diff --git a/psf-memo-client/test/property/account-page.property.test.js b/psf-memo-client/test/property/account-page.property.test.js
new file mode 100644
index 0000000..a275412
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+++ b/psf-memo-client/test/property/account-page.property.test.js
@@ -0,0 +1,92 @@
+/*
+  Property tests for the account page avatar display logic.
+
+  The unit tests probe a few fixed inputs. These properties cover broad input
+  combinations so the invariants hold everywhere:
+
+    - precedence: getDisplayAvatarUrl prefers the profile store URL, then the
+      fallback URL, then null.
+    - consistency: hasAvatarImage is true exactly when getAvatarImageUrl is
+      non-null, and getAvatarImageUrl always equals getDisplayAvatarUrl.
+    - round trip: getAvatarUrl returns exactly the URL stored in the profile
+      store (or null when none is stored).
+*/
+
+'use strict'
+
+const test = require('node:test')
+const { seededRandom, forAll } = require('./harness')
+const AccountPage = require('../../src/services/account-page')
+
+const rng = seededRandom(20260905)
+
+// A pool of plausible avatar URLs so generated inputs vary.
+const URL_POOL = [
+  'https://example.com/avatar.png',
+  'https://cdn.example.com/pics/me.jpg',
+  'https://x.io/avatar.png',
+  'https://static.example.org/img/me.webp'
+]
+
+// Generate a URL or null.
+function maybeUrl () {
+  if (rng() < 0.5) return null
+  return URL_POOL[Math.floor(rng() * URL_POOL.length)]
+}
+
+function makeProfiles () {
+  const avatarUrls = {}
+  return {
+    setAvatarUrl: (addr, url) => { avatarUrls[addr] = url },
+    getAvatarUrl: (addr) => avatarUrls[addr] || null
+  }
+}
+
+function makeWallet (address = 'bitcoincash:qqlrzp23w08434twmvr4fxw672whkjy0py26r63g3d') {
+  return { walletInfo: { cashAddress: address } }
+}
+
+// Build a page with an optional stored profile URL and return it.
+function makePage (profileUrl) {
+  const profiles = makeProfiles()
+  const wallet = makeWallet()
+  const page = new AccountPage({ wallet, profiles })
+  if (profileUrl) profiles.setAvatarUrl(wallet.walletInfo.cashAddress, profileUrl)
+  return page
+}
+
+test('getDisplayAvatarUrl prefers the profile URL, then the fallback, then null', async () => {
+  await forAll(
+    (i) => ({ profileUrl: maybeUrl(), fallback: maybeUrl() }),
+    ({ profileUrl, fallback }) => {
+      const page = makePage(profileUrl)
+      const expected = profileUrl || fallback || null
+      return page.getDisplayAvatarUrl(fallback) === expected
+    },
+    { label: 'getDisplayAvatarUrl precedence' }
+  )
+})
+
+test('hasAvatarImage and getAvatarImageUrl are consistent with getDisplayAvatarUrl', async () => {
+  await forAll(
+    (i) => ({ profileUrl: maybeUrl(), fallback: maybeUrl() }),
+    ({ profileUrl, fallback }) => {
+      const page = makePage(profileUrl)
+      const url = page.getAvatarImageUrl(fallback)
+      return page.hasAvatarImage(fallback) === (url !== null) &&
+        url === page.getDisplayAvatarUrl(fallback)
+    },
+    { label: 'avatar image consistency' }
+  )
+})
+
+test('getAvatarUrl round-trips the stored profile URL', async () => {
+  await forAll(
+    (i) => maybeUrl(),
+    (url) => {
+      const page = makePage(url)
+      return page.getAvatarUrl() === url
+    },
+    { label: 'getAvatarUrl round trip' }
+  )
+})