diff --git a/.agent/phases/todo/46_mobile_hamburger_nav/00_phase.md b/.agent/phases/complete/46_mobile_hamburger_nav/00_phase.md
similarity index 100%
rename from .agent/phases/todo/46_mobile_hamburger_nav/00_phase.md
rename to .agent/phases/complete/46_mobile_hamburger_nav/00_phase.md
diff --git a/.agent/phases/todo/46_mobile_hamburger_nav/01_hamburger_markup_all_pages.md b/.agent/phases/complete/46_mobile_hamburger_nav/01_hamburger_markup_all_pages.md
similarity index 100%
rename from .agent/phases/todo/46_mobile_hamburger_nav/01_hamburger_markup_all_pages.md
rename to .agent/phases/complete/46_mobile_hamburger_nav/01_hamburger_markup_all_pages.md
diff --git a/.agent/phases/todo/46_mobile_hamburger_nav/02_toggle_behavior.md b/.agent/phases/complete/46_mobile_hamburger_nav/02_toggle_behavior.md
similarity index 100%
rename from .agent/phases/todo/46_mobile_hamburger_nav/02_toggle_behavior.md
rename to .agent/phases/complete/46_mobile_hamburger_nav/02_toggle_behavior.md
diff --git a/.agent/phases/todo/46_mobile_hamburger_nav/03_hamburger_e2e_and_commit.md b/.agent/phases/complete/46_mobile_hamburger_nav/03_hamburger_e2e_and_commit.md
similarity index 100%
rename from .agent/phases/todo/46_mobile_hamburger_nav/03_hamburger_e2e_and_commit.md
rename to .agent/phases/complete/46_mobile_hamburger_nav/03_hamburger_e2e_and_commit.md
diff --git a/frontend/assets/header.js b/frontend/assets/header.js
index d39d6b4..4204875 100644
--- a/frontend/assets/header.js
+++ b/frontend/assets/header.js
@@ -21,6 +21,18 @@
  *     contract on the SAME cached whoami (one fetch, no extra request);
  *   • the sign-out click binding (POST /api/logout → reload) — moved
  *     here from app.js so there is exactly one implementation;
+ *   • the mobile hamburger binding (phase 46, owner permission
+ *     2026-08-27, TODO.md L9) — at ≤640px (CSS hides the button
+ *     elsewhere) the #nav-toggle button opens the nav as an animated
+ *     dropdown (#app-nav .is-open — the 180ms slide+fade state from
+ *     task 01's CSS): a click toggles it with aria-expanded kept in
+ *     sync, a nav link click shuts it (the navigation happens anyway),
+ *     Esc shuts it and returns focus to the toggle, and resizing back
+ *     to >640px drops the open state (matchMedia change) so
+ *     aria-expanded stays honest. One binding for all six pages; a
+ *     page without either element is a no-op. The binding toggles
+ *     ONLY the container — the nav links keep their ship-hidden
+ *     whoami contract (hidden links stay hidden inside the menu);
  *   • the steering-notes controls (phase 15, moved here from app.js in
  *     phase 34) — the #steering-toggle open/close + the #steering-panel
  *     list (newest-first, textContent-rendered, per-note delete, count
@@ -181,6 +193,46 @@ if (signOutBtn) {
   });
 }
 
+/* ---------- mobile hamburger (phase 46; module-owned) ----------
+ * ≤640px only (CSS hides the button elsewhere): #nav-toggle opens the
+ * nav as a dropdown (#app-nav .is-open — the animated state, task 01
+ * CSS). One binding for all six pages; a page without either element
+ * is a no-op, like the rest of this module. The nav LINKS keep their
+ * ship-hidden whoami contract (hidden links stay hidden inside the
+ * menu) — this binding only toggles the container. */
+const navToggle = document.querySelector("#nav-toggle");
+const appNav = document.querySelector("#app-nav");
+
+function setNavMenu(open) {
+  if (!appNav || !navToggle) return;
+  appNav.classList.toggle("is-open", open);
+  navToggle.setAttribute("aria-expanded", open ? "true" : "false");
+}
+
+if (navToggle && appNav) {
+  navToggle.addEventListener("click", () =>
+    setNavMenu(!appNav.classList.contains("is-open")));
+  // A link click navigates (or closes same-page) — shut the menu.
+  appNav.addEventListener("click", (e) => {
+    if (e.target.closest("a")) setNavMenu(false);
+  });
+  // Esc closes while open (document-level; the sync failure modal's
+  // Esc acts only while IT is open — the two never fight for a key).
+  document.addEventListener("keydown", (e) => {
+    if (e.key === "Escape" && appNav.classList.contains("is-open")) {
+      setNavMenu(false);
+      navToggle.focus(); // focus returns to the opener
+    }
+  });
+  // Resize back to desktop: the inline nav reappears — no stale open
+  // state (the .is-open class is scoped by the ≤640px CSS anyway, but
+  // dropping it keeps aria-expanded honest).
+  const mq = window.matchMedia("(max-width: 640px)");
+  const onMqChange = () => { if (!mq.matches) setNavMenu(false); };
+  if (mq.addEventListener) mq.addEventListener("change", onMqChange);
+  else mq.addListener(onMqChange); // older engines, defensive
+}
+
 /* ---------- steering notes (phase 15; module-owned from phase 34) ----------
  *
  * The owner's tuning notes steer every future answer: they live in
diff --git a/frontend/assets/styles.css b/frontend/assets/styles.css
index 6f9ed68..0a861eb 100644
--- a/frontend/assets/styles.css
+++ b/frontend/assets/styles.css
@@ -274,6 +274,14 @@ html::after {
 .nav-link:hover { background: var(--brand-soft); color: var(--brand-ink); }
 .nav-link.is-active { background: var(--brand); color: var(--bg); }
 
+/* Phase 46 (owner permission 2026-08-27, TODO.md L9): the mobile
+   hamburger button — desktop is byte-identical to before (the control
+   is absent outside the ≤640px block, which re-displays it and turns
+   the nav into the dropdown). :focus-visible inherits the global 3px
+   outline rule; the 44px target + the rest of the look live in the
+   ≤640px block below. */
+.nav-toggle { display: none; }
+
 /* "New chat" reset (phase 14): ghost pill in the chat header, hover like
    a nav link. ink-soft on surface ≈6.9:1; hover pair brand-ink/brand-soft
    ≈6.9:1 — both WCAG AA. Icon-only below 640px (aria-label keeps the
@@ -2163,8 +2171,66 @@ details.thinking .thinking-text ul { margin: 0 0 0.5rem; }
     text-overflow: ellipsis;
     white-space: nowrap;
   }
-  .nav-link { padding: 0.3rem 0.25rem; font-size: 0.72rem; }
-  .app-nav { gap: 0.05rem; }
+  /* Phase 46 (owner permission 2026-08-27, TODO.md L9): the nav links
+     LEAVE the bar at phone widths — the old pill-squeeze rules for
+     .nav-link / .app-nav (0.72rem pills, 0.05rem gap, in place of this
+     comment) are superseded by the #nav-toggle dropdown below. The
+     action pills' squeeze rules further down are untouched, and the
+     900px tablet block keeps squeezing the INLINE nav at 641–900px
+     (the hamburger is absent there). */
+  .nav-toggle {
+    display: inline-flex;
+    align-items: center;
+    justify-content: center;
+    width: 44px;
+    height: 44px;
+    padding: 0;
+    color: var(--ink);
+    background: none;
+    border: 0;
+    border-radius: var(--radius-sm);
+    cursor: pointer;
+  }
+  .nav-toggle:hover { background: var(--brand-soft); color: var(--brand-ink); }
+  /* The icon is sized (an unsized inline SVG would default to 300px
+     and blow the bar out); 20px reads as a proper hamburger inside
+     the 44px target. */
+  .nav-toggle svg { width: 20px; height: 20px; display: block; }
+  /* The nav becomes the dropdown. The containing block is the sticky
+     .app-header (.header-inner is not positioned), so the menu spans
+     the header's full width — edge to edge — intended on mobile;
+     z-index 21 = header (20) + 1, above the bar content. */
+  .app-nav {
