diff --git a/psf-memo-client/acceptance/lib/handlers.js b/psf-memo-client/acceptance/lib/handlers.js
index 03340c3..c128a24 100644
--- a/psf-memo-client/acceptance/lib/handlers.js
+++ b/psf-memo-client/acceptance/lib/handlers.js
@@ -3298,20 +3298,14 @@ const handlers = [
     name: 'click post options button',
     pattern: /^I click the post options button for the post with txid (.+)$/,
     run (m, example, world) {
-      const txid = resolveParam(m[1], example)
-      const menu = getPostOptionsMenu(world, txid)
-      Object.assign(menu, PostOptions.togglePostOptions(menu))
-      world.activeMenuTxid = txid
+      togglePostOptionsMenu(world, resolveParam(m[1], example))
     }
   },
   {
     name: 'click post options button again',
     pattern: /^I click the post options button again for the post with txid (.+)$/,
     run (m, example, world) {
-      const txid = resolveParam(m[1], example)
-      const menu = getPostOptionsMenu(world, txid)
-      Object.assign(menu, PostOptions.togglePostOptions(menu))
-      world.activeMenuTxid = txid
+      togglePostOptionsMenu(world, resolveParam(m[1], example))
     }
   },
   {
@@ -3362,16 +3356,14 @@ const handlers = [
     name: 'click outside post options menu',
     pattern: /^I click outside the post options menu$/,
     run (m, example, world) {
-      const menu = getPostOptionsMenu(world, world.activeMenuTxid)
-      Object.assign(menu, PostOptions.handlePostOptionsOutsideClick(menu))
+      transitionActivePostOptionsMenu(world, PostOptions.handlePostOptionsOutsideClick)
     }
   },
   {
     name: 'press Escape key',
     pattern: /^I press the Escape key$/,
     run (m, example, world) {
-      const menu = getPostOptionsMenu(world, world.activeMenuTxid)
-      Object.assign(menu, PostOptions.handlePostOptionsEscape(menu))
+      transitionActivePostOptionsMenu(world, PostOptions.handlePostOptionsEscape)
     }
   },
   {
@@ -3379,9 +3371,7 @@ const handlers = [
     pattern: /^I press the ArrowDown key$/,
     run (m, example, world) {
       const txid = world.activeMenuTxid
-      const menu = getPostOptionsMenu(world, txid)
-      Object.assign(
-        menu,
+      transitionActivePostOptionsMenu(world, (menu) =>
         PostOptions.focusFirstPostOption(menu, PostOptions.postOptionsItems(txid))
       )
     }
@@ -3412,6 +3402,19 @@ function getPostOptionsMenu (world, txid) {
   return world.postOptionsMenus[txid]
 }
 
+// Apply a post options state transition to the active menu.
+function transitionActivePostOptionsMenu (world, transition) {
+  const menu = getPostOptionsMenu(world, world.activeMenuTxid)
+  Object.assign(menu, transition(menu))
+}
+
+// Toggle a post's options menu and make it the active menu.
+function togglePostOptionsMenu (world, txid) {
+  const menu = getPostOptionsMenu(world, txid)
+  Object.assign(menu, PostOptions.togglePostOptions(menu))
+  world.activeMenuTxid = txid
+}
+
 // The posts currently rendered by the page the scenario has opened.
 function postsOnCurrentPage (world) {
   const path = world.currentPath || ''
diff --git a/psf-memo-client/src/components/post-feed/post-options-menu.js b/psf-memo-client/src/components/post-feed/post-options-menu.js
index 5610a66..af4a272 100644
--- a/psf-memo-client/src/components/post-feed/post-options-menu.js
+++ b/psf-memo-client/src/components/post-feed/post-options-menu.js
@@ -16,9 +16,8 @@ const React = require('react')
 const {
   postOptionsItems,
   togglePostOptions,
-  focusFirstPostOption,
-  handlePostOptionsEscape,
-  handlePostOptionsOutsideClick
+  handlePostOptionsOutsideClick,
+  postOptionsKeyCommand
 } = require('../../services/post-options')
 
 function PostOptionsMenu ({
@@ -48,15 +47,11 @@ function PostOptionsMenu ({
   }, [state.open])
 
   const handleKeyDown = (event) => {
-    if (event.key === 'Escape') {
-      setState((previous) => handlePostOptionsEscape(previous))
-      return
-    }
+    const command = postOptionsKeyCommand(event.key, items)
+    if (!command) return
 
