diff --git a/packages/web/src/components/CodeCaptcha.tsx b/packages/web/src/components/CodeCaptcha.tsx
index 861adc8..b02dd7f 100644
--- a/packages/web/src/components/CodeCaptcha.tsx
+++ b/packages/web/src/components/CodeCaptcha.tsx
@@ -418,8 +418,12 @@ export function CodeCaptcha({
               {/* Math Problem or Canvas Code Image */}
               <div className="flex-1 flex items-center justify-center">
                 {currentStyle === 'math' ? (
-                  <div className="text-center py-8">
-                    <p className="text-sm text-gray-400 mb-2">What is:</p>
+                  // The "What is:" label floats at the top so the NUMBER is the
+                  // vertically-centered element — otherwise the label pushed the
+                  // number below the panel center and the lone refresh button
+                  // (panel-centered) sat above it.
+                  <div className="relative w-full text-center py-8 flex items-center justify-center min-h-[5.5rem]">
+                    <span className="absolute top-1 left-0 right-0 text-sm text-gray-400">What is:</span>
                     <p className="text-5xl font-bold text-teal-300 tracking-wider">
                       {mathProblem} = ?
                     </p>
diff --git a/tests/diagnostics/captcha-layout.spec.ts b/tests/diagnostics/captcha-layout.spec.ts
new file mode 100644
index 0000000..4c67b41
--- /dev/null
+++ b/tests/diagnostics/captcha-layout.spec.ts
@@ -0,0 +1,74 @@
+import { test, expect, Page } from '@playwright/test';
+import * as fs from 'fs';
+import * as path from 'path';
+
+/**
+ * CodeCaptcha (ALTCHA-style) layout diagnostic. Measures whether the refresh
+ * ("try different style") button is vertically centered against the challenge
+ * content, in BOTH the math state (no speaker button) and the text/complex
+ * state (speaker button present). Report-only — no app behavior changed.
+ */
+const OUT = path.resolve(process.cwd(), 'test-artifacts/captcha');
+
+async function measure(page: Page) {
+  return page.evaluate(() => {
+    const refresh = document.querySelector('button[title="Try different style"]') as HTMLElement | null;
+    const speaker = document.querySelector('button[title="Listen to code"]') as HTMLElement | null;
+    // the challenge box (the bordered panel) and the math number / canvas
+    const num = [...document.querySelectorAll('p')].find((p) => /=\s*\?/.test(p.textContent || '')) as HTMLElement | null;
+    const canvas = document.querySelector('canvas') as HTMLElement | null;
+    const content = (num ?? canvas) as HTMLElement | null;
+    const box = refresh?.closest('.rounded-lg') as HTMLElement | null;
+    const c = (el: HTMLElement | null) => { if (!el) return null; const r = el.getBoundingClientRect(); return { top: Math.round(r.top), bottom: Math.round(r.bottom), cy: Math.round(r.top + r.height / 2), h: Math.round(r.height) }; };
+    return {
+      style: num ? 'math' : (canvas ? 'image' : 'unknown'),
+      hasSpeaker: !!speaker,
+      refresh: c(refresh),
+      content: c(content),
+      panel: c(box),
+    };
+  });
+}
+
+test.describe('captcha layout diagnostic @geometry', () => {
+  test('refresh button vertical centering (math vs speaker state)', async ({ page }) => {
+    fs.mkdirSync(OUT, { recursive: true });
+    await page.setViewportSize({ width: 1280, height: 900 });
+    await page.goto('/signup');
+    await page.waitForTimeout(1500);
+    await page.locator('button[title="Try different style"]').first().waitFor({ timeout: 15000 });
+
+    const results: any[] = [];
+    // State 1: as first shown (math, no speaker)
+    let m = await measure(page);
+    await page.screenshot({ path: path.join(OUT, `state-${m.style}-speaker${m.hasSpeaker}.png`), clip: m.panel ? { x: 0, y: Math.max(0, m.panel.top - 20), width: 1280, height: m.panel.h + 40 } : undefined }).catch(() => {});
+    results.push(m);
+
+    // Click refresh until we land on an image/text style (speaker appears), to
+    // compare. Bounded so we don't loop forever if RNG keeps picking math.
+    for (let i = 0; i < 12 && !(results.find((r) => r.hasSpeaker)); i++) {
+      await page.locator('button[title="Try different style"]').click();
+      await page.waitForTimeout(500);
+      const cur = await measure(page);
+      if (cur.style !== results[results.length - 1].style || cur.hasSpeaker !== results[results.length - 1].hasSpeaker) {
+        await page.screenshot({ path: path.join(OUT, `state-${cur.style}-speaker${cur.hasSpeaker}.png`), clip: cur.panel ? { x: 0, y: Math.max(0, cur.panel.top - 20), width: 1280, height: cur.panel.h + 40 } : undefined }).catch(() => {});
+        results.push(cur);
+      }
+    }
+
+    const report = results.map((r) => ({
+      style: r.style,
+      hasSpeaker: r.hasSpeaker,
+      refreshCy: r.refresh?.cy,
+      contentCy: r.content?.cy,
+      panelCy: r.panel?.cy,
+      refreshVsContent: r.refresh && r.content ? r.refresh.cy - r.content.cy : null,
+      refreshVsPanel: r.refresh && r.panel ? r.refresh.cy - r.panel.cy : null,
+    }));
+    fs.writeFileSync(path.join(OUT, 'report.json'), JSON.stringify(report, null, 2));
+    // eslint-disable-next-line no-console
+    for (const r of report) console.log('[captcha] ' + JSON.stringify(r));
+
+    expect(report.length, 'measured at least the math state').toBeGreaterThan(0);
+  });
+});