+    position: absolute;
+    top: 100%;
+    left: 0;
+    right: 0;
+    margin-left: 0;
+    flex-direction: column;
+    gap: 0;
+    background: var(--surface);
+    border-bottom: 1px solid var(--line);
+    box-shadow: var(--shadow-lg);
+    padding: 0.5rem 0;
+    z-index: 21;
+    /* Closed state (default): invisible and non-interactive — task 02's
+       header.js is the only opener (.is-open + aria-expanded). */
+    visibility: hidden;
+    opacity: 0;
+    transform: translateY(-8px);
+    pointer-events: none;
+    transition: opacity 180ms ease, transform 180ms ease, visibility 0s linear 180ms;
+  }
+  .app-nav.is-open {
+    visibility: visible;
+    opacity: 1;
+    transform: none;
+    pointer-events: auto;
+    transition: opacity 180ms ease, transform 180ms ease, visibility 0s;
+  }
+  /* Menu rows: comfortable ≥44px targets (0.75rem × 2 + the 1rem line)
+     and readable text — replaces the old .nav-link pill squeeze. */
+  .app-nav .nav-link { padding: 0.75rem 1.25rem; font-size: 1rem; }
   .new-chat-btn { padding: 0.4rem 0.3rem; }
   .new-chat-label { display: none; }
   .new-chat-btn svg { display: block; }
@@ -2248,3 +2314,13 @@ details.thinking .thinking-text ul { margin: 0 0 0.5rem; }
   .footer-inner { flex-direction: column; gap: 0.2rem; text-align: center; }
   main { padding-bottom: env(safe-area-inset-bottom, 0); }
 }
+
+/* Phase 46: prefers-reduced-motion stills the mobile menu — no
+   180ms slide+fade; open/close snaps (the visibility/opacity flip
+   applies instantly) and stays correct. BOTH states are named: the
+   .is-open rule (0,2,0) would otherwise out-specify a bare .app-nav
+   (0,1,0) and the OPEN transition would still animate. */
+@media (prefers-reduced-motion: reduce) {
+  .app-nav,
+  .app-nav.is-open { transition: none; }
+}
diff --git a/frontend/document.html b/frontend/document.html
index 77eed78..0167ea8 100644
--- a/frontend/document.html
+++ b/frontend/document.html
@@ -27,7 +27,14 @@
           <svg class="brand-mark" aria-hidden="true" viewBox="0 0 64 64"><path d="M32 4 55 18v28L32 60 9 46V18Z" fill="#121a2e" stroke="#6d78f2" stroke-width="4" stroke-linejoin="round"/><circle cx="32" cy="32" r="6.5" fill="#6d78f2"/><path d="M32 25.5V16M32 48v-9.5M25.5 32H16M48 32h-9.5" stroke="#22d3ee" stroke-width="3" stroke-linecap="round"/></svg>
           <span class="brand-text">Brain of <strong>Reese</strong></span>
         </span>
-        <nav class="app-nav" aria-label="Primary">
+        <!-- Phase 46 (owner permission 2026-08-27, `TODO.md` L9): the
+             mobile hamburger — visible ≤640px only (CSS); opens the nav as
+             an animated dropdown. Behavior: assets/header.js. -->
+        <button type="button" class="nav-toggle" id="nav-toggle"
+                aria-expanded="false" aria-controls="app-nav" aria-label="Menu">
+          <svg aria-hidden="true" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.7" stroke-linecap="round"><path d="M4 7h16M4 12h16M4 17h16"/></svg>
+        </button>
+        <nav class="app-nav" id="app-nav" aria-label="Primary">
           <a href="/" class="nav-link">Chat</a>
           <!-- Phase 19 (now every page — phase 34, owner confirmation
                2026-08-26): the Sources link is admin-only (owner
diff --git a/frontend/git-sources.html b/frontend/git-sources.html
index 006ce01..d8ed56a 100644
--- a/frontend/git-sources.html
+++ b/frontend/git-sources.html
@@ -24,7 +24,14 @@
         <svg class="brand-mark" aria-hidden="true" viewBox="0 0 64 64"><path d="M32 4 55 18v28L32 60 9 46V18Z" fill="#121a2e" stroke="#6d78f2" stroke-width="4" stroke-linejoin="round"/><circle cx="32" cy="32" r="6.5" fill="#6d78f2"/><path d="M32 25.5V16M32 48v-9.5M25.5 32H16M48 32h-9.5" stroke="#22d3ee" stroke-width="3" stroke-linecap="round"/></svg>
         <span class="brand-text">Brain of <strong>Reese</strong></span>
       </span>
-      <nav class="app-nav" aria-label="Primary">
+      <!-- Phase 46 (owner permission 2026-08-27, `TODO.md` L9): the
+           mobile hamburger — visible ≤640px only (CSS); opens the nav as
+           an animated dropdown. Behavior: assets/header.js. -->
+      <button type="button" class="nav-toggle" id="nav-toggle"
+              aria-expanded="false" aria-controls="app-nav" aria-label="Menu">
+        <svg aria-hidden="true" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.7" stroke-linecap="round"><path d="M4 7h16M4 12h16M4 17h16"/></svg>
+      </button>
+      <nav class="app-nav" id="app-nav" aria-label="Primary">
         <a href="/" class="nav-link">Chat</a>
         <!-- Phase 19 (now every page — phase 34, owner confirmation
              2026-08-26): the Sources link is admin-only (owner
diff --git a/frontend/index.html b/frontend/index.html
index eff0e0d..a1440ed 100644
--- a/frontend/index.html
+++ b/frontend/index.html
@@ -17,7 +17,14 @@
         <svg class="brand-mark" aria-hidden="true" viewBox="0 0 64 64"><path d="M32 4 55 18v28L32 60 9 46V18Z" fill="#121a2e" stroke="#6d78f2" stroke-width="4" stroke-linejoin="round"/><circle cx="32" cy="32" r="6.5" fill="#6d78f2"/><path d="M32 25.5V16M32 48v-9.5M25.5 32H16M48 32h-9.5" stroke="#22d3ee" stroke-width="3" stroke-linecap="round"/></svg>
         <span class="brand-text">Brain of <strong>Reese</strong></span>
       </span>
-      <nav class="app-nav" aria-label="Primary">
+      <!-- Phase 46 (owner permission 2026-08-27, `TODO.md` L9): the
+           mobile hamburger — visible ≤640px only (CSS); opens the nav as
+           an animated dropdown. Behavior: assets/header.js. -->
+      <button type="button" class="nav-toggle" id="nav-toggle"
+              aria-expanded="false" aria-controls="app-nav" aria-label="Menu">
+        <svg aria-hidden="true" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.7" stroke-linecap="round"><path d="M4 7h16M4 12h16M4 17h16"/></svg>
+      </button>
+      <nav class="app-nav" id="app-nav" aria-label="Primary">
         <a href="/" class="nav-link is-active" aria-current="page">Chat</a>
         <!-- Phase 19 (now every page — phase 34, owner confirmation
              2026-08-26): the Sources link is admin-only (owner
diff --git a/frontend/login.html b/frontend/login.html
index fb612e5..804031b 100644
--- a/frontend/login.html
+++ b/frontend/login.html
@@ -18,7 +18,14 @@
         <svg class="brand-mark" aria-hidden="true" viewBox="0 0 64 64"><path d="M32 4 55 18v28L32 60 9 46V18Z" fill="#121a2e" stroke="#6d78f2" stroke-width="4" stroke-linejoin="round"/><circle cx="32" cy="32" r="6.5" fill="#6d78f2"/><path d="M32 25.5V16M32 48v-9.5M25.5 32H16M48 32h-9.5" stroke="#22d3ee" stroke-width="3" stroke-linecap="round"/></svg>
         <span class="brand-text">Brain of <strong>Reese</strong></span>
       </span>
-      <nav class="app-nav" aria-label="Primary">
+      <!-- Phase 46 (owner permission 2026-08-27, `TODO.md` L9): the
+           mobile hamburger — visible ≤640px only (CSS); opens the nav as
+           an animated dropdown. Behavior: assets/header.js. -->
+      <button type="button" class="nav-toggle" id="nav-toggle"
+              aria-expanded="false" aria-controls="app-nav" aria-label="Menu">
+        <svg aria-hidden="true" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.7" stroke-linecap="round"><path d="M4 7h16M4 12h16M4 17h16"/></svg>
+      </button>
+      <nav class="app-nav" id="app-nav" aria-label="Primary">
         <a href="/" class="nav-link">Chat</a>
