ui: declarative per-page tab titles via definePage title

tests/test-render-lifecycle.js

@@ -116,11 +116,12 @@ const flush = () => new Promise(r => setTimeout(r, 20));
  * loadCredentials: refreshing=true before the fetch, credentials=<new array>
  * and refreshing=false after — fresh values on every run).
  */
-function makePage(label, counters) {
+function makePage(label, counters, title) {
     const state = reactive({ loading: true, done: 0 });
     return {
         state,
         page: definePage({
+            title: title || undefined,
             init: () => state,
             async load(s) {
                 counters.loads++;
@@ -227,6 +228,62 @@ test('two #comp containers: updates in one root do not disturb the other', async
     assertEq(c.unmounts, 0, 'neither page unmounted');
 });
 
+/* ── Tab title (definePage `title`) ─────────────────────────── */
+
+test('mounting a titled page sets document.title', async () => {
+    const c = freshCounters();
+    const { page } = makePage('T', c, 'Titled - Vacuum Wall');
+    const main = new FakeEl('div');
+    document.title = 'base';
+    render(main, () => hComp(page, '/titled'));
+    await flush();
+    assertEq(document.title, 'Titled - Vacuum Wall', 'title applied on mount');
+});
+
+test('a page without a title leaves document.title untouched', async () => {
+    const c = freshCounters();
+    const { page } = makePage('U', c);
+    const main = new FakeEl('div');
+    document.title = 'unchanged';
+    render(main, () => hComp(page, '/untitled'));
+    await flush();
+    assertEq(document.title, 'unchanged', 'no title → document.title untouched');
+});
+
+test('navigation updates document.title; remount re-applies idempotently', async () => {
+    const c = freshCounters();
+    const a = makePage('A', c, 'Alpha - Vacuum Wall');
+    const b = makePage('B', c, 'Beta - Vacuum Wall');
+    const nav = reactive({ path: '/page-a' });
+    const main = new FakeEl('div');
+    render(main, () => hComp(nav.path === '/page-a' ? a.page : b.page, nav.path));
+    await flush();
+    assertEq(document.title, 'Alpha - Vacuum Wall', 'A title on first mount');
+
+    nav.path = '/page-b';
+    await flush();
+    assertEq(document.title, 'Beta - Vacuum Wall', 'B title after navigation');
+
+    nav.path = '/page-a';
+    await flush();
+    assertEq(document.title, 'Alpha - Vacuum Wall', 'A title re-applied on remount');
+});
+
+test('mounting an untitled page does not reset a previously set title', async () => {
+    const c = freshCounters();
+    const a = makePage('A', c, 'Alpha - Vacuum Wall');
+    const b = makePage('B', c);
+    const nav = reactive({ path: '/page-a' });
+    const main = new FakeEl('div');
+    render(main, () => hComp(nav.path === '/page-a' ? a.page : b.page, nav.path));
+    await flush();
+    assertEq(document.title, 'Alpha - Vacuum Wall', 'baseline');
+
+    nav.path = '/page-b';
+    await flush();
+    assertEq(document.title, 'Alpha - Vacuum Wall', 'untitled mount keeps prior title');
+});
+
 /* ── Runner ─────────────────────────────────────────────────── */
 (async () => {
     for (const { name, fn } of tests) {