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diff --git a/web/test/task-card-di.test.mjs b/web/test/task-card-di.test.mjs
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+// task-card-di.test.mjs — Unit tests for the createTaskCard DI doc param,
+// log-tail placeholder (PENDING/QUEUED), and elapsed timer (RUNNING).
+//
+// Run with: node --test web/test/task-card-di.test.mjs
+
+import { describe, it } from 'node:test';
+import assert from 'node:assert/strict';
+import { createTaskCard } from '../app.js';
+
+// ── Mock DOM ───────────────────────────────────────────────────────────────────
+
+function makeEl(tag) {
+  return {
+    tag,
+    className: '',
+    textContent: '',
+    title: '',
+    hidden: false,
+    dataset: {},
+    children: [],
+    classList: { add() {} },
+    append(...nodes) {
+      for (const n of nodes) {
+        if (n != null && typeof n === 'object') this.children.push(n);
+      }
+    },
+    appendChild(child) {
+      if (child != null) this.children.push(child);
+      return child;
+    },
+    addEventListener() {},
+    setAttribute() {},
+    getAttribute() { return null; },
+  };
+}
+
+function makeDoc() {
+  return {
+    createElement(tag) { return makeEl(tag); },
+  };
+}
+
+// Depth-first search for first element with the given class name.
+function findByClass(el, cls) {
+  for (const child of el.children || []) {
+    if (typeof child.className === 'string' &&
+        child.className.split(' ').includes(cls)) return child;
+    const found = findByClass(child, cls);
+    if (found) return found;
+  }
+  return null;
+}
+
+// ── Tests: DI doc param ────────────────────────────────────────────────────────
+
+describe('createTaskCard doc DI param', () => {
+  it('accepts a custom doc and uses it for createElement', () => {
+    const created = [];
+    const doc = {
+      createElement(tag) {
+        const el = makeEl(tag);
+        created.push(tag);
+        return el;
+      },
+    };
+    createTaskCard({ id: 't1', state: 'QUEUED', name: 'Test Task' }, doc);
+    assert.ok(created.length > 0, 'doc.createElement should have been called');
+    assert.ok(created.includes('div'), 'should create at least one div');
+    assert.ok(created.includes('span'), 'should create at least one span');
+  });
+
+  it('returns a card element whose tag is div', () => {
+    const card = createTaskCard({ id: 't1', state: 'QUEUED', name: 'Test' }, makeDoc());
+    assert.equal(card.tag, 'div');
+    assert.equal(card.className, 'task-card');
+    assert.equal(card.dataset.taskId, 't1');
+  });
+});
+
+// ── Tests: log-tail placeholder (QUEUED) ──────────────────────────────────────
+
+describe('log-tail placeholder for queue column', () => {
+  it('QUEUED task has a task-log-placeholder element', () => {
+    const card = createTaskCard({ id: 't1', state: 'QUEUED', name: 'Test' }, makeDoc());
+    const placeholder = findByClass(card, 'task-log-placeholder');
+    assert.ok(placeholder, 'QUEUED card should have a task-log-placeholder element');
+  });
+
+  it('QUEUED task log-tail placeholder text is "Waiting to start\u2026"', () => {
+    const card = createTaskCard({ id: 't1', state: 'QUEUED', name: 'Test' }, makeDoc());
+    const placeholder = findByClass(card, 'task-log-placeholder');
+    assert.equal(placeholder.textContent, 'Waiting to start\u2026');
+  });
+
+  it('QUEUED task has a task-log-tail wrapper containing the placeholder', () => {
+    const card = createTaskCard({ id: 't1', state: 'QUEUED', name: 'Test' }, makeDoc());
+    const logTail = findByClass(card, 'task-log-tail');
+    assert.ok(logTail, 'QUEUED card should have a task-log-tail wrapper');
+    const placeholder = findByClass(logTail, 'task-log-placeholder');
+    assert.ok(placeholder, 'task-log-tail should contain task-log-placeholder');
+  });
+
+  it('RUNNING task does not have a task-log-placeholder', () => {
+    const card = createTaskCard({ id: 't1', state: 'RUNNING', name: 'Test' }, makeDoc());
+    const placeholder = findByClass(card, 'task-log-placeholder');
+    assert.equal(placeholder, null, 'RUNNING card should not have a task-log-placeholder');
+  });
+
+  it('COMPLETED task does not have a task-log-placeholder', () => {
+    const card = createTaskCard({ id: 't1', state: 'COMPLETED', name: 'Test' }, makeDoc());
+    const placeholder = findByClass(card, 'task-log-placeholder');
+    assert.equal(placeholder, null, 'COMPLETED card should not have a task-log-placeholder');
+  });
+});
+
+// ── Tests: elapsed timer (RUNNING) ────────────────────────────────────────────
+
+describe('elapsed timer for RUNNING tasks', () => {
+  it('RUNNING task has a running-elapsed span', () => {
+    const card = createTaskCard(
+      { id: 't1', state: 'RUNNING', name: 'Test', updated_at: '2024-01-01T00:00:00Z' },
+      makeDoc(),
+    );
+    const elapsed = findByClass(card, 'running-elapsed');
+    assert.ok(elapsed, 'RUNNING card should have a running-elapsed element');
+  });
+
+  it('RUNNING task running-elapsed has data-started-at from task.updated_at', () => {
+    const card = createTaskCard(
+      { id: 't1', state: 'RUNNING', name: 'Test', updated_at: '2024-06-15T12:00:00Z' },
+      makeDoc(),
+    );
+    const elapsed = findByClass(card, 'running-elapsed');
+    assert.equal(elapsed.dataset.startedAt, '2024-06-15T12:00:00Z');
+  });
+
+  it('RUNNING task running-elapsed data-started-at is empty string when updated_at is absent', () => {
+    const card = createTaskCard(
+      { id: 't1', state: 'RUNNING', name: 'Test' },
+      makeDoc(),
+    );
+    const elapsed = findByClass(card, 'running-elapsed');
+    assert.equal(elapsed.dataset.startedAt, '');
+  });
+
+  it('running-elapsed is inside the card header', () => {
+    const card = createTaskCard(
+      { id: 't1', state: 'RUNNING', name: 'Test', updated_at: '2024-01-01T00:00:00Z' },
+      makeDoc(),
+    );
+    // The header is the first child of the card (a div.task-card-header).
+    const header = findByClass(card, 'task-card-header');
+    assert.ok(header, 'card should have a task-card-header');
+    const elapsed = findByClass(header, 'running-elapsed');
+    assert.ok(elapsed, 'running-elapsed should be inside the task-card-header');
+  });
+
+  it('QUEUED task does not have a running-elapsed span', () => {
+    const card = createTaskCard({ id: 't1', state: 'QUEUED', name: 'Test' }, makeDoc());
+    const elapsed = findByClass(card, 'running-elapsed');
+    assert.equal(elapsed, null, 'QUEUED card should not have a running-elapsed element');
+  });
+
+  it('COMPLETED task does not have a running-elapsed span', () => {
+    const card = createTaskCard({ id: 't1', state: 'COMPLETED', name: 'Test' }, makeDoc());
+    const elapsed = findByClass(card, 'running-elapsed');
+    assert.equal(elapsed, null, 'COMPLETED card should not have a running-elapsed element');
+  });
+});