-    if (event.key === 'ArrowDown') {
-      event.preventDefault()
-      setState((previous) => focusFirstPostOption(previous, items))
-    }
+    if (command.preventDefault) event.preventDefault()
+    setState((previous) => command.transition(previous))
   }
 
   return React.createElement(
diff --git a/psf-memo-client/src/services/post-options.js b/psf-memo-client/src/services/post-options.js
index a992be7..74ea937 100644
--- a/psf-memo-client/src/services/post-options.js
+++ b/psf-memo-client/src/services/post-options.js
@@ -69,6 +69,25 @@ function handlePostOptionsOutsideClick (state) {
   return closePostOptions(state)
 }
 
+// Resolve a key press to the menu's next state. Returns null for keys that are
+// not menu shortcuts. ArrowDown reveals the menu and focuses its first item;
+// Escape closes it. preventDefault is true for keys that would otherwise scroll
+// the page.
+function postOptionsKeyCommand (key, items = []) {
+  if (key === 'Escape') {
+    return { transition: handlePostOptionsEscape, preventDefault: false }
+  }
+
+  if (key === 'ArrowDown') {
+    return {
+      transition: (state) => focusFirstPostOption(state, items),
+      preventDefault: true
+    }
+  }
+
+  return null
+}
+
 module.exports = {
   BLOCK_EXPLORER_LABEL,
   BLOCK_EXPLORER_TX_BASE,
@@ -80,5 +99,6 @@ module.exports = {
   togglePostOptions,
   focusFirstPostOption,
   handlePostOptionsEscape,
-  handlePostOptionsOutsideClick
+  handlePostOptionsOutsideClick,
+  postOptionsKeyCommand
 }
diff --git a/psf-memo-client/test/property/post-options.property.test.js b/psf-memo-client/test/property/post-options.property.test.js
new file mode 100644
index 0000000..0cced88
--- /dev/null
+++ b/psf-memo-client/test/property/post-options.property.test.js
@@ -0,0 +1,198 @@
+/*
+  Property tests for the post options menu.
+
+  The unit tests probe post-options at a few fixed fixtures. These properties
+  pin down the service's and the component's invariants over broad random
+  inputs:
+
+    - explorerTxUrl composes the block explorer base with the txid and returns
+      '' for every falsy input.
+    - postOptionsItems always offers the block explorer link first, with the
+      expected label, target, and rel, and an href equal to explorerTxUrl.
+    - Close transitions are idempotent and always clear focus; open preserves
+      focus; toggle is an involution on the open flag.
+    - focusFirstPostOption (ArrowDown) opens and focuses index 0 when items
+      exist, and is a no-op with no items.
+    - The key command maps only Escape and ArrowDown, never prevents the
+      default for anything else.
+    - The rendered component always shows the button, shows menu items only
+      when open, makes exactly the focused item tabbable, and 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 PostOptions = require('../../src/services/post-options')
+const PostOptionsMenu = require('../../src/components/post-feed/post-options-menu')
+
+const rng = seededRandom(20260916)
+
+const HEX = '0123456789abcdef'
+const OTHER_KEYS = ['Enter', 'Tab', 'ArrowUp', 'ArrowLeft', 'Escape ', 'escape', '']
+
+function randomTxid () {
+  const n = intGen(rng, 1, 64)()
+  let out = ''
+  for (let i = 0; i < n; i++) out += HEX[Math.floor(rng() * HEX.length)]
+  return out
+}
+
+function randomState () {
+  return { open: rng() < 0.5, focusedIndex: intGen(rng, -1, 3)() }
+}
+
+function render (props) {
+  return ReactDOMServer.renderToStaticMarkup(
+    React.createElement(PostOptionsMenu, props)
+  )
+}
+
+test('explorerTxUrl composes the base and the txid', async () => {
+  await forAll(
+    () => randomTxid(),
+    async (txid) =>
+      PostOptions.explorerTxUrl(txid) === `${PostOptions.BLOCK_EXPLORER_TX_BASE}/${txid}`,
+    { label: 'explorerTxUrl composition', samples: 2000 }
+  )
+})
+
+test('explorerTxUrl returns an empty string for every falsy input', async () => {
+  await forAll(
+    () => [undefined, null, '', 0, false][intGen(rng, 0, 4)()],
+    async (value) => PostOptions.explorerTxUrl(value) === '',
+    { label: 'explorerTxUrl falsy inputs', samples: 500 }
+  )
+})
+
+test('postOptionsItems always puts the block explorer link first', async () => {
+  await forAll(
+    () => randomTxid(),
+    async (txid) => {
+      const items = PostOptions.postOptionsItems(txid)
+      if (items.length === 0) return false
+      const first = items[0]
+      return first.id === 'block-explorer' &&
+        first.label === PostOptions.BLOCK_EXPLORER_LABEL &&
+        first.target === '_blank' &&
+        first.rel === 'noopener noreferrer' &&
+        first.href === PostOptions.explorerTxUrl(txid)
+    },
+    { label: 'postOptionsItems block explorer first', samples: 2000 }
+  )
+})
+
+test('close transitions are idempotent and clear focus', async () => {
