diff --git a/psf-memo-client/acceptance/lib/handlers.js b/psf-memo-client/acceptance/lib/handlers.js
index 4c7ec00..99396eb 100644
--- a/psf-memo-client/acceptance/lib/handlers.js
+++ b/psf-memo-client/acceptance/lib/handlers.js
@@ -3173,11 +3173,7 @@ const handlers = [
     name: 'feed shows no link',
     pattern: /^the feed shows no link$/,
     run (m, example, world) {
-      const rendered = getRenderedFeed(world)
-      const found = rendered.some((html) => anchorsIn(html).length > 0)
-      if (found) {
-        throw new Error('Feed unexpectedly shows a link.')
-      }
+      assertFeedHasNoElement(world, anchorsIn, 'Feed unexpectedly shows a link.')
     }
   },
   {
@@ -3237,11 +3233,7 @@ const handlers = [
     name: 'feed shows no image',
     pattern: /^the feed shows no image$/,
     run (m, example, world) {
-      const rendered = getRenderedFeed(world)
-      const found = rendered.some((html) => imagesIn(html).length > 0)
-      if (found) {
-        throw new Error('Feed unexpectedly shows an image.')
-      }
+      assertFeedHasNoElement(world, imagesIn, 'Feed unexpectedly shows an image.')
     }
   },
   {
@@ -3279,6 +3271,15 @@ function getRenderedFeed (world) {
   return world.renderedFeed
 }
 
+// Fail when any rendered feed HTML contains an element matched by extract.
+function assertFeedHasNoElement (world, extract, message) {
+  const rendered = getRenderedFeed(world)
+  const found = rendered.some((html) => extract(html).length > 0)
+  if (found) {
+    throw new Error(message)
+  }
+}
+
 // Extract the anchors from a rendered HTML string. The acceptance adapter
 // renders a small, controlled HTML subset, so a regex match is sufficient.
 function anchorsIn (html) {
diff --git a/psf-memo-client/src/components/post-feed/post-content.js b/psf-memo-client/src/components/post-feed/post-content.js
index 1c61195..df4dc8e 100644
--- a/psf-memo-client/src/components/post-feed/post-content.js
+++ b/psf-memo-client/src/components/post-feed/post-content.js
@@ -16,6 +16,7 @@ const {
   isImageUrl,
   imageAltText
 } = require('../../services/post-links')
+const { addFailedImage } = require('../../services/failed-images')
 
 // A post image that falls back to a plain link if the image fails to load.
 function PostImage ({ href, alt, failed, onError }) {
@@ -56,12 +57,7 @@ function PostContent ({ text = '', initialFailedImages }) {
   const children = []
 
   const failImage = (href) => {
-    setFailedImages((previous) => {
-      if (previous.has(href)) return previous
-      const next = new Set(previous)
-      next.add(href)
-      return next
-    })
+    setFailedImages((previous) => addFailedImage(previous, href))
   }
 