         <!-- Phase 19 (now every page — phase 34, owner confirmation
              2026-08-26): the Sources link is admin-only (owner
diff --git a/frontend/sources.html b/frontend/sources.html
index d79045a..4553b2b 100644
--- a/frontend/sources.html
+++ b/frontend/sources.html
@@ -17,7 +17,14 @@
         <svg class="brand-mark" aria-hidden="true" viewBox="0 0 64 64"><path d="M32 4 55 18v28L32 60 9 46V18Z" fill="#121a2e" stroke="#6d78f2" stroke-width="4" stroke-linejoin="round"/><circle cx="32" cy="32" r="6.5" fill="#6d78f2"/><path d="M32 25.5V16M32 48v-9.5M25.5 32H16M48 32h-9.5" stroke="#22d3ee" stroke-width="3" stroke-linecap="round"/></svg>
         <span class="brand-text">Brain of <strong>Reese</strong></span>
       </span>
-      <nav class="app-nav" aria-label="Primary">
+      <!-- Phase 46 (owner permission 2026-08-27, `TODO.md` L9): the
+           mobile hamburger — visible ≤640px only (CSS); opens the nav as
+           an animated dropdown. Behavior: assets/header.js. -->
+      <button type="button" class="nav-toggle" id="nav-toggle"
+              aria-expanded="false" aria-controls="app-nav" aria-label="Menu">
+        <svg aria-hidden="true" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.7" stroke-linecap="round"><path d="M4 7h16M4 12h16M4 17h16"/></svg>
+      </button>
+      <nav class="app-nav" id="app-nav" aria-label="Primary">
         <a href="/" class="nav-link">Chat</a>
         <!-- Phase 19 (now every page — phase 34, owner confirmation
              2026-08-26): the Sources link is admin-only (owner
diff --git a/frontend/tuning.html b/frontend/tuning.html
index 3862040..f121a59 100644
--- a/frontend/tuning.html
+++ b/frontend/tuning.html
@@ -17,7 +17,14 @@
         <svg class="brand-mark" aria-hidden="true" viewBox="0 0 64 64"><path d="M32 4 55 18v28L32 60 9 46V18Z" fill="#121a2e" stroke="#6d78f2" stroke-width="4" stroke-linejoin="round"/><circle cx="32" cy="32" r="6.5" fill="#6d78f2"/><path d="M32 25.5V16M32 48v-9.5M25.5 32H16M48 32h-9.5" stroke="#22d3ee" stroke-width="3" stroke-linecap="round"/></svg>
         <span class="brand-text">Brain of <strong>Reese</strong></span>
       </span>
-      <nav class="app-nav" aria-label="Primary">
+      <!-- Phase 46 (owner permission 2026-08-27, `TODO.md` L9): the
+           mobile hamburger — visible ≤640px only (CSS); opens the nav as
+           an animated dropdown. Behavior: assets/header.js. -->
+      <button type="button" class="nav-toggle" id="nav-toggle"
+              aria-expanded="false" aria-controls="app-nav" aria-label="Menu">
+        <svg aria-hidden="true" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.7" stroke-linecap="round"><path d="M4 7h16M4 12h16M4 17h16"/></svg>
+      </button>
+      <nav class="app-nav" id="app-nav" aria-label="Primary">
         <a href="/" class="nav-link">Chat</a>
         <!-- Phase 19 (now every page — phase 34, owner confirmation
              2026-08-26): the Sources link is admin-only (owner
diff --git a/tests/e2e/test_mobile_hamburger_nav.py b/tests/e2e/test_mobile_hamburger_nav.py
new file mode 100644
index 0000000..0ded8a8
--- /dev/null
+++ b/tests/e2e/test_mobile_hamburger_nav.py
@@ -0,0 +1,414 @@
+"""Phase 46 E2E (Playwright): the mobile hamburger dropdown nav.
+
+Story: ``.agent/user_stories/mobile-hamburger-nav.md``
+TODO.md L9 (owner permission 2026-08-27): "The navbar on mobile is way
+too squished. Make it a hamburger dropdown menu with a nice animation."
+
+Run in isolation (mock LLM; DB up: ``podman compose up -d db``):
+
+    uv run pytest tests/e2e/test_mobile_hamburger_nav.py -v --no-cov
+
+Contract under test: at ≤640px the nav links LEAVE the bar — a 44px
+``#nav-toggle`` hamburger opens ``#app-nav`` as an animated (180ms
+slide+fade) edge-to-edge dropdown with comfortable rows, the auth
+visibility contract intact INSIDE the menu; at >640px the bar is
+byte-identical to pre-phase-46 (hamburger absent, inline pills). No
+document is ever needed — the suite exercises the shared header only.
+
+The conftest ``page`` fixture is 1280×800, so the mobile tests create
+fresh 375×812 pages via the session ``browser`` fixture (one page per
+test; the reduced-motion test gets its own context).
+
+Test → story mapping (Playwright Mapping Rule):
+
+1. ``test_mobile_hamburger_visible_and_bar_roomy`` — 375px: the toggle
+   is a ≥44px visible button (``aria-expanded="false"``, closed), the
+   inline nav links are not visible in the bar (the closed dropdown is
+   opacity 0 + visibility hidden), and the page does not overflow
+   horizontally.
+2. ``test_anonymous_menu_contents`` — anonymous at 375px: the menu
+   shows EXACTLY one visible link ("Chat"); the three admin-only links
+   stay ``hidden`` inside the menu; the open flips ``aria-expanded``.
+3. ``test_admin_menu_contents`` — admin at 375px: the menu shows all
+   four links (the whoami reveal works inside the menu).
+4. ``test_link_click_navigates_and_closes`` — admin at 375px: clicking
+   "Sources" navigates to /sources.html and the menu on the arrival
+   page ships closed.
+5. ``test_esc_and_outside_close`` — Esc closes AND returns focus to the
+   toggle; an outside click does NOT close (accepted — see the test
+   docstring for why).
+6. ``test_animation_and_reduced_motion`` — motion allowed: the
+   180ms opacity/transform transition pair is live and the open flips
+   class + aria; ``reducedMotion: "reduce"``: no transition in EITHER
+   state (the .is-open state included — the specificity trap) and
+   open/close still works.
+7. ``test_desktop_unchanged`` — 1280×800 regression: the hamburger is
+   ``display: none`` and the inline nav renders in the bar exactly as
+   before (admin: all four links, all inside the header band).
+"""
+from __future__ import annotations
+
+import re
+
+from playwright.sync_api import Browser, Page, ViewportSize, expect
+
+from e2e.auth_helpers import login
+
+MOBILE: ViewportSize = {"width": 375, "height": 812}  # the story's phone viewport
+DESKTOP: ViewportSize = {"width": 1280, "height": 800}  # the conftest page size
+
+NAV_LINKS = ("#app-nav a[href='/']", "#nav-sources", "#nav-git-sources", "#nav-tuning")
+LINK_TEXTS = ("Chat", "Sources", "Git sources", "Tuning")
+
+
+def _mobile_page(browser: Browser) -> Page:
+    """A fresh 375×812 page (the conftest ``page`` is 1280×800)."""
+    return browser.new_page(viewport=MOBILE)
+
+
+def _wait_settled_anonymous(page: Page) -> None:
+    """Wait until whoami has resolved for the anonymous visitor (Sign in
+    visible — the phase-16 settled state the header pins)."""
+    expect(page.locator("#sign-in-link")).to_be_visible(timeout=10_000)
+
+
+def _wait_settled_admin(page: Page) -> None:
+    """Wait until whoami has resolved for the admin (Sign out visible)
+    AND the whoami reveal has un-hidden the admin-only nav links (the
+    menu-contents assertions must run on a settled auth state)."""
+    expect(page.locator("#sign-out-btn")).to_be_visible(timeout=10_000)
+    page.wait_for_function(
+        "() => !document.querySelector('#nav-sources').hasAttribute('hidden')",
+        timeout=10_000,
+    )
+
+
+def _visible_nav_links(page: Page) -> list[str]:
+    """The texts of the nav links that are actually visible (Playwright
+    visibility: non-empty box AND not visibility:hidden/display:none —
+    so the closed dropdown and the ``hidden`` admin links both count as
+    invisible)."""
