Prove the pager pages instead of proving the row count moves

The E2E waited for the number of `.atom-row` elements to change, but the
search list and the browse list share that class, so the count it watched
was 12 browse rows plus one search hit. A pager that did nothing still
passed. Rows now carry `data-atom` and the two lists carry `data-testid`,
and the test asserts the ordered id list: page one holds exactly PAGE_SIZE
rows, page two shares none of them, page two holds total - PAGE_SIZE rows,
and Previous restores the first list.

Both mutations the reviewer suggested now fail: dropping setCursor and
loadBrowse from nextPage gives "Next page did not swap the page: the pager
is not paging", and appending instead of replacing gives "the next page
repeated 12 of 12 atoms from the first page".

The record also said 130 lines for App.tsx when it is 131, and quoted a
mount refusal the harness had cut off mid-sentence; the refusal's own
remediation ("set ELY_EYE_MODEL_DIR to the model snapshot") is the useful
half, so the slice is 200 now and the quote is the product's full sentence.

frontend/scripts/verify-ui.mjs

@@ -8,6 +8,8 @@ await mkdir(outputDir, { recursive: true });
 
 const apiBase = process.env.ELY_EYE_API ?? 'http://127.0.0.1:8765';
 const uiUrl = process.env.ELY_EYE_UI_URL ?? 'http://127.0.0.1:5173/';
+// Mirrors PAGE_SIZE in frontend/src/components/MemoryPanel.tsx; the pager is only provable against a known page size.
+const PAGE_SIZE = 12;
 
 async function api(route, body) {
   const response = await fetch(`${apiBase}${route}`, {
@@ -134,13 +136,51 @@ try {
   throw error;
 }
 await page.getByLabel('Modality').selectOption('');
-const firstPageRows = await page.locator('.atom-list .atom-row').count();
-await page.getByTitle('Next page').click();
+// Paging is proved by row identity, not row count: the search list above uses the same row class,
+// so a count that "changes" can be the search hit appearing and going away.
 await page.waitForFunction(
-  (count) => document.querySelectorAll('.atom-list .atom-row').length !== count,
-  firstPageRows,
+  (size) =>
+    document.querySelectorAll('[data-testid="browse-list"] .atom-row').length === size,
+  PAGE_SIZE,
+  { timeout: 15_000 },
 );
+const firstIds = await page.locator('[data-testid="browse-list"] .atom-row').evaluateAll((rows) =>
+  rows.map((row) => row.getAttribute('data-atom') ?? ''),
+);
+await page.getByTitle('Next page').click();
+try {
+  await page.waitForFunction((previous) => {
+    const ids = Array.from(document.querySelectorAll('[data-testid="browse-list"] .atom-row')).map(
+      (row) => row.getAttribute('data-atom') ?? '',
+    );
+    return ids.length > 0 && ids.join(',') !== previous.join(',');
+  }, firstIds, { timeout: 15_000 });
+} catch {
+  await evidence('the next page showed the same atoms as the first');
+  throw new Error('Next page did not swap the page: the pager is not paging');
+}
+const secondIds = await page.locator('[data-testid="browse-list"] .atom-row').evaluateAll((rows) =>
+  rows.map((row) => row.getAttribute('data-atom') ?? ''),
+);
+const repeated = secondIds.filter((id) => firstIds.includes(id));
+if (repeated.length > 0) {
+  throw new Error(`the next page repeated ${repeated.length} of ${firstIds.length} atoms from the first page`);
+}
+const behind = await apiGet('/api/atoms?limit=1');
+if (secondIds.length !== behind.total - PAGE_SIZE) {
+  throw new Error(
+    `the second page held ${secondIds.length} rows, expected ${behind.total - PAGE_SIZE} of ${behind.total} atoms`,
+  );
+}
 await page.getByTitle('Previous page').click();
+await page.waitForFunction(
+  (expected) =>
+    Array.from(document.querySelectorAll('[data-testid="browse-list"] .atom-row'))
+      .map((row) => row.getAttribute('data-atom') ?? '')
+      .join(',') === expected.join(','),
+  firstIds,
+  { timeout: 15_000 },
+);
 
 // 3. forget: remove a memory and watch it leave the store.
 await page.getByPlaceholder('where are the keys').fill('spare glasses');
@@ -168,7 +208,7 @@ if (await mountedPill.isVisible().catch(() => false)) {
   await page.getByText(/unmount ui-smoke/).waitFor();
 } else {
   await refusal.waitFor();
-  observed.mount = `refused: ${(await refusal.innerText()).slice(0, 120)}`;
+  observed.mount = `refused: ${(await refusal.innerText()).slice(0, 200)}`;
   const cartridges = await apiGet('/api/cartridges');
   const cartridge = cartridges.find((entry) => entry.name === 'ui-smoke');
   if (!cartridge) {