+  await forAll(
+    () => randomState(),
+    async (state) => {
+      const transitions = [
+        PostOptions.closePostOptions,
+        PostOptions.handlePostOptionsEscape,
+        PostOptions.handlePostOptionsOutsideClick
+      ]
+      for (const transition of transitions) {
+        const once = transition(state)
+        const twice = transition(once)
+        if (once.open !== false || once.focusedIndex !== -1) return false
+        if (JSON.stringify(once) !== JSON.stringify(twice)) return false
+      }
+      return true
+    },
+    { label: 'post options close idempotence', samples: 2000 }
+  )
+})
+
+test('open preserves focus and toggle is an involution on open', async () => {
+  await forAll(
+    () => randomState(),
+    async (state) => {
+      const opened = PostOptions.openPostOptions(state)
+      if (opened.open !== true) return false
+      if (opened.focusedIndex !== state.focusedIndex) return false
+      const twice = PostOptions.togglePostOptions(PostOptions.togglePostOptions(state))
+      return twice.open === state.open
+    },
+    { label: 'post options open and toggle', samples: 2000 }
+  )
+})
+
+test('focusFirstPostOption opens and focuses index 0 only when items exist', async () => {
+  await forAll(
+    () => randomState(),
+    async (state) => {
+      const items = PostOptions.postOptionsItems(randomTxid())
+      const focused = PostOptions.focusFirstPostOption(state, items)
+      if (focused.open !== true || focused.focusedIndex !== 0) return false
+      const empty = PostOptions.focusFirstPostOption(state, [])
+      return JSON.stringify(empty) === JSON.stringify(state)
+    },
+    { label: 'post options focus first', samples: 2000 }
+  )
+})
+
+test('the key command maps only Escape and ArrowDown', async () => {
+  await forAll(
+    () => ({ key: OTHER_KEYS[intGen(rng, 0, OTHER_KEYS.length - 1)()], txid: randomTxid() }),
+    async ({ key, txid }) => {
+      const items = PostOptions.postOptionsItems(txid)
+      if (PostOptions.postOptionsKeyCommand(key, items) !== null) return false
+
+      const escape = PostOptions.postOptionsKeyCommand('Escape', items)
+      if (!escape || escape.preventDefault !== false) return false
+      if (escape.transition(PostOptions.initialPostOptionsState()).open !== false) return false
+
+      const arrowDown = PostOptions.postOptionsKeyCommand('ArrowDown', items)
+      if (!arrowDown || arrowDown.preventDefault !== true) return false
+      const next = arrowDown.transition(PostOptions.initialPostOptionsState())
+      return next.open === true && next.focusedIndex === 0
+    },
+    { label: 'post options key command', samples: 1000 }
+  )
+})
+
+test('the rendered menu shows the button always and items only when open', async () => {
+  await forAll(
+    () => ({ txid: randomTxid(), open: rng() < 0.5 }),
+    async ({ txid, open }) => {
+      const html = render({ txid, initialOpen: open })
+      if (!html.includes('aria-label="Post options"')) return false
+      if (!html.includes(`aria-expanded="${open ? 'true' : 'false'}"`)) return false
+      if (html.includes(PostOptions.BLOCK_EXPLORER_LABEL) !== open) return false
+      if (open && !html.includes(`href="${PostOptions.explorerTxUrl(txid)}"`)) return false
+      if (open && !html.includes('target="_blank"')) return false
+      return true
+    },
+    { label: 'post options render open and closed', samples: 1000 }
+  )
+})
+
+test('exactly the focused menu item is tabbable', async () => {
+  await forAll(
+    () => ({ txid: randomTxid(), focusedIndex: intGen(rng, -1, 0)() }),
+    async ({ txid, focusedIndex }) => {
+      const html = render({ txid, initialOpen: true, initialFocusedIndex: focusedIndex })
+      const tabbable = (html.match(/tabindex="0"/g) || []).length
+      return tabbable === (focusedIndex === 0 ? 1 : 0)
+    },
+    { label: 'post options tabbable item', samples: 500 }
+  )
+})
+
+test('rendering the same props twice yields the same markup', async () => {
+  await forAll(
+    () => ({
+      txid: randomTxid(),
+      initialOpen: rng() < 0.5,
+      initialFocusedIndex: intGen(rng, -1, 1)()
+    }),
+    async (props) => {
+      const first = render(props)
+      const second = render(props)
+      return first === second
+    },
+    { label: 'post options render determinism', samples: 500 }
+  )
+})
diff --git a/psf-memo-client/test/unit/post-options.test.js b/psf-memo-client/test/unit/post-options.test.js
index db93202..72c91e2 100644
--- a/psf-memo-client/test/unit/post-options.test.js
+++ b/psf-memo-client/test/unit/post-options.test.js
@@ -101,6 +101,45 @@ test('focusing the first item is a no-op with no items', () => {
   assert.equal(focused.focusedIndex, -1)
 })
 