+    return [
+        page.locator(sel).inner_text()
+        for sel in NAV_LINKS
+        if page.locator(sel).is_visible()
+    ]
+
+
+def _open_menu(page: Page) -> None:
+    page.click("#nav-toggle")
+    expect(page.locator("#nav-toggle")).to_have_attribute("aria-expanded", "true")
+    # to_have_class(string) is an EXACT match on the class attribute —
+    # the nav is "app-nav is-open", so match the token with a regex.
+    expect(page.locator("#app-nav")).to_have_class(re.compile(r"\bis-open\b"))
+    expect(page.locator("#app-nav")).to_have_css("opacity", "1")
+
+
+def _assert_menu_closed(page: Page) -> None:
+    expect(page.locator("#nav-toggle")).to_have_attribute("aria-expanded", "false")
+    assert "is-open" not in (page.locator("#app-nav").get_attribute("class") or ""), (
+        "the closed menu must not carry the .is-open state"
+    )
+
+
+# ---------------------------------------------------------------------------
+# 1. Bar: the toggle is a roomy 44px target and the nav is out of the bar
+# ---------------------------------------------------------------------------
+
+
+def test_mobile_hamburger_visible_and_bar_roomy(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC1/AC5: at 375px the bar carries a ≥44px ``#nav-toggle`` (closed,
+    ``aria-expanded="false"``), the inline nav links are NOT visible in
+    the bar (the closed dropdown is opacity 0 + visibility hidden — the
+    layout box is top:100% less the 8px slide offset, so the story's
+    opacity-0 branch is what pins it), and there is no horizontal
+    overflow — the old squished pills are gone, so the bar has room."""
+    page = _mobile_page(browser)
+    try:
+        page.goto(app_url)
+        _wait_settled_anonymous(page)
+
+        # The hamburger: a visible ≥44px×44px touch target (the phase-07
+        # floor), shipped closed.
+        toggle = page.locator("#nav-toggle")
+        expect(toggle).to_be_visible()
+        box = toggle.bounding_box()
+        assert box is not None, "the toggle must have a box"
+        assert box["width"] >= 44 and box["height"] >= 44, (
+            f"the toggle must be a ≥44px touch target, got "
+            f"{box['width']:.0f}×{box['height']:.0f}"
+        )
+        expect(toggle).to_have_attribute("aria-expanded", "false")
+
+        # The inline nav links are not visible in the bar: the closed
+        # dropdown is opacity 0 + visibility hidden. (The layout box is
+        # top:100% minus the 8px slide offset — inside the band — but
+        # invisible, which is the acceptance branch: opacity 0.)
+        assert page.evaluate(
+            "() => getComputedStyle(document.querySelector('#app-nav')).opacity"
+        ) == "0", "the closed menu must be opacity 0"
+        assert page.evaluate(
+            "() => getComputedStyle(document.querySelector('#app-nav')).visibility"
+        ) == "hidden", "the closed menu must be visibility hidden"
+        for sel in NAV_LINKS:
+            assert not page.locator(sel).is_visible(), (
+                f"{sel} must not be visible in the bar with the menu closed"
+            )
+
+        # No horizontal overflow at 375px (the old four squished text
+        # pills are gone from the bar).
+        assert page.evaluate(
+            "() => document.documentElement.scrollWidth"
+        ) <= page.evaluate("() => window.innerWidth"), (
+            "the 375px bar must not overflow horizontally"
+        )
+    finally:
+        page.close()
+
+
+# ---------------------------------------------------------------------------
+# 2. Menu contents per auth state (the whoami contract inside the menu)
+# ---------------------------------------------------------------------------
+
+
+def test_anonymous_menu_contents(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC2 (anonymous): at 375px the opened menu shows EXACTLY one
+    visible link — "Chat". The three admin-only links keep their
+    ship-hidden state INSIDE the menu (the phase-19/35 contract is
+    preserved by reusing the same <nav> element); opening flips
+    aria-expanded true."""
+    page = _mobile_page(browser)
+    try:
+        page.goto(app_url)
+        _wait_settled_anonymous(page)
+        _assert_menu_closed(page)
+
+        _open_menu(page)
+        assert _visible_nav_links(page) == ["Chat"], (
+            "anonymous: the menu must show exactly one visible link (Chat)"
+        )
+        for sel in ("#nav-sources", "#nav-git-sources", "#nav-tuning"):
+            expect(page.locator(sel)).to_be_hidden()
+
+        # A second click closes it again — aria-expanded round-trips.
+        page.click("#nav-toggle")
+        _assert_menu_closed(page)
+    finally:
+        page.close()
+
+
+def test_admin_menu_contents(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC2 (admin): at 375px the opened menu shows ALL FOUR links —
+    Chat / Sources / Git sources / Tuning — i.e. the whoami reveal
+    works inside the menu exactly as it does inline (one <nav>, one
+    set of links, the same hidden attributes header.js drives)."""
+    page = _mobile_page(browser)
+    try:
+        login(page, app_url, next="/")
+        _wait_settled_admin(page)
+
+        _open_menu(page)
+        assert _visible_nav_links(page) == list(LINK_TEXTS), (
+            f"admin: the menu must show all four links, got {_visible_nav_links(page)}"
+        )
+        for sel in NAV_LINKS:
+            expect(page.locator(sel)).to_be_visible()
+    finally:
+        page.close()
+
+
+# ---------------------------------------------------------------------------
+# 3. Link close + navigation
+# ---------------------------------------------------------------------------
+
+
+def test_link_click_navigates_and_closes(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC4: a menu link click navigates AND closes the menu — and the
+    arrival page ships the fresh (closed) header: aria-expanded false,
+    no .is-open, menu invisible."""
+    page = _mobile_page(browser)
+    try:
+        login(page, app_url, next="/")
+        _wait_settled_admin(page)
+
+        _open_menu(page)
+        expect(page.locator("#nav-sources")).to_be_visible()
+        page.click("#nav-sources")
+        expect(page).to_have_url(app_url + "/sources.html", timeout=15_000)
+
+        # The arrival page: a fresh header, shipped closed.
+        _assert_menu_closed(page)
+        expect(page.locator("#app-nav")).to_be_hidden()
+    finally:
+        page.close()
+
+
+# ---------------------------------------------------------------------------
+# 4. Esc close (+ focus return) and the accepted outside-click behavior
+# ---------------------------------------------------------------------------
+
+
+def test_esc_and_outside_close(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC4: Esc closes the menu AND returns focus to the toggle (the
+    opener — a keyboard user never loses their place).
+
+    Accepted behavior (NOT a defect, per the task-02 contract and story
+    AC 4): an OUTSIDE click does not close the menu. The locked close
+    set is Esc + link + resize — the story's AC 4 lists exactly those
+    three, and the owner-locked scope (2026-08-27) does not include a
+    backdrop click (there is no backdrop element at all — the menu is
+    the nav itself dropping out of the sticky header). This test pins
+    the menu STAYING OPEN on an outside click so an accidental
+    backdrop-close implementation cannot sneak in later."""
+    page = _mobile_page(browser)
+    try:
+        page.goto(app_url)
+        _wait_settled_anonymous(page)
+
+        # Esc closes + refocuses the opener.
+        _open_menu(page)
+        page.keyboard.press("Escape")
+        _assert_menu_closed(page)
+        assert page.evaluate("() => document.activeElement.id") == "nav-toggle", (
+            "Esc-close must return focus to the #nav-toggle opener"
+        )
+
+        # Outside click: the menu STAYS open (accepted behavior — the
+        # locked close set is Esc + link + resize, not backdrop click).
+        _open_menu(page)
+        page.locator("footer span").first.click()  # a neutral, non-link point
+        expect(page.locator("#nav-toggle")).to_have_attribute("aria-expanded", "true")
+        assert "is-open" in (page.locator("#app-nav").get_attribute("class") or ""), (
+            "accepted behavior: an outside click must NOT close the menu"
+        )
+        # …and the menu is still fully usable (Esc still settles it).