   for (const segment of parsePostText(text)) {
diff --git a/psf-memo-client/src/services/failed-images.js b/psf-memo-client/src/services/failed-images.js
new file mode 100644
index 0000000..921d33f
--- /dev/null
+++ b/psf-memo-client/src/services/failed-images.js
@@ -0,0 +1,21 @@
+/*
+  Pure state transition for tracking post images that failed to load.
+
+  This is kept free of React and the DOM so the transition can be unit tested
+  directly. The PostContent component uses it as the reducer for its
+  failed-image state.
+*/
+
+/**
+ * Add a failed image URL to the set. Returns the same set when the URL is
+ * already present, so React can bail out of a no-op update; otherwise returns
+ * a new set containing the added URL. The input set is never mutated.
+ */
+function addFailedImage (failedImages, href) {
+  if (failedImages.has(href)) return failedImages
+  const next = new Set(failedImages)
+  next.add(href)
+  return next
+}
+
+module.exports = { addFailedImage }
diff --git a/psf-memo-client/test/property/post-content.property.test.js b/psf-memo-client/test/property/post-content.property.test.js
new file mode 100644
index 0000000..bd13c98
--- /dev/null
+++ b/psf-memo-client/test/property/post-content.property.test.js
@@ -0,0 +1,111 @@
+/*
+  Property tests for the post content renderer.
+
+  The unit tests probe PostContent at a few fixed fixtures. These properties
+  pin down the rendering invariants for URL-like tokens over broad random
+  inputs:
+
+    - An image URL renders as an <img> inside a new-tab anchor, keeps its full
+      URL as the src (query string included), and is never repeated as visible
+      text.
+    - A non-image URL renders as a plain new-tab anchor with no <img>.
+    - Surrounding text is preserved and rendering is deterministic.
+*/
+
+'use strict'
+
+const test = require('node:test')
+const React = require('react')
+const ReactDOMServer = require('react-dom/server')
+const { seededRandom, forAll, intGen } = require('./harness')
+const PostContent = require('../../src/components/post-feed/post-content')
+
+const rng = seededRandom(20260916)
+
+const IMAGE_EXTENSIONS = ['jpg', 'jpeg', 'png', 'gif', 'webp', 'bmp']
+
+function render (text) {
+  return ReactDOMServer.renderToStaticMarkup(
+    React.createElement(PostContent, { text })
+  )
+}
+
+function randomName () {
+  const alphabet = 'abcdefghijklmnopqrstuvwxyz0123456789'
+  const n = intGen(rng, 1, 8)()
+  let out = ''
+  for (let i = 0; i < n; i++) out += alphabet[Math.floor(rng() * alphabet.length)]
+  return out
+}
+
+function randomHost () {
+  return ['example.com', 'cdn.example.org', 'i.imgur.com'][Math.floor(rng() * 3)]
+}
+
+// Tail values that are safe in HTML attributes (no &, ", <, >, or ').
+function randomTail () {
+  const kind = Math.floor(rng() * 3)
+  if (kind === 0) return ''
+  if (kind === 1) return `?w=${intGen(rng, 1, 2000)()}`
+  return '#section'
+}
+
+function randomImageUrl () {
+  const ext = IMAGE_EXTENSIONS[Math.floor(rng() * IMAGE_EXTENSIONS.length)]
+  const dir = ['', 'pics/', 'a/b/'][Math.floor(rng() * 3)]
+  return `https://${randomHost()}/${dir}${randomName()}.${ext}${randomTail()}`
+}
+
+function randomNonImageUrl () {
+  if (Math.floor(rng() * 3) === 0) {
+    return `https://${randomHost()}/page${randomTail()}`
+  }
+  return `https://${randomHost()}/${randomName()}.svg${randomTail()}`
+}
+
+function visibleText (html) {
+  return html.replace(/<[^>]+>/g, '')
+}
+
+test('an image URL renders as an <img> in a new-tab anchor and never as visible text', async () => {
+  await forAll(
+    () => randomImageUrl(),
+    async (url) => {
+      const html = render(`before ${url} after`)
+      if (!/<img[^>]+src="/.test(html)) return false
+      if (!html.includes(`src="${url}"`)) return false
+      if (!/<a[^>]+target="_blank"/.test(html)) return false
+      const text = visibleText(html)
+      if (text.includes(url)) return false
+      return text.includes('before') && text.includes('after')
+    },
+    { label: 'post-content image rendering', samples: 300 }
+  )
+})
+
+test('a non-image URL renders as a plain new-tab anchor with no image', async () => {
+  await forAll(
+    () => randomNonImageUrl(),
+    async (url) => {
+      const html = render(`before ${url} after`)
+      if (html.includes('<img')) return false
+      if (!html.includes(`href="${url}"`)) return false
+      if (!/<a[^>]+target="_blank"/.test(html)) return false
+      return visibleText(html).includes('before') && visibleText(html).includes('after')
+    },
+    { label: 'post-content non-image rendering', samples: 300 }
+  )
+})
+
+test('rendering the same text is deterministic', async () => {
+  await forAll(
+    () => randomImageUrl(),
+    async (url) => {
+      const text = `x ${url} y`
+      const first = render(text)
+      const second = render(text)
+      return first === second
+    },
+    { label: 'post-content determinism', samples: 200 }
+  )
+})
diff --git a/psf-memo-client/test/property/post-links.property.test.js b/psf-memo-client/test/property/post-links.property.test.js
index 9600d45..16be945 100644
--- a/psf-memo-client/test/property/post-links.property.test.js
+++ b/psf-memo-client/test/property/post-links.property.test.js
@@ -22,7 +22,11 @@
 const test = require('node:test')
 const assert = require('node:assert/strict')
 const { seededRandom, forAll, intGen } = require('./harness')
-const { parsePostLinks } = require('../../src/services/post-links')
+const {
+  parsePostLinks,
+  isImageUrl,
+  imageAltText
+} = require('../../src/services/post-links')
 
 const rng = seededRandom(20260916)
 
