docs(tiles): the count menu, the open/close animation and the paced open

- docs/tile-grid-plan.md: owner decision 10 (right-click Tiles is a
  2 / 4 / 6 count menu, default 6, remembered per device; the session
  picker is gone; decision 8's "picker on right-click" and "exactly the
  stored set" superseded) with the owner's answers on the details; three
  as-built bullets (the count menu, the animation, painting first); the
  Tiles-button bullet rewritten for the count; the entry points, the
  capacity note, the multi-user row and the Escape invariant follow.
- docs/architecture-invariants.md: the Opening paragraph rewritten (the
  count, the stored grid in its cells, the menu owning its Escape, the
  paced connect and focusOnConnect, the motion rules); the z-index list
  names the count menu and the closing grid's still copy.
- CLAUDE.md: the tile grid paragraph and the z-index line.
- Wiki: Tile Grid (the click, the count menu, the animation, reduced
  motion) and Keyboard Shortcuts (right-click Tiles).

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

docs/architecture-invariants.md

@@ -809,7 +809,7 @@ Further detail: with many sessions the horizontal strip stops being scannable, w
 
 ⚠️ **Chords.** `toggle-tile-grid` (Ctrl+Shift+G), `focus-tile-*` (Alt+Shift+Arrows), `move-tile-*` (Ctrl+Shift+Arrows), `zoom-tile` (Alt+Shift+Enter) and `remove-tile` (unbound) are registry entries kept OUT of `SHORTCUT_ACTIONS`: `tileShortcutFor` decides whether one applies (the toggle while the grid is open, or where one could open AND `showTileGridButton` is on, an owner decision: with the setting off the chord is inert and passes through like any unbound key; the rest only while it is open), the capture handler dispatches it, and the main terminal's and every tile's xterm key handler return false for it, for every event type and BEFORE the Shift+Enter gate (Alt+Shift+Enter would otherwise send `S-Enter`). Outside the grid the focus chords reach the terminal untouched. The move chords also apply while a tile is zoomed (a no-op, so their keys never reach the CLI). The arrow chords, focus and move, never apply in a text field other than xterm's own textarea (`isTextFieldTarget`), where shifted arrows select.
 
-⚠️ **Opening.** The Tiles button's click and `Ctrl+Shift+G` are one function, `toggleTileGrid` (owner decision 8), so the two cannot drift. It opens the grid at once on `tileGridOpenSet` (constants.js, pure): (a) the stored grid if any of its sessions survive, opened EXACTLY (`openTileGrid(..., { mergeSplit: false })`: an open split closes and its sessions do not join), (b) else an open split's two sessions, (c) else the picker's list (tab order, no detached sessions) up to `_tileGridLimit().capacity`, the active session always included and focused. Ctrl/Cmd+click with the grid closed opens the same set plus the clicked session. The picker is on right-click (`oncontextmenu`, which calls `preventDefault` for the browser menu); with the grid open it is preselected with the current tiles and Open REPLACES them (close without reselect, null `activeSessionId`, reopen, as "Open group as tiles" does).
+⚠️ **Opening.** The Tiles button's click and `Ctrl+Shift+G` are one function, `toggleTileGrid` (owner decision 8), so the two cannot drift. It opens the grid at once with the remembered count of tiles (`codeman:tile-count`, 2, 4 or 6, default 6, owner decision 10; at most `_tileGridLimit().capacity`), on `tileGridOpenSet` (constants.js, pure): (a) the stored grid if any of its sessions survive (an open split closes and is not seeded first: `openTileGrid(..., { mergeSplit: false })`), (b) else an open split's two sessions, (c) else the open sessions in tab order (no detached ones), the active session always included and focused; then `tileGridSetForCount` trims it from the end (the session to focus kept) or fills it from tab order to the count. A stored grid comes back with its tiles in their cells (`reformTileCells`: a count change is a shape change under `fitTileCells`, the added tiles fill the empty cells first): the count supersedes decision 8's "exactly the stored set", and only the page-load restore brings back exactly what was stored. Ctrl/Cmd+click with the grid closed opens the count in total, the clicked session among them and focused. Right-click (`oncontextmenu`, which also fires for Shift+F10 and the Menu key, and calls `preventDefault` for the browser menu) is the 2 / 4 / 6 count menu (`openTileCountMenu`); with the grid open a pick re-forms it (`_reformTileGrid`: the focused tile always stays, every joining tile is mounted and laid out before any connects, so each fits once). ⚠️ The menu owns its Escape: the global handler closes it alone and gives the keyboard back to the Tiles button, like the tab-group menu. ⚠️ Opening builds the tiles' terminals one per animation frame (`_connectTilesPaced`, the focused one first, a run token stops a stale run), so `openTileGrid` returns before they exist: a focus asked for meanwhile is handed over in `_connectTile` (`focusOnConnect`), never for `focus: false`, and `_connectTile` connects a tile once (`entry.connected`, reset by `_remountTile`). ⚠️ Motion (the grid's own, on by default): tiles enter staggered (`.tile--entering`, `--tile-enter-index`), a terminal stays transparent until its first capture lands (`.tile--revealing`, cleared by the load queue's idle, 15 s backstop), and the toggle's close leaves an inert cloned still copy (`_ghostTileGrid`, no xterm or socket) that holds until the single view's `selectSession` settles (at most 700 ms) and then fades; every keyframe animates opacity and transform only (FitAddon reads the untransformed box, so still one PTY resize per tile), nothing moves and no copy is made under `prefers-reduced-motion`, and `.main.webview-active` hides the copy.
 