+        page.keyboard.press("Escape")
+        _assert_menu_closed(page)
+    finally:
+        page.close()
+
+
+# ---------------------------------------------------------------------------
+# 5. Animation + prefers-reduced-motion
+# ---------------------------------------------------------------------------
+
+
+def test_animation_and_reduced_motion(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC3: motion allowed — the menu carries the 180ms opacity/transform
+    transition pair and opening flips the .is-open class + aria-expanded
+    in lockstep. reducedMotion: "reduce" — no transition in EITHER state
+    (the .is-open rule is higher-specificity than a bare .app-nav rule,
+    so the override must name both — pinned here against the live
+    computed style) and open/close still works, instantly."""
+    # Motion allowed: the 180ms slide+fade pair is live.
+    page = _mobile_page(browser)
+    try:
+        page.goto(app_url)
+        _wait_settled_anonymous(page)
+        report = page.evaluate(
+            "() => { const cs = getComputedStyle(document.querySelector('#app-nav'));"
+            " return { duration: cs.transitionDuration, property: cs.transitionProperty };"
+            " }"
+        )
+        assert "0.18s" in report["duration"], (
+            f"the menu must transition in 180ms, got {report['duration']!r}"
+        )
+        assert "opacity" in report["property"] and "transform" in report["property"], (
+            f"the transition must cover the opacity/transform slide+fade, "
+            f"got {report['property']!r}"
+        )
+        # Opening flips class + aria together (the animated state).
+        _open_menu(page)
+        expect(page.locator("#nav-toggle")).to_have_attribute("aria-expanded", "true")
+        page.keyboard.press("Escape")
+        _assert_menu_closed(page)
+    finally:
+        page.close()
+
+    # Reduced motion: stills in both states, open/close still works.
+    context = browser.new_context(
+        reduced_motion="reduce", viewport=MOBILE
+    )
+    rpage = context.new_page()
+    try:
+        rpage.goto(app_url)
+        _wait_settled_anonymous(rpage)
+
+        def _stilled(el: str) -> str:
+            return rpage.evaluate(
+                f"() => getComputedStyle(document.querySelector('{el}')).transitionDuration"
+            )
+
+        assert _stilled("#app-nav") == "0s", (
+            f"reduced motion: closed state must not transition, got {_stilled('#app-nav')!r}"
+        )
+        rpage.click("#nav-toggle")
+        expect(rpage.locator("#nav-toggle")).to_have_attribute("aria-expanded", "true")
+        expect(rpage.locator("#app-nav")).to_have_class(re.compile(r"\bis-open\b"))
+        assert _stilled("#app-nav") == "0s", (
+            "reduced motion: the .is-open state must not transition either "
+            "(the override must out-specificity .app-nav.is-open)"
+        )
+        rpage.keyboard.press("Escape")
+        _assert_menu_closed(rpage)
+        assert not rpage.locator("#app-nav").is_visible(), (
+            "reduced motion: the closed menu must be invisible"
+        )
+    finally:
+        context.close()
+
+
+# ---------------------------------------------------------------------------
+# 6. Desktop regression: the bar is byte-identical to pre-phase-46
+# ---------------------------------------------------------------------------
+
+
+def test_desktop_unchanged(
+    browser: Browser, app_url: str, db_ready: None
+) -> None:
+    """AC6 (regression): at 1280×800 the hamburger is absent
+    (``display: none`` — outside the ≤640px block) and the inline nav
+    renders in the bar exactly as before — admin sees all four links,
+    every one of them INSIDE the header band (no dropdown at this
+    width; the phase-34/35 bar contract is intact)."""
+    page = browser.new_page(viewport=DESKTOP)
+    try:
+        login(page, app_url, next="/")
+        _wait_settled_admin(page)
+
+        # The hamburger is absent on desktop (global display:none).
+        toggle = page.locator("#nav-toggle")
+        expect(toggle).to_be_hidden()
+        assert page.evaluate(
+            "() => getComputedStyle(document.querySelector('#nav-toggle')).display"
+        ) == "none", "the toggle must be display:none outside the ≤640px block"
+
+        # The inline nav: all four links visible, each box inside the
+        # header band (the dropdown positioning only applies ≤640px).
+        expect(page.locator("#app-nav")).to_be_visible()
+        header_box = page.locator("header.app-header").bounding_box()
+        assert header_box is not None
+        for sel in NAV_LINKS:
+            link = page.locator(sel)
+            expect(link).to_be_visible()
+            box = link.bounding_box()
+            assert box is not None
+            assert box["y"] >= header_box["y"] - 1, f"{sel}: link is above the header"
+            assert box["y"] + box["height"] <= header_box["y"] + header_box["height"] + 1, (
+                f"{sel}: the inline link must sit inside the header band"
+            )
+        assert _visible_nav_links(page) == list(LINK_TEXTS)
+    finally:
+        page.close()
diff --git a/tests/e2e/test_shared_header.py b/tests/e2e/test_shared_header.py
index e341278..fc96574 100644
--- a/tests/e2e/test_shared_header.py
+++ b/tests/e2e/test_shared_header.py
@@ -119,7 +119,7 @@ def _bar_selector(page_kind: str) -> str:
     return ".doc-header .app-header" if page_kind == "viewer" else ".app-header"
 
 
-def assert_shared_bar(page: Page, admin: bool, page_kind: str) -> None:
+def assert_shared_bar(page: Page, admin: bool, page_kind: str, mobile: bool = False) -> None:
     """Assert the phase-19 shared-bar contract on the page the ``page``
     is already showing.
 
@@ -128,6 +128,13 @@ def assert_shared_bar(page: Page, admin: bool, page_kind: str) -> None:
     in the HTML, so "exactly one is visible" means /api/whoami resolved
     and header.js (``initSharedHeader``) did its toggle — before any
     assertion runs.
+
+    ``mobile`` (phase 46, owner permission 2026-08-27, ``TODO.md`` L9):
+    at ≤640px the nav links no longer sit inline — the bar carries the
+    44px ``#nav-toggle`` hamburger and the nav ships as the CLOSED
+    (invisible) dropdown. Per-role link visibility INSIDE the menu is
+    pinned by ``test_mobile_hamburger_nav.py`` (phase 46, task 03); this
+    helper pins the bar-level contract only.
     """
     # Settled auth state: exactly one of Sign in / Sign out is visible
     # (phase-16 semantics, now owned by the shared module).
@@ -147,14 +154,24 @@ def assert_shared_bar(page: Page, admin: bool, page_kind: str) -> None:
     # hidden and are revealed for admin (phase-16 UX revision, owner
     # permission 2026-08-23; the soft-gate page and the A10 API split
     # are untouched).
-    expect(page.locator(".app-nav a[href='/']")).to_be_visible()
-    for link_id in ("#nav-sources", "#nav-tuning"):
-        nav = page.locator(link_id)
-        assert nav.count() == 1, f"one {link_id} expected on the {page_kind} page"
-        if admin:
-            expect(nav).to_be_visible()
-        else:
-            expect(nav).to_be_hidden()
+    #
+    # Phase 46 (owner permission 2026-08-27, ``TODO.md`` L9): at ≤640px
+    # the links live in the #nav-toggle dropdown instead — the bar
+    # shows the hamburger and the nav is the closed (invisible +
+    # non-interactive) panel; the per-role link visibility inside the
+    # menu is pinned by test_mobile_hamburger_nav.py (phase 46 task 03).
+    if mobile:
+        expect(page.locator("#nav-toggle")).to_be_visible()
+        expect(page.locator("#app-nav")).to_be_hidden()
+    else:
+        expect(page.locator(".app-nav a[href='/']")).to_be_visible()
+        for link_id in ("#nav-sources", "#nav-tuning"):
+            nav = page.locator(link_id)
+            assert nav.count() == 1, f"one {link_id} expected on the {page_kind} page"
+            if admin:
+                expect(nav).to_be_visible()
+            else:
+                expect(nav).to_be_hidden()
 
     if page_kind == "viewer":
         # The document itself has settled (rendered, not Loading…/not-found)
@@ -342,6 +359,12 @@ def test_sign_out_from_viewer_returns_to_anonymous(
 # ---------------------------------------------------------------------------
 # 6. Mobile (375×812): 58px bars, no horizontal overflow, in BOTH auth
 #    states — the new pills never grow the bar
+#
+#    Phase 46 adaptation (owner permission 2026-08-27, ``TODO.md`` L9):
+#    at ≤640px the nav links leave the bar — the hamburger (#nav-toggle)
+#    is visible and the nav is the closed dropdown; the per-role link
+#    visibility inside the menu is pinned by
+#    test_mobile_hamburger_nav.py (phase 46, task 03).
