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diff --git a/web/test/tab-badges.test.mjs b/web/test/tab-badges.test.mjs
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+++ b/web/test/tab-badges.test.mjs
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+// tab-badges.test.mjs — TDD tests for computeTabBadgeCounts
+//
+// Tests the pure function that computes badge counts for the
+// 'interrupted', 'ready', and 'running' tabs.
+//
+// Run with: node --test web/test/tab-badges.test.mjs
+
+import { describe, it } from 'node:test';
+import assert from 'node:assert/strict';
+
+// ── Inline implementation (will be replaced by import once exported) ───────────
+
+const INTERRUPTED_STATES = new Set(['CANCELLED', 'FAILED', 'BUDGET_EXCEEDED', 'BLOCKED']);
+
+function computeTabBadgeCounts(tasks) {
+  let interrupted = 0;
+  let ready = 0;
+  let running = 0;
+  for (const t of tasks) {
+    if (INTERRUPTED_STATES.has(t.state)) interrupted++;
+    if (t.state === 'READY') ready++;
+    if (t.state === 'RUNNING') running++;
+  }
+  return { interrupted, ready, running };
+}
+
+// ── Helpers ────────────────────────────────────────────────────────────────────
+
+function makeTask(state) {
+  return { id: state, name: `task-${state}`, state };
+}
+
+// ── Tests ──────────────────────────────────────────────────────────────────────
+
+describe('computeTabBadgeCounts', () => {
+  it('returns all zeros for empty task list', () => {
+    assert.deepEqual(computeTabBadgeCounts([]), { interrupted: 0, ready: 0, running: 0 });
+  });
+
+  it('counts RUNNING tasks', () => {
+    const tasks = [makeTask('RUNNING'), makeTask('RUNNING'), makeTask('QUEUED')];
+    const counts = computeTabBadgeCounts(tasks);
+    assert.equal(counts.running, 2);
+    assert.equal(counts.ready, 0);
+    assert.equal(counts.interrupted, 0);
+  });
+
+  it('counts READY tasks', () => {
+    const tasks = [makeTask('READY'), makeTask('READY'), makeTask('QUEUED')];
+    const counts = computeTabBadgeCounts(tasks);
+    assert.equal(counts.ready, 2);
+    assert.equal(counts.running, 0);
+    assert.equal(counts.interrupted, 0);
+  });
+
+  it('counts CANCELLED as interrupted', () => {
+    const counts = computeTabBadgeCounts([makeTask('CANCELLED')]);
+    assert.equal(counts.interrupted, 1);
+  });
+
+  it('counts FAILED as interrupted', () => {
+    const counts = computeTabBadgeCounts([makeTask('FAILED')]);
+    assert.equal(counts.interrupted, 1);
+  });
+
+  it('counts BUDGET_EXCEEDED as interrupted', () => {
+    const counts = computeTabBadgeCounts([makeTask('BUDGET_EXCEEDED')]);
+    assert.equal(counts.interrupted, 1);
+  });
+
+  it('counts BLOCKED as interrupted', () => {
+    const counts = computeTabBadgeCounts([makeTask('BLOCKED')]);
+    assert.equal(counts.interrupted, 1);
+  });
+
+  it('does not count COMPLETED as interrupted', () => {
+    const counts = computeTabBadgeCounts([makeTask('COMPLETED')]);
+    assert.equal(counts.interrupted, 0);
+  });
+
+  it('does not count TIMED_OUT as interrupted', () => {
+    const counts = computeTabBadgeCounts([makeTask('TIMED_OUT')]);
+    assert.equal(counts.interrupted, 0);
+  });
+
+  it('counts across multiple states simultaneously', () => {
+    const tasks = [
+      makeTask('RUNNING'),
+      makeTask('RUNNING'),
+      makeTask('READY'),
+      makeTask('CANCELLED'),
+      makeTask('FAILED'),
+      makeTask('BLOCKED'),
+      makeTask('QUEUED'),
+      makeTask('COMPLETED'),
+    ];
+    const counts = computeTabBadgeCounts(tasks);
+    assert.equal(counts.running, 2);
+    assert.equal(counts.ready, 1);
+    assert.equal(counts.interrupted, 3);
+  });
+
+  it('returns zero for a tab when no tasks match that state', () => {
+    const tasks = [makeTask('QUEUED'), makeTask('PENDING'), makeTask('COMPLETED')];
+    const counts = computeTabBadgeCounts(tasks);
+    assert.equal(counts.running, 0);
+    assert.equal(counts.ready, 0);
+    assert.equal(counts.interrupted, 0);
+  });
+});