diff --git a/src/equivalence.ts b/src/equivalence.ts
new file mode 100644
index 0000000..82bfdd5
--- /dev/null
+++ b/src/equivalence.ts
@@ -0,0 +1,46 @@
+// A3 (WO59): mechanical equivalence checking between two systems.
+//
+// Probes a sample set through both systems and reports the agreement
+// ratio plus the distinguishing samples. Mirrors the ruby
+// Interscript::Equivalence contract (ruby lib/interscript/equivalence.rb).
+
+import { transliterate } from "./index.js"
+
+export interface DistinguishingSample {
+  sample: string
+  first: string
+  second: string
+}
+
+export interface EquivalenceResult {
+  tested: number
+  matched: number
+  ratio: number
+  distinguishing: DistinguishingSample[]
+}
+
+export function checkEquivalence(
+  first: string,
+  second: string,
+  samples: string[],
+): EquivalenceResult {
+  let tested = 0
+  let matched = 0
+  const distinguishing: DistinguishingSample[] = []
+  for (const sample of samples) {
+    tested += 1
+    const a = transliterate(first, sample)
+    const b = transliterate(second, sample)
+    if (a === b) {
+      matched += 1
+    } else {
+      distinguishing.push({ sample, first: a, second: b })
+    }
+  }
+  return {
+    tested,
+    matched,
+    ratio: tested === 0 ? 1.0 : matched / tested,
+    distinguishing,
+  }
+}
diff --git a/test/equivalence.test.ts b/test/equivalence.test.ts
new file mode 100644
index 0000000..f6c5ac4
--- /dev/null
+++ b/test/equivalence.test.ts
@@ -0,0 +1,69 @@
+import { describe, it, expect, beforeEach } from "vitest"
+import { configure, transliterate } from "../src/index.js"
+import { iscBundledStrategy } from "../src/isc/loader.js"
+import { checkEquivalence } from "../src/equivalence.js"
+
+const A = `system "TSTA:xx-Latn:Latn:1" {
+  metadata {
+    authority_id tsta
+    id 1
+    language iso-639-2:xx
+    source_script Latn
+    destination_script Latn
+  }
+  stage main { parallel { sub { from "a" to "x" } } }
+}`
+const B = `system "TSTB:xx-Latn:Latn:2" {
+  metadata {
+    authority_id tstb
+    id 2
+    language iso-639-2:xx
+    source_script Latn
+    destination_script Latn
+  }
+  stage main { parallel { sub { from "a" to "y" } } }
+}`
+const B_EQUIV = `system "TSTB2:xx-Latn:Latn:3" {
+  metadata {
+    authority_id tstb2
+    id 3
+    language iso-639-2:xx
+    source_script Latn
+    destination_script Latn
+  }
+  stage main { parallel { sub { from "a" to "x" } } }
+}`
+
+describe("checkEquivalence (A3)", () => {
+  beforeEach(() => {
+    configure({
+      strategies: [iscBundledStrategy({ TSTA: A, TSTB: B, TSTB2: B_EQUIV })],
+    })
+  })
+
+  it("reports ratio 1 and no distinguishing samples for equivalent systems", () => {
+    const r = checkEquivalence("TSTA", "TSTB2", ["ba", "a", "zzz"])
+    expect(r.tested).toBe(3)
+    expect(r.matched).toBe(3)
+    expect(r.ratio).toBe(1)
+    expect(r.distinguishing).toEqual([])
+  })
+
+  it("collects the minimal distinguishing samples", () => {
+    const r = checkEquivalence("TSTA", "TSTB", ["zzz", "ba"])
+    expect(r.tested).toBe(2)
+    expect(r.matched).toBe(1)
+    expect(r.ratio).toBe(0.5)
+    expect(r.distinguishing).toEqual([{ sample: "ba", first: "bx", second: "by" }])
+  })
+
+  it("empty sample set is vacuously equivalent", () => {
+    const r = checkEquivalence("TSTA", "TSTB", [])
+    expect(r.tested).toBe(0)
+    expect(r.ratio).toBe(1)
+  })
+
+  it("transliterate works through the configured strategies", () => {
+    expect(transliterate("TSTA", "ba")).toBe("bx")
+  })
+})