 ⚠️ **zh-CN.** Every string the grid puts on screen has its own entry in i18n.js's `ZH_CN` (or a `translateDynamic` pattern for counts, exit codes and the header tooltip's state plus duration, which requires the duration: bare state words stay out of the table, see mobile-overview.js), so nothing reaches the generic leading-verb fallback. `test/tile-grid-i18n.test.ts` drives the real tile code through every state that writes text, harvests each string and requires a full translation (and the same English back in `en`); a new tile string needs its entry or that test fails. Session and group names stay user text (`data-i18n-skip`). ⚠️ A refresh that skips unchanged text must compare with the last ENGLISH value it set (`entry.headerLabel`, `entry.overlayLabel`, `entry.zoomLabel`), never the DOM: in zh-CN the DOM holds the translation, so a DOM compare rewrites English on every `session:updated` for the observer to translate again.
 
@@ -1005,7 +1005,7 @@ Tests: `test/mobile-prompt-composer.test.ts` (in the CI gate, deliberately not u
 
 ### Z-index layers
 
-**Z-index layers**: subagent windows (1000), split picker menu (1000, `.split-picker-menu`), Tiles picker (1000, `.tile-picker-menu`), plan agents (1100), mobile/tablet fixed header (1200, `mobile.css`), modals on ≤768px (1300 — must beat the fixed header or the modal close button is buried), log viewers (2000), connection-loss overlay (2500, above the fixed header and modals), image popups (3000), response viewer (5000, backdrop 4999), file-preview overlay (5100 — must outrank the response viewer, which can launch it; at its old 2000 a path clicked in the chat opened BEHIND the chat), toasts/path picker (10000+, deliberately above the preview), the custom-model center-status banner (10001, `.center-status-banner` — `[hidden]` must re-assert `display: none` over its own `display: flex`, same trap as `.home-sessions[hidden]`, or `dismiss()` leaves an invisible click-blocker dead centre on screen), the swap-confirm and context-warning modals (10010, `#customModelSwapConfirmModal`/`#customModelContextWarningModal` — must clear both the plain `.modal` z-index of 1000 and the center-status banner it can appear over), terminal touch-selection bar (900 — above terminal content and the local-echo overlay, deliberately BELOW floating agent windows so it can never cover their controls), local echo overlay (7), iOS IME composition preview (EFFECTIVE layer depends on its home: with local echo on it is part of the local echo overlay at 7, drawn by `setComposition()` as an underlined tail after the pending text; with local echo off it is a span at z-index 6 inside `.xterm-helpers`, but `.xterm-helpers` is its own z-index 5 stacking context, so the span's effective layer is 5. That is below the overlay's 7, which is why the span cannot be used while the overlay holds text: typed text never reaches the PTY before Enter, the PTY cursor that places the span stays at the prompt start, and the overlay's opaque line div covers it).
+**Z-index layers**: subagent windows (1000), split picker menu (1000, `.split-picker-menu`), Tiles count menu (1000, `.tile-count-menu`), the closing grid's still copy (`.tile-grid-ghosts`, z-index 3 inside `.main`, over the single view coming back; hidden under `.main.webview-active`), plan agents (1100), mobile/tablet fixed header (1200, `mobile.css`), modals on ≤768px (1300 — must beat the fixed header or the modal close button is buried), log viewers (2000), connection-loss overlay (2500, above the fixed header and modals), image popups (3000), response viewer (5000, backdrop 4999), file-preview overlay (5100 — must outrank the response viewer, which can launch it; at its old 2000 a path clicked in the chat opened BEHIND the chat), toasts/path picker (10000+, deliberately above the preview), the custom-model center-status banner (10001, `.center-status-banner` — `[hidden]` must re-assert `display: none` over its own `display: flex`, same trap as `.home-sessions[hidden]`, or `dismiss()` leaves an invisible click-blocker dead centre on screen), the swap-confirm and context-warning modals (10010, `#customModelSwapConfirmModal`/`#customModelContextWarningModal` — must clear both the plain `.modal` z-index of 1000 and the center-status banner it can appear over), terminal touch-selection bar (900 — above terminal content and the local-echo overlay, deliberately BELOW floating agent windows so it can never cover their controls), local echo overlay (7), iOS IME composition preview (EFFECTIVE layer depends on its home: with local echo on it is part of the local echo overlay at 7, drawn by `setComposition()` as an underlined tail after the pending text; with local echo off it is a span at z-index 6 inside `.xterm-helpers`, but `.xterm-helpers` is its own z-index 5 stacking context, so the span's effective layer is 5. That is below the overlay's 7, which is why the span cannot be used while the overlay holds text: typed text never reaches the PTY before Enter, the PTY cursor that places the span stays at the prompt start, and the overlay's opaque line div covers it).
 
 ## Security layers