, B_EQUIV])
+def test_sources_parse(src):
+    Engine(isc_to_tree(src))