@@ -171,3 +175,104 @@ test('parsePostLinks stringifies nullish and non-string input', () => {
   assert.deepEqual(parsePostLinks(undefined), [{ type: 'text', text: '' }])
   assert.deepEqual(parsePostLinks(12345), [{ type: 'text', text: '12345' }])
 })
+
+const IMAGE_EXTENSIONS = ['jpg', 'jpeg', 'png', 'gif', 'webp', 'bmp']
+const NON_IMAGE_EXTENSIONS = ['svg', 'pdf', 'txt', 'html', 'json', 'js']
+
+function randomCase (value) {
+  let out = ''
+  for (const ch of value) {
+    out += rng() < 0.5 ? ch.toLowerCase() : ch.toUpperCase()
+  }
+  return out
+}
+
+function randomName () {
+  const alphabet = 'abcdefghijklmnopqrstuvwxyz0123456789'
+  const n = intGen(rng, 1, 10)()
+  let out = ''
+  for (let i = 0; i < n; i++) out += alphabet[Math.floor(rng() * alphabet.length)]
+  return out
+}
+
+function randomHost () {
+  return ['example.com', 'cdn.example.org', 'i.imgur.com', 'images.example.net'][Math.floor(rng() * 4)]
+}
+
+function randomQueryOrFragment () {
+  const kind = Math.floor(rng() * 4)
+  if (kind === 0) return ''
+  if (kind === 1) return `?w=${intGen(rng, 1, 2000)()}`
+  if (kind === 2) return '#section'
+  return '?a=1&b=2#frag'
+}
+
+function randomImageUrl () {
+  const ext = randomCase(IMAGE_EXTENSIONS[Math.floor(rng() * IMAGE_EXTENSIONS.length)])
+  const dir = ['', 'pics/', 'a/b/', 'img/'][Math.floor(rng() * 4)]
+  return `https://${randomHost()}/${dir}${randomName()}.${ext}${randomQueryOrFragment()}`
+}
+
+function randomNonImageUrl () {
+  if (Math.floor(rng() * 3) === 0) {
+    return `https://${randomHost()}/page${randomQueryOrFragment()}`
+  }
+  const ext = NON_IMAGE_EXTENSIONS[Math.floor(rng() * NON_IMAGE_EXTENSIONS.length)]
+  return `https://${randomHost()}/${randomName()}.${ext}${randomQueryOrFragment()}`
+}
+
+test('isImageUrl recognizes supported image extensions regardless of case or query', async () => {
+  await forAll(
+    () => randomImageUrl(),
+    async (url) => isImageUrl(url) === true,
+    { label: 'isImageUrl image urls', samples: 2000 }
+  )
+})
+
+test('isImageUrl rejects non-image paths even when a query mentions an image', async () => {
+  await forAll(
+    () => randomNonImageUrl(),
+    async (url) => isImageUrl(url) === false,
+    { label: 'isImageUrl non-image urls', samples: 2000 }
+  )
+})
+
+test('isImageUrl and imageAltText never throw and are deterministic for arbitrary input', async () => {
+  await forAll(
+    () => randomText(),
+    async (text) => {
+      let image, alt, imageAgain, altAgain
+      try {
+        image = isImageUrl(text)
+        alt = imageAltText(text)
+        imageAgain = isImageUrl(text)
+        altAgain = imageAltText(text)
+      } catch {
+        return false
+      }
+      if (typeof image !== 'boolean') return false
+      if (typeof alt !== 'string' || alt.length === 0) return false
+      return image === imageAgain && alt === altAgain
+    },
+    { label: 'isImageUrl/imageAltText robustness', samples: 3000 }
+  )
+})
+
+test('imageAltText returns the URL filename, ignoring query string and fragment', async () => {
+  await forAll(
+    () => randomImageUrl(),
+    async (url) => imageAltText(url) === new URL(url).pathname.split('/').pop(),
+    { label: 'imageAltText filename', samples: 2000 }
+  )
+})
+
+test('parsePostLinks keeps an image URL intact so isImageUrl still recognizes it', async () => {
+  await forAll(
+    () => randomImageUrl(),
+    async (url) => {
+      const link = parsePostLinks(`see ${url} now`).find((segment) => segment.type === 'link')
+      return Boolean(link) && link.href === url && isImageUrl(link.href) === true
+    },
+    { label: 'parsePostLinks image url round trip', samples: 2000 }
+  )
+})
diff --git a/psf-memo-client/test/unit/failed-images.test.js b/psf-memo-client/test/unit/failed-images.test.js
new file mode 100644
index 0000000..7a0f1a8
--- /dev/null
+++ b/psf-memo-client/test/unit/failed-images.test.js
@@ -0,0 +1,37 @@
+/*
+  Unit tests for the failed-image state transition used by the post renderer.
+
+  The transition is pure: it either returns the same set (when the URL is
+  already tracked, so React can skip a re-render) or a new set with the URL
+  added, and it never mutates the input set.
+*/
+
+'use strict'
+
+const test = require('node:test')
+const assert = require('node:assert/strict')
+const { addFailedImage } = require('../../src/services/failed-images')
+
+const URL_A = 'https://i.imgur.com/swCI56T.jpeg'
+const URL_B = 'https://cdn.example.com/pics/Sunset.PNG'
+
+test('addFailedImage returns a new set containing the added URL', () => {
+  const original = new Set()
+  const next = addFailedImage(original, URL_A)
+  assert.notEqual(next, original)
+  assert.deepEqual([...next], [URL_A])
+  assert.equal(original.size, 0)
+})
+
+test('addFailedImage returns the same set when the URL is already present', () => {
+  const original = new Set([URL_A])
+  const next = addFailedImage(original, URL_A)
+  assert.equal(next, original)
+})
+
+test('addFailedImage preserves existing entries and does not mutate the input', () => {
+  const original = new Set([URL_A])
+  const next = addFailedImage(original, URL_B)
+  assert.deepEqual([...next].sort(), [URL_B, URL_A].sort())
+  assert.deepEqual([...original], [URL_A])
+})