 # ---------------------------------------------------------------------------
 
 
@@ -359,15 +382,16 @@ def test_mobile_bar_fits_and_heights_held(
         ):
             page.goto(app_url + path)
             # 58px at 375px is asserted inside assert_shared_bar…
-            assert_shared_bar(page, admin=admin, page_kind=kind)
-            # …and the pills (icon-only at ≤640px) fit without overflow.
+            assert_shared_bar(page, admin=admin, page_kind=kind, mobile=True)
+            # …and the pills (icon-only at ≤640px) + the hamburger fit
+            # without overflow.
             _assert_no_overflow(page, f"{kind} @375px (admin={admin})")
 
     # Anonymous: the two icon pills are Sign in + New chat.
     check_all(admin=False)
 
-    # Signed in: Sign out + the Sources nav link join the bars — and the
-    # bar never grows.
+    # Signed in: Sign out joins the bars (the admin-only nav links join
+    # the MENU, not the bar — phase 46) — and the bar never grows.
     login(page, app_url, next="/")
     expect(page).to_have_url(app_url + "/")
     check_all(admin=True)
diff --git a/tests/unit/test_hamburger_nav.py b/tests/unit/test_hamburger_nav.py
new file mode 100644
index 0000000..d3ae1e6
--- /dev/null
+++ b/tests/unit/test_hamburger_nav.py
@@ -0,0 +1,509 @@
+"""Unit: the mobile hamburger nav — markup + CSS contract (phase 46).
+
+TODO.md L9 (owner permission 2026-08-27): "The navbar on mobile is way too
+squished. Make it a hamburger dropdown menu with a nice animation."
+
+This module pins the source-level contract for tasks 01 and 02:
+
+* all SIX pages carry the identical ``#nav-toggle`` button (``aria-expanded``
+  / ``aria-controls="app-nav"`` / ``aria-label="Menu"``), positioned inside
+  the shared ``.header-inner`` row immediately before the nav — and the nav
+  itself keeps the single ``<nav class="app-nav" id="app-nav">`` (no
+  duplicated links, so the whoami reveal keeps working unchanged);
+* desktop is byte-identical to before: ``.nav-toggle { display: none }``
+  OUTSIDE any media query (the inline nav is untouched at >640px);
+* the ≤640px block turns the nav into the animated dropdown: the 44px
+  toggle, the edge-to-edge absolute panel (containing block = the sticky
+  ``.app-header``, z-index header+1), the closed state (invisible +
+  non-interactive), the ``.is-open`` state, the 180ms transition pair, the
+  comfortable menu rows, and the ``prefers-reduced-motion`` override;
+* the superseded ≤640px nav-pill squeeze rules are gone (the 900px tablet
+  block still squeezes the inline nav at 641–900px, and the action pills'
+  squeeze rules + the 58px bar height are untouched);
+* the header.js toggle behavior (task 02) is ONE module-owned binding —
+  the same import-time pattern as the sign-out/steering bindings: null-
+  safe lookups of ``#nav-toggle`` + ``#app-nav``, a ``setNavMenu`` that
+  syncs BOTH the ``.is-open`` class and ``aria-expanded``, a click
+  toggle, a delegated nav-link close, an Esc close that refocuses the
+  opener, and a matchMedia resize-back-to-desktop close; the binding
+  touches ONLY the container (the ship-hidden whoami links are left to
+  ``initSharedHeader``).
+
+The browser behavior (open/close, Esc, link-close, resize-close, the menu's
+animated states) is E2E-covered by ``tests/e2e/test_mobile_hamburger_nav.py``
+(task 03).
+"""
+from __future__ import annotations
+
+import re
+from pathlib import Path
+
+FRONTEND = Path(__file__).resolve().parents[2] / "frontend"
+ASSETS = FRONTEND / "assets"
+STYLES_CSS = ASSETS / "styles.css"
+
+#: The six pages of the app (phase 46: the shared bar contract extends to
+#: the phase-35 git-sources page — the hamburger is part of that bar).
+PAGES = (
+    FRONTEND / "index.html",
+    FRONTEND / "sources.html",
+    FRONTEND / "document.html",
+    FRONTEND / "git-sources.html",
+    FRONTEND / "login.html",
+    FRONTEND / "tuning.html",
+)
+
+NAV_TAG = '<nav class="app-nav" id="app-nav" aria-label="Primary">'
+
+
+def _text(path: Path) -> str:
+    assert path.is_file(), f"missing frontend file: {path}"
+    return path.read_text(encoding="utf-8")
+
+
+def _css() -> str:
+    """styles.css with comments stripped (a comment may legally carry
+    braces — e.g. the [hidden] rule documents the UA snippet — so the
+    brace-matching helpers below must never see them)."""
+    return re.sub(r"/\*.*?\*/", "", _text(STYLES_CSS), flags=re.S)
+
+
+def _media_block(css: str, query: str) -> str:
+    """The full text of the FIRST ``@media <query>`` block (brace-matched,
+    nested rules included verbatim)."""
+    m = re.search(re.escape(query) + r"[^{]*\{", css)
+    assert m, f"missing {query!r} media query in styles.css"
+    depth = 0
+    for i in range(m.end() - 1, len(css)):
+        if css[i] == "{":
+            depth += 1
+        elif css[i] == "}":
+            depth -= 1
+            if depth == 0:
+                return css[m.start() : i + 1]
+    raise AssertionError(f"unbalanced braces in {query!r} media block")
+
+
+def _global_css(css: str) -> str:
+    """The rules OUTSIDE any @media block (the desktop baseline), in file
+    order."""
+    out: list[str] = []
+    pos = 0
+    while True:
+        m = re.search(r"@media[^{]*\{", css[pos:])
+        if not m:
+            out.append(css[pos:])
+            break
+        start = pos + m.end() - 1  # the @media's own opening brace
+        depth = 0
+        i = start
+        while i < len(css):
+            if css[i] == "{":
+                depth += 1
+            elif css[i] == "}":
+                depth -= 1
+                if depth == 0:
+                    break
+            i += 1
+        out.append(css[pos:start])
+        pos = i + 1
+    return "".join(out)
+
+
+def _rule_block(css: str, selector: str) -> str:
+    """The first rule body for ``selector`` (e.g. ``.app-nav.is-open``)."""
+    m = re.search(re.escape(selector) + r"[^{}]*\{([^}]*)\}", css)
+    assert m, f"missing rule for {selector!r}"
+    return m.group(1)
+
+
+# ---------- markup: the identical toggle + labeled nav on all six pages ----------
+
+
+def test_all_six_pages_carry_the_hamburger_toggle() -> None:
+    """Every page carries the #nav-toggle button with the full aria
+    contract: a real button (type=button), aria-expanded defaulting to
+    "false", aria-controls pointing at the nav, the accessible name
+    "Menu", and the 3-line SVG icon (aria-hidden — the name comes from
+    aria-label). Exactly once per page (no duplicated control)."""
+    for html in PAGES:
+        text = _text(html)
+        tags = re.findall(r"<button[^>]*id=\"nav-toggle\"[^>]*>", text)
+        assert len(tags) == 1, f"{html.name}: exactly one #nav-toggle (found {len(tags)})"
+        tag = tags[0]
+        assert 'type="button"' in tag, f"{html.name}: the toggle must be a real button"
+        assert 'class="nav-toggle"' in tag, f"{html.name}: the toggle class is missing"
+        assert 'aria-expanded="false"' in tag, (
+            f"{html.name}: the toggle ships closed (aria-expanded=false)"
+        )
+        assert 'aria-controls="app-nav"' in tag, (
+            f"{html.name}: aria-controls must point at the nav's id"
+        )
+        assert 'aria-label="Menu"' in tag, f"{html.name}: the toggle is labeled 'Menu'"
+        # The button body is the aria-hidden 3-line hamburger icon.
