Merge #544: lineage lines as routed trees, every family shown, the selected one emphasized

docs/wiki/Driving-Codeman-From-An-Agent.md

@@ -189,7 +189,7 @@ followed by a wait races, and reports the previous turn's state.
 ## Lineage
 
 A create request can name the session that spawned it, through a body field or a header, and
-the dashboard then draws a lineage arc from parent to child. The skill sets it automatically.
+the dashboard then draws a lineage line from parent to child. The skill sets it automatically.
 
 It is resolved rather than trusted: an unresolvable parent is dropped silently rather than
 failing the spawn, because a cosmetic field must never break a worker.

docs/wiki/Mobile-Guide.md

@@ -158,7 +158,7 @@ enough to fix a typo an agent introduced while you are away from your desk.
   enforces it.
 - The Approvals bell. Phones get the NEEDS YOU strips on the home screen instead.
 - The desktop home tab rail, which needs a wide window.
-- Lineage arcs, which are a desktop overlay.
+- Lineage lines, which are a desktop overlay.
 
 ## Gotchas
 

docs/wiki/Settings-Reference.md

@@ -91,7 +91,7 @@ every session or only the active tab.
 | Vertical Rail Order    | *By activity* (default) sorts the rail the way the home screens are sorted; *Manual* keeps your tab order and drag-reordering. |
 | Tall Tabs              | Taller tab strip.                                                                          |
 | Pop-out Button on Tabs | Adds the detach control to tabs, with a per-tab override.                                  |
-| Spawn Lineage Lines    | Arcs from a parent tab to sessions it spawned. Desktop only, on by default.                |
+| Spawn Lineage Lines    | Lines from each tab to the sessions it spawned; the selected tab's family is drawn thicker. Desktop only, on by default. |
 | Auto-name Sessions     | Titles a new tab after its first prompt, keeping the case prefix (`w3-myapp: fix the login redirect`). Synced, off by default. See [The Dashboard](The-Dashboard#automatic-session-names). |
 | Overview Home Screen   | The phone home screen. On by default.                                                      |
 

docs/wiki/The-Dashboard.md

@@ -84,13 +84,18 @@ title is derived locally from the prompt's first sentence; no text leaves the ma
 On phones the strip scrolls horizontally instead of wrapping, and the active tab is always
 scrolled into view. It is not reordered to the front, so the `Alt+N` numbering stays stable.
 
-### Lineage arcs
+### Lineage lines
 
 When one session spawns another (an agent starting a worker through the API), Codeman draws
-a coloured arc under the strip connecting parent to child, with one colour per child. It is
-how a fan-out of eight workers stays readable.
+lines from the parent to each child, in the parent's colour, routed through the gaps between
+tab rows so they never cover a tab or the terminal. Every family is always shown; selecting
+a tab draws its own family thicker and brighter. A dashed branch means that child is
+working. It is how a fan-out of eight workers stays readable.
 
-Desktop only, and on by default. Turn it off in **App Settings → Appearance**. Arcs are
+While any tab has spawned another, the strip keeps a little extra room between rows for the
+lines, so switching tabs never changes the header height.
+
+Desktop only, and on by default. Turn it off in **App Settings → Appearance**. Lines are
 skipped for tabs scrolled out of the strip.
 
 ## Header controls

docs/wiki/Watching-Agents-Work.md

@@ -22,13 +22,18 @@ transcript: what it was asked to do, what it is doing, and what it returned.
 This is the feature that makes a fan-out legible. Without it, a lead session that spawned
 eight workers looks like a stalled terminal for several minutes.
 
-## Session lineage arcs
+## Session lineage lines
 
-The tab strip draws a coloured arc from a parent tab to any tab it spawned, one colour per
-child. That covers the other direction of fan-out: not subagents inside one session, but
-whole sessions started by an agent through the API.
+The tab strip draws lines from every tab to the tabs it spawned. That covers the other
+direction of fan-out: not subagents inside one session, but whole sessions started by an
+agent through the API.
 
-Desktop only, on by default, and toggled in **App Settings → Appearance**. Arcs are skipped
+The lines form one tree per spawning tab, in that tab's colour, and run only through the
+gaps between tab rows, so they never cover a tab name or the terminal. Select a tab and its
+family (the tabs it spawned, or its parent and siblings) is drawn thicker and brighter. A
+dashed branch means that child is working.
+
+Desktop only, on by default, and toggled in **App Settings → Appearance**. Lines are skipped
 for tabs scrolled out of view.
 
 See [Driving Codeman From An Agent](Driving-Codeman-From-An-Agent) for the spawning side.