diff --git a/lib/interscript/equivalence.rb b/lib/interscript/equivalence.rb
new file mode 100644
index 00000000..6fbcab68
--- /dev/null
+++ b/lib/interscript/equivalence.rb
@@ -0,0 +1,46 @@
+# frozen_string_literal: true
+
+module Interscript
+  # A3 (WO59): mechanical equivalence checking between two systems.
+  #
+  # Probes a sample set through both systems and reports the agreement
+  # ratio plus the minimal distinguishing samples. The sample set is
+  # caller-supplied or derived from the systems' own embedded tests.
+  class Equivalence
+    def self.check(first, second, samples:)
+      new(first, second).check(samples)
+    end
+
+    # Embedded test inputs of the given systems (the natural probe set
+    # for near-equivalent authorities).
+    def self.samples_from_tests(*codes)
+      codes.flat_map do |code|
+        Array(Interscript.parse(code).tests&.data).map(&:first).compact
+      end.uniq
+    end
+
+    def initialize(first, second)
+      @first = first
+      @second = second
+    end
+
+    def check(samples)
+      distinguishing = []
+      tested = 0
+      matched = 0
+      samples.each do |sample|
+        tested += 1
+        a = Interscript.transliterate(@first, sample)
+        b = Interscript.transliterate(@second, sample)
+        if a == b
+          matched += 1
+        else
+          distinguishing << { sample: sample, first: a, second: b }
+        end
+      end
+      ratio = tested.zero? ? 1.0 : matched.fdiv(tested)
+      { tested: tested, matched: matched, ratio: ratio,
+        distinguishing: distinguishing }
+    end
+  end
+end
diff --git a/spec/interscript/equivalence_spec.rb b/spec/interscript/equivalence_spec.rb
new file mode 100644
index 00000000..6263c0ee
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+++ b/spec/interscript/equivalence_spec.rb
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+# frozen_string_literal: true
+
+require "json"
+require "tmpdir"
+require "interscript/equivalence"
+
+RSpec.describe Interscript::Equivalence do
+  def write_map(dir, name, body)
+    path = File.join(dir, "#{name}.isc")
+    File.write(path, body)
+    path
+  end
+
+  def identical_pair(dir)
+    body = <<~ISC
+      system "TST:xx-Latn:Latn:1" {
+        metadata {
+          authority_id tst
+          id 1
+          language iso-639-2:xx
+          source_script Latn
+          destination_script Latn
+        }
+        tests { "ab" ->  "ab" }
+        stage main { parallel { sub "a" "a" } }
+      }
+    ISC
+    [write_map(dir, "tst-a-1", body), write_map(dir, "tst-b-1", body.gsub("tst-a-1", "tst-b-1"))]
+  end
+
+  it "reports full agreement for identical systems" do
+    Dir.mktmpdir do |dir|
+      a, b = identical_pair(dir)
+      Interscript.load_path.unshift(dir)
+      begin
+        result = described_class.check("tst-a-1", "tst-b-1", samples: ["ab", "abc", "b"])
+        expect(result[:ratio]).to eq(1.0)
+        expect(result[:distinguishing]).to be_empty
+      ensure
+        Interscript.load_path.delete(dir)
+      end
+    end
+  end
+
+  it "finds the minimal distinguishing sample for divergent systems" do
+    Dir.mktmpdir do |dir|
+      body_a = <<~ISC
+        system "TST:xx-Latn:Latn:1" {
+          metadata {
+            authority_id tst
+            id 1
+            language iso-639-2:xx
+            source_script Latn
+            destination_script Latn
+          }
+          stage main { parallel { sub "a" "x" } }
+        }
+      ISC
+      body_b = body_a.gsub('sub "a" "x"', 'sub "a" "y"').gsub("id 1", "id 2")
+      write_map(dir, "tst-c-1", body_a)
+      write_map(dir, "tst-c-2", body_b)
+      Interscript.load_path.unshift(dir)
+      begin
+        result = described_class.check("tst-c-1", "tst-c-2", samples: ["a", "b"])
+        expect(result[:ratio]).to eq(0.5)
+        expect(result[:distinguishing]).to eq([{ sample: "a", first: "x", second: "y" }])
+      ensure
+        Interscript.load_path.delete(dir)
+      end
+    end
+  end
+end
diff --git a/spec/isc/semantics_spec.rb b/spec/isc/semantics_spec.rb
new file mode 100644
index 00000000..fc01075d
--- /dev/null
+++ b/spec/isc/semantics_spec.rb
@@ -0,0 +1,58 @@
+# frozen_string_literal: true
+
+# WO80/A4 — normative rulings for the ISC semantic surface. Each vector
+# pins the reference behavior; IS-1 v2 documents these as normative
+# sections (the spec text accretes one section per ruled point).
+
+require "tmpdir"
+
+RSpec.describe "ISC semantics — parallel composition" do
+  def with_map(name, body)
+    dir = Dir.mktmpdir
+    File.write(File.join(dir, name), body)
+    Interscript.load_path.unshift(dir)
+    yield
+  ensure
+    Interscript.load_path.delete(dir) if dir
+  end
+
+  it "rules: a parallel block is single-pass longest-match" do
+    with_map("tst-long-1.isc", <<~ISC) do
+      system "TST:xx-Latn:Latn:1" {
+        metadata {
+          authority_id tst
+          id 1
+          language iso-639-2:xx
+          source_script Latn
+          destination_script Latn
+        }
+        stage main { parallel {
+          sub "b" "Y"
+          sub "ab" "X"
+        } }
+      }
+    ISC
+      expect(Interscript.transliterate("tst-long-1", "ab")).to eq("X")
+    end
+  end
+
+  it "rules: duplicate rules in a parallel resolve last-declared-wins" do
+    with_map("tst-tie-1.isc", <<~ISC) do
+      system "TST:xx-Latn:Latn:2" {
+        metadata {
+          authority_id tst
+          id 2
+          language iso-639-2:xx
+          source_script Latn
+          destination_script Latn
+        }
+        stage main { parallel {
+          sub "a" "1"
+          sub "a" "2"
+        } }
+      }
+    ISC
+      expect(Interscript.transliterate("tst-tie-1", "a")).to eq("2")
+    end
+  end
+end