+        end = text.find("</button>", text.find('id="nav-toggle"'))
+        body = text[text.find('id="nav-toggle"') : end]
+        assert 'aria-hidden="true"' in body, f"{html.name}: the icon is aria-hidden"
+        assert "M4 7h16M4 12h16M4 17h16" in body, (
+            f"{html.name}: the icon is the 3-line hamburger path"
+        )
+
+
+def test_toggle_lives_in_the_shared_bar_right_before_the_nav() -> None:
+    """The toggle is part of the shared bar block: inside the
+    .header-inner row, immediately before the <nav> — the same position
+    on every page (phase-34 identical-bar contract)."""
+    for html in PAGES:
+        text = _text(html)
+        inner = text.find('<div class="container header-inner">')
+        assert inner != -1, f"{html.name}: missing the shared .header-inner row"
+        toggle = text.find('id="nav-toggle"', inner)
+        nav = text.find(NAV_TAG, inner)
+        assert -1 < toggle < nav, (
+            f"{html.name}: the toggle must sit in the shared row, before the nav"
+        )
+        # The toggle is the only new element between the brand and the nav
+        # (no stray control broke the phase-34 order).
+        segment = text[inner:nav]
+        assert 'class="brand"' in segment, f"{html.name}: brand precedes the toggle"
+        assert 'id="steering-toggle"' not in segment, (
+            f"{html.name}: the toggle must not follow the action controls"
+        )
+
+
+def test_all_six_pages_carry_the_labeled_nav_with_id() -> None:
+    """The nav keeps its single element + label and gains ONLY the id
+    (the whoami reveal targets the same four links — no duplicated
+    markup, so the phase-19/35 visibility rules apply inside the menu
+    exactly as before)."""
+    for html in PAGES:
+        text = _text(html)
+        assert text.count(NAV_TAG) == 1, (
+            f"{html.name}: exactly one <nav class='app-nav' id='app-nav' "
+            "aria-label='Primary'> (no duplicated nav)"
+        )
+        # The four links, all still shipping inside that nav (the
+        # admin-only three keep their hidden attributes).
+        region = text[text.find(NAV_TAG) : text.find("</nav>")]
+        for link in ('href="/" class="nav-link', 'id="nav-sources" hidden',
+                     'id="nav-git-sources" hidden', 'id="nav-tuning" hidden'):
+            assert link in region, f"{html.name}: nav lost {link!r}"
+
+
+# ---------- CSS: desktop byte-identical, mobile dropdown ----------
+
+
+def test_toggle_is_absent_on_desktop_outside_media_queries() -> None:
+    """Global (non-media) CSS hides the toggle — the desktop bar is
+    byte-identical to pre-phase-46 (the ≤640px block re-displays it)."""
+    css = _global_css(_css())
+    block = _rule_block(css, ".nav-toggle")
+    assert "display: none" in block, (
+        ".nav-toggle must be display:none outside media queries (desktop)"
+    )
+
+
+def test_header_z_index_is_20_so_the_dropdown_uses_21() -> None:
+    """The dropdown's z-index is the header's z-index + 1 — pinned as a
+    RELATIONSHIP (if the header z-index ever moves, the menu must move
+    with it)."""
+    css = _css()
+    header = _rule_block(_global_css(css), ".app-header")
+    m = re.search(r"z-index:\s*(\d+)", header)
+    assert m, "the .app-header must keep its z-index"
+    assert int(m.group(1)) + 1 == 21, "the dropdown is pinned at header+1 (21)"
+    mobile = _media_block(css, "@media (max-width: 640px)")
+    assert "z-index: 21" in _rule_block(mobile, ".app-nav")
+
+
+def test_mobile_block_renders_the_44px_toggle() -> None:
+    """At ≤640px the toggle is a 44px×44px button (the phase-07 touch
+    floor), ghost look like the other pills, a hover state in the
+    .steering-toggle:hover family, and a SIZED icon (an unsized inline
+    SVG defaults to 300px and would blow the bar out at 360px).
+    :focus-visible needs no rule — the global 3px outline applies."""
+    mobile = _media_block(_css(), "@media (max-width: 640px)")
+    block = _rule_block(mobile, ".nav-toggle")
+    for decl in (
+        "display: inline-flex",
+        "align-items: center",
+        "justify-content: center",
+        "width: 44px",
+        "height: 44px",
+        "border: 0",
+        "border-radius: var(--radius-sm)",
+        "cursor: pointer",
+    ):
+        assert decl in block, f"mobile .nav-toggle missing {decl!r}"
+    assert "color: var(--ink)" in block, "the icon ink is the page ink"
+    hover = _rule_block(mobile, ".nav-toggle:hover")
+    assert "background: var(--brand-soft)" in hover
+    assert "color: var(--brand-ink)" in hover, (
+        "hover matches the .steering-toggle:hover family (≈6.9:1 pair)"
+    )
+    icon = _rule_block(mobile, ".nav-toggle svg")
+    assert "width: 20px" in icon and "height: 20px" in icon, (
+        "the hamburger icon must be sized (no 300px default)"
+    )
+
+
+def test_mobile_block_turns_the_nav_into_the_dropdown() -> None:
+    """The closed (default) mobile nav is the invisible, non-interactive
+    dropdown panel: absolute edge-to-edge under the sticky .app-header
+    (the containing block — .header-inner is not positioned), the
+    surface background + hairline + existing shadow token, and the
+    slide+fade closed state with the 180ms transition pair."""
+    mobile = _media_block(_css(), "@media (max-width: 640px)")
+    block = _rule_block(mobile, ".app-nav")
+    for decl in (
+        "position: absolute",
+        "top: 100%",
+        "left: 0",
+        "right: 0",
+        "flex-direction: column",
+        "background: var(--surface)",
+        "border-bottom: 1px solid var(--line)",
+        "box-shadow: var(--shadow-lg)",
+        "z-index: 21",
+        # closed state — invisible and non-interactive
+        "visibility: hidden",
+        "opacity: 0",
+        "transform: translateY(-8px)",
+        "pointer-events: none",
+        # the 180ms slide+fade (visibility is the delayed snap)
+        "transition: opacity 180ms ease, transform 180ms ease, visibility 0s linear 180ms",
+    ):
+        assert decl in block, f"mobile .app-nav dropdown missing {decl!r}"
+    assert "gap: 0" in block, "column menu rows stack with no pill gap"
+    assert "margin-left: 0" in block, (
+        "the desktop margin-left:auto must not shift the absolute panel"
+    )
+
+
+def test_mobile_open_state_is_the_only_opener() -> None:
+    """The .is-open state (added by task 02's header.js) flips every
+    closed-state property back, with the matching 180ms transition and
+    an UNDELAYED visibility snap (the menu can never linger visible but
+    dead while closing)."""
+    mobile = _media_block(_css(), "@media (max-width: 640px)")
+    block = _rule_block(mobile, ".app-nav.is-open")
+    for decl in (
+        "visibility: visible",
+        "opacity: 1",
+        "transform: none",
+        "pointer-events: auto",
+        "transition: opacity 180ms ease, transform 180ms ease, visibility 0s",
+    ):
+        assert decl in block, f".app-nav.is-open missing {decl!r}"
+
+
+def test_mobile_menu_rows_are_comfortable_targets() -> None:
+    """The menu rows supersede the pill-squeeze: 1rem text with 0.75rem
+    vertical padding (≥44px with the line box) — the old 0.72rem /
+    0.3rem 0.25rem squeeze is gone from the ≤640px block."""
+    mobile = _media_block(_css(), "@media (max-width: 640px)")
+    rows = _rule_block(mobile, ".app-nav .nav-link")
+    assert "padding: 0.75rem 1.25rem" in rows
+    assert "font-size: 1rem" in rows
+    # The superseded squeeze rules are GONE from the ≤640px block…
+    assert "0.72rem" not in mobile, "the 0.72rem nav-pill font is superseded"
+    assert "padding: 0.3rem 0.25rem" not in mobile, (
+        "the 0.3rem 0.25rem nav-pill padding is superseded"
+    )
+    assert "gap: 0.05rem" not in mobile, "the 0.05rem nav gap is superseded"
+    # …while the rest of the block is untouched: the tablet block still
+    # squeezes the inline nav at 641–900px, the action pills keep their
+    # icon-only squeeze, and the 58px bar height is pinned.
