Collapsible lanes — frontmatter-backed slim strips outside the width division

A lane folds to a fixed slim vertical strip carrying its glyph, its card-count
badge and its title turned on its side, and the strip is deliberately not part
of the window's division: the expanded lanes' units divide what is left once
each folded strip's fixed width has come off the top, so folding a lane is a
re-divide trigger of the Show/Hide Trash family — the window never moves and
the siblings grow into what the lane gave up.

The state is a first-class lane frontmatter key, `collapsed: true`, and
document state exactly as `width` is: the files are the board, so an agent
folds a lane by writing one key. Absent means expanded, expanding removes the
key rather than writing `false` (the remove-at-default family beside a
one-unit `width`, the empty rename's `title` and the None well's
`background`), and the lane's `width` rides along untouched so expanding
restores the lane the user had. The read is `width`'s leniency one type over —
a boolean scalar or a quoted boolean word reads as itself, everything else has
no reading at all and renders as expanded, bytes preserved either way.

Toggling is the header's always-visible collapse chevron, the lane context
menu's single Collapse Lane / Expand Lane row, and a plain click anywhere on
the strip; a modified click on the strip stays the ordinary selection grammar,
so a folded lane is still selectable by pointer. The title reads bottom-up and
is justified to the top of the room below the strip's chrome (owner ruling
2026-08-08), truncating against the strip's own height.

While folded the lane draws no cards at all, which is what makes every
exclusion true by construction rather than by a guard per gesture: no card
face means no marquee target and no navigation frame, and no registered grid
means the masonry's drop zones have nothing to resolve against. What did need
code is the half that names absolute destinations — the option-arrow jumps and
the arrow seed scan past a folded lane, the lane domain's down-arrow is inert
on one, and New Card skips it (a selection inside one falls through to the
last-active lane, the stale selection's rule). A drop on the strip appends at
the lane's end, cards and Finder files alike, with an accent edge standing in
for the shadow the strip has no masonry to open; there is no hover-to-auto-
expand yet. Lane reorder works on the strip, and a dragged folded lane carries
its fold, so its shadow and its replica are the strip rather than its units.

The write is `writeLaneWidths` clause for clause — one `updateIndex` bracket,
the same stamp behaviour, the same three do-nothing paths — with two new
`WriteOperation` cases and two new undo verbs rather than one of each, because
a banner or an Edit-menu row that said "resize" after Collapse Lane would name
a control the user never touched.

Claude-Session: https://claude.ai/code/session_014PtZdPwqZuqEDLc6wZMtEy

Kanban/UI/Board/NavigationMath.swift

@@ -13,7 +13,11 @@ import CoreGraphics
 ///
 /// **It is also how the hidden trash stays invisible for free**: a hidden column registers nothing,
 /// so there is nothing here to filter out — 04's "hidden, it is invisible to every gesture" needs no
-/// code of its own.
+/// code of its own. **A collapsed lane's cards ride the same mechanism** (03-board-ui.md § Lane ▸
+/// Collapsed lanes: "cards inside are not rendered"): a lane drawn as a slim strip lays out no card
+/// faces, so it registers no frames and `nearest` cannot step into one. The `⌥`-jumps are the half
+/// that *does* need code, because they name an absolute destination rather than a neighbour — see
+/// `firstCard(scanning:filter:)`.
 ///
 /// Pure and `CoreGraphics`-only, for `SelectionGrammar`'s reason: the branches become lines of test
 /// rather than gestures to drive, and the four arrow handlers stay thin over it.
@@ -85,6 +89,33 @@ public enum NavigationMath {
         }
         return best?.id
     }
+
+    /// **The first card the board is actually showing**, scanning `lanes` in the order given — the
+    /// landing every absolute keyboard destination shares: ⌥←/⌥→'s first/last lane, and the seed an
+    /// arrow from an empty selection takes (04-interactions.md ▸ Grammar).
+    ///
+    /// Three ways a lane is scanned past, and they are one rule — *the user cannot see into it*:
+    ///
+    /// - it holds no cards;
+    /// - the search query hid all of them (04 § Search — "a jump that landed nowhere because the end
+    ///   lane happens to be empty would be a dead key", and a lane the query emptied is empty to the
+    ///   eye);
+    /// - it is **collapsed** (03-board-ui.md § Lane ▸ Collapsed lanes): the slim strip draws no card
+    ///   faces at all, so a jump that landed on one would select something rendered nowhere and leave
+    ///   the arrows with no frame to step from. The strip itself stays selectable **as a lane**, which
+    ///   is the lane domain's business and not this scan's.
+    ///
+    /// Pure, and here rather than in the view for `SortMath`'s reason: the three skips are lines of
+    /// test instead of a board to drive.
+    public static func firstCard(
+        scanning lanes: some Sequence<Lane>,
+        filter: SearchFilter = .inactive
+    ) -> ItemID? {
+        for lane in lanes where !LaneLayoutMath.isCollapsed(lane) {
+            if let card = lane.cards.first(where: { filter.matches($0) }) { return card.id }
+        }
+        return nil
+    }
 }
 
 // MARK: - Within-lane sort