+test('the Escape key command closes the menu without preventing default', () => {
+  const command = PostOptions.postOptionsKeyCommand(
+    'Escape',
+    PostOptions.postOptionsItems(TXID)
+  )
+
+  assert.equal(command.preventDefault, false)
+  const next = command.transition(
+    PostOptions.openPostOptions(PostOptions.initialPostOptionsState())
+  )
+  assert.equal(next.open, false)
+  assert.equal(next.focusedIndex, -1)
+})
+
+test('the ArrowDown key command focuses the first item and prevents default', () => {
+  const command = PostOptions.postOptionsKeyCommand(
+    'ArrowDown',
+    PostOptions.postOptionsItems(TXID)
+  )
+
+  assert.equal(command.preventDefault, true)
+  const next = command.transition(PostOptions.initialPostOptionsState())
+  assert.equal(next.open, true)
+  assert.equal(next.focusedIndex, 0)
+})
+
+test('the ArrowDown key command keeps the menu closed when there are no items', () => {
+  const command = PostOptions.postOptionsKeyCommand('ArrowDown', [])
+  const next = command.transition(PostOptions.initialPostOptionsState())
+
+  assert.equal(next.open, false)
+  assert.equal(next.focusedIndex, -1)
+})
+
+test('other keys have no menu command', () => {
+  assert.equal(PostOptions.postOptionsKeyCommand('Enter', PostOptions.postOptionsItems(TXID)), null)
+  assert.equal(PostOptions.postOptionsKeyCommand('Tab', []), null)
+})
+
 test('the closed menu renders the post options button but no items', () => {
   const html = renderMenu()