+    tablet = _media_block(_css(), "@media (max-width: 900px)")
+    assert re.search(r"\.nav-link\s*\{[^}]*0\.85rem", tablet), (
+        "the 900px tablet squeeze of the inline nav must be untouched"
+    )
+    assert "gap: 0.15rem" in tablet, "the 900px nav gap squeeze must be untouched"
+    for untouched in (
+        ".new-chat-label { display: none; }",
+        ".auth-label { display: none; }",
+        ".sync-label { display: none; }",
+        ":root { --header-h: 58px; }",
+    ):
+        assert untouched in mobile, f"the ≤640px block lost {untouched!r}"
+
+
+def test_reduced_motion_stills_the_menu() -> None:
+    """prefers-reduced-motion kills the 180ms slide+fade in BOTH states —
+    open/close snaps (the visibility/opacity flip applies instantly) and
+    stays correct. The override must name .app-nav.is-open too: that rule
+    carries higher specificity (0,2,0) than a bare .app-nav (0,1,0), so
+    without it the OPEN transition would still animate under the
+    preference (verified live in Chromium, phase 46 task 03)."""
+    css = _css()
+    blocks = []
+    for m in re.finditer(r"@media \(prefers-reduced-motion: reduce\)[^{]*\{", css):
+        depth = 0
+        for i in range(m.end() - 1, len(css)):
+            if css[i] == "{":
+                depth += 1
+            elif css[i] == "}":
+                depth -= 1
+                if depth == 0:
+                    blocks.append(css[m.start() : i + 1])
+                    break
+    assert any(
+        ".app-nav.is-open" in b and "transition: none" in b for b in blocks
+    ), (
+        "a prefers-reduced-motion block must still .app-nav in BOTH the "
+        "closed and .is-open states (specificity: a bare .app-nav rule "
+        "loses to .app-nav.is-open)"
+    )
+
+
+# ---------- header.js: the module-owned toggle binding (task 02) ----------
+
+HEADER_JS = ASSETS / "header.js"
+
+
+def _js() -> str:
+    return _text(HEADER_JS)
+
+
+def _hamburger_section(js: str) -> str:
+    """The header.js mobile-hamburger section (from its banner comment to
+    the next section banner), so the pins target the binding and not
+    unrelated code that happens to mention the same ids."""
+    start = js.find("/* ---------- mobile hamburger")
+    assert start != -1, "missing the mobile hamburger section in header.js"
+    end = js.find("/* ----------", start + 1)
+    assert end != -1, "the hamburger section must end before the next section"
+    return js[start:end]
+
+
+def _js_clean(code: str) -> str:
+    """JS with block + line comments stripped (comments may legally
+    contain keywords — the pins below must match executable code
+    only). The hamburger section carries no string literals with ``//``
+    in them, so the line-comment strip is safe here."""
+    code = re.sub(r"/\*.*?\*/", "", code, flags=re.S)
+    return re.sub(r"//[^\n]*", "", code)
+
+
+def test_header_js_looks_up_toggle_and_nav_null_safe() -> None:
+    """The binding follows the module's import-time pattern (like the
+    sign-out binding): look up #nav-toggle and #app-nav with
+    querySelector at import, and guard the whole binding block behind
+    ``navToggle && appNav`` — a page lacking either element is a
+    complete no-op."""
+    js = _js()
+    assert 'document.querySelector("#nav-toggle")' in js, (
+        "header.js must look up the #nav-toggle button"
+    )
+    assert 'document.querySelector("#app-nav")' in js, (
+        "header.js must look up the #app-nav container"
+    )
+    section = _hamburger_section(js)
+    assert "if (navToggle && appNav)" in section, (
+        "the binding block must be null-safe (navToggle && appNav guard)"
+    )
+
+
+def test_set_nav_menu_syncs_both_class_and_aria() -> None:
+    """The single state setter syncs BOTH surfaces at once — the
+    animated ``.is-open`` class on the nav AND the toggle's
+    aria-expanded (true/false) — so the ARIA state can never drift
+    from the visual state."""
+    section = _hamburger_section(_js())
+    assert "function setNavMenu(open)" in section, (
+        "a setNavMenu state setter must own the open/close transition"
+    )
+    assert 'appNav.classList.toggle("is-open", open)' in section, (
+        "setNavMenu must set/unset the .is-open class on the nav"
+    )
+    assert 'navToggle.setAttribute("aria-expanded"' in section, (
+        "setNavMenu must keep aria-expanded in sync"
+    )
+    assert '"true"' in section and '"false"' in section, (
+        "aria-expanded must be set to the explicit true/false strings"
+    )
+
+
+def test_click_on_the_toggle_toggles_the_menu() -> None:
+    """Clicking the toggle flips the CURRENT state (read from the
+    .is-open class, not a local boolean — a second binding could
+    never desync it)."""
+    section = _hamburger_section(_js())
+    assert 'navToggle.addEventListener("click"' in section, (
+        "the toggle button must own the click-to-open/close binding"
+    )
+    assert "setNavMenu(!appNav.classList.contains(\"is-open\"))" in section, (
+        "the click must toggle the menu off its current .is-open state"
+    )
+
+
+def test_delegated_nav_link_click_closes_the_menu() -> None:
+    """A click on ANY nav link (delegated on the nav container — the
+    links keep their hidden/whoami contract, so no per-link binding)
+    shuts the menu; the navigation then proceeds normally."""
+    section = _hamburger_section(_js())
+    assert 'appNav.addEventListener("click"' in section, (
+        "link-close must be delegated on the nav container"
+    )
+    assert "e.target.closest(\"a\")" in section, (
+        "the delegation must hit-test for a link (e.target.closest('a'))"
+    )
+    assert "setNavMenu(false)" in section, "a link click must close the menu"
+
+
+def test_escape_closes_the_menu_and_refocuses_the_opener() -> None:
+    """Esc (document-level keydown) closes the menu only while it is
+    open, and focus returns to the toggle — the opener — so a keyboard
+    user never loses their place."""
+    section = _js_clean(_hamburger_section(_js()))
+    assert 'document.addEventListener("keydown"' in section, (
+        "Esc-close must be a document-level keydown binding"
+    )
+    assert 'e.key === "Escape"' in section, "the handler must match the Escape key"
+    assert 'appNav.classList.contains("is-open")' in section, (
+        "Esc must act only while the menu is open"
+    )
+    assert "setNavMenu(false)" in section, "Esc must close the menu"
+    assert "navToggle.focus()" in section, (
+        "Esc-close must return focus to the toggle (the opener)"
+    )
+
+
+def test_resizing_back_to_desktop_closes_the_menu() -> None:
+    """Crossing back above 640px drops the open state (matchMedia
+    change): the inline nav reappears and aria-expanded stays honest
+    (the ≤640px CSS scopes .is-open anyway, but the class is dropped
+    so a resize round-trip never ships a stale true). The modern
+    addEventListener API is used with the older addListener as a
+    defensive fallback."""
+    section = _hamburger_section(_js())
+    assert 'window.matchMedia("(max-width: 640px)")' in section, (
+        "the resize cleanup must watch the SAME ≤640px breakpoint as the CSS"
+    )
+    assert "if (!mq.matches) setNavMenu(false)" in section, (
+        "leaving mobile (mq no longer matches) must close the menu"
+    )
+    assert 'mq.addEventListener("change"' in section, (
+        "the modern MediaQueryList listener must be used"
+    )
+    assert "mq.addListener(" in section, "the older-engine addListener fallback"
+
+
+def test_the_binding_toggles_only_the_container() -> None:
+    """The auth visibility contract is untouched: the binding never
+    assigns ``.hidden`` and never touches the whoami links — hidden
+    links stay hidden inside the menu, exactly as on the inline bar.
+    Only the .is-open container class + aria-expanded move."""
+    section = _js_clean(_hamburger_section(_js()))
+    assert ".hidden" not in section, (
+        "the hamburger binding must not hide/reveal any element"
+    )
+    for link in ("nav-sources", "nav-git-sources", "nav-tuning"):
+        assert link not in section, (
+            f"the hamburger binding must not touch the {link!r} link"
+        )
+    # The only class the section manipulates is the container's state.
+    class_toggles = re.findall(r"classList\.(?:add|remove|toggle)\(\s*\"([^\"]+)\"", section)
+    assert class_toggles == ["is-open"], (
+        f"only the container .is-open class may move (found {class_toggles})"
+    )