fix(ui): make session lineage lines read as arcs, not straight threads

The lines that join a tab to the workers its codeman skill spawned were
drawn with numbers tuned against two tabs sitting side by side, and they
degraded in exactly the two situations the feature is actually used in.

1. A spawned worker is appended to the END of the strip, so the real span
   between a lead and its worker is 800-1500px. With the dip clamped at
   44px that is a 33px sag: the arc reads as a straight line drawn across
   the terminal instead of a bracket hanging under the strip. The dip now
   grows at 0.085/px and clamps at 104.

2. When the desktop strip wraps (tabs-two-rows / tabs-auto-wrap), a parent
   on row 1 and its child on row 2 are ~14px apart, and the cross-row
   branch drew parent-bottom to child-TOP: a flat line hidden inside the
   row gap, with siblings overprinting each other. Both ends now anchor on
   the tab BOTTOM with the control points below the LOWER row, so a wrapped
   pair gets the same bracket a flat strip gets. That deletes the branch:
   one shape covers both.

Visibility, at 1:1 rather than in a zoomed mockup: 2 -> 2.5px stroke,
4 4 -> 5 5 dashes (lineage-flow moves with them, -16 -> -20), opacity
.55 -> .72, and a second wider glow so the contrast comes from the halo
rather than from more weight, keeping the line under the subagent lines'
3px. A working child is bright (.95) outside the reduced-motion block, so
turning motion off no longer also dims every worker's arc. Sibling nesting
6 -> 8px and the direction dot 3 -> 3.5px to match the heavier stroke.

Verified at 1:1 in a harness driving the real styles.css and the real
computeLineagePath over three layouts (adjacent workers, workers at the
far end of a full strip, wrapped two-row strip) on a dark and a light
skin. test/session-lineage-lines.test.ts pins both regressions.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

docs/architecture-invariants.md

@@ -84,7 +84,7 @@ Implementation detail extracted from `CLAUDE.md` so that file stays small enough
 
 **Resolved, not trusted** (`resolveParentSessionId()`, route-helpers.ts): exact id first, then a UNIQUE prefix of ≥8 chars (ids reach agents truncated — mux names and a Docker export's `$CODEMAN_SESSION_ID` both carry 8), and an ambiguous prefix resolves to NOTHING rather than to a guess. The parent must be a live session the caller can already see (`canAccessOwned`) AND carry the same owner as the session being created, so a multi-user caller cannot staple their session under someone else's tab. ⚠️ **Everything unresolvable is DROPPED, never a 400**: a stale id from a cached skill preamble must cost a decorative line, not a worker. ⚠️ It is decoration at every layer — never an ownership, permission or lifecycle signal; a child outlives its parent, and the Session ctor refuses a self-parent (reachable only via recovery, where both values come off disk). It rides `toState()` into `session_created` / `session_updated`, so there is **no new SSE event**, and `server.ts`'s recovery path restores it so lineage survives a restart.
 
-**Rendering is an additional LAYER, not a second pass** (`session-lineage.js`, loadorder 15.6): `_updateConnectionLinesImmediate()` (subagent-windows.js) calls `_appendLineageConnectionLines(svg, rects)` at its tail, exactly like ultracode's two layers, so all of them share ONE batched read→write reflow and the same `tab:<id>` rect cache. Geometry is pure and unit-tested in `computeLineagePath()` (constants.js): both endpoints live in one horizontal strip, so the subagent shape (tab-bottom → window-top) has nothing to aim at, and same-row pairs get a shallow U-bridge HANGING BELOW the strip (dip scales with distance, plus a per-sibling step so several children of one parent nest instead of overprinting), while a wrapped strip (`tabs-two-rows`/`tabs-auto-wrap`) falls back to the vertical bezier.
+**Rendering is an additional LAYER, not a second pass** (`session-lineage.js`, loadorder 15.6): `_updateConnectionLinesImmediate()` (subagent-windows.js) calls `_appendLineageConnectionLines(svg, rects)` at its tail, exactly like ultracode's two layers, so all of them share ONE batched read→write reflow and the same `tab:<id>` rect cache. Geometry is pure and unit-tested in `computeLineagePath()` (constants.js): both endpoints live in one horizontal strip, so the subagent shape (tab-bottom → window-top) has nothing to aim at, and every pair gets a U-bridge HANGING BELOW the strip, anchored on both tabs' BOTTOM edges (dip scales with distance, plus a per-sibling step so several children of one parent nest instead of overprinting, plus the row offset when the strip has wrapped). ⚠️ **A wrapped strip used to get its own shape, and that shape was the bug** (fixed 2026-08-14): `tabs-two-rows`/`tabs-auto-wrap` put a parent on row 1 ~14px above its child on row 2, so the old parent-bottom → child-TOP bezier had 14px to bend in and drew a flat line inside the row gap, siblings overprinting. Hanging the control points below the LOWER row gives the wrapped case the same bracket as the flat one and deletes the branch. The same pass raised the dip clamp (44 → 104, 0.06 → 0.085/px) because a skill worker is appended to the END of the strip, where the old cap flattened an 800-1500px span into a straight thread across the terminal, and traded weight for a second, wider glow (2 → 2.5px, `4 4` → `5 5` dashes at `-20`, opacity .55 → .72 / .95 working) because the original styling vanished into terminal text at 1:1.
 
 ⚠️ **Desktop only, for a z-index reason**: the overlay is `z-index: 999` and the desktop header is 100, so arcs paint OVER it — which is exactly what lets them touch tab bottoms. Under 1024px mobile.css makes the header `position: fixed; z-index: 1200` and would bury them, and the phone strip is a scroller where both endpoints are rarely on screen at once. Raising the SVG to ~1250 (above the fixed header, below modals at 1300) is the phase-2 option, and needs a real check against the mobile overview and the drawer.
 

docs/session-lineage-lines-plan.md

@@ -93,17 +93,37 @@ The path math itself lives in `constants.js` as a pure
 ### 4.2 Geometry
 
 Both endpoints are tabs in one horizontal strip, so the subagent shape (tab-bottom →
-window-top) does not apply. Two cases:
+window-top) does not apply. **One case**, a **U-bridge hanging below the strip** that
+touches both tabs on their bottom edge:
 
-- **Same row** (the normal case): a shallow **U-bridge hanging below the strip**.
-  `y0 = max(parent.bottom, child.bottom)`, dip
-  `d = clamp(14 + |x2 - x1| * 0.06, 16, 44) + depth * 6`, path
-  `M x1 y0 C x1 y0+d, x2 y0+d, x2 y0`. `depth` is the child's index among its
-  siblings, so several children of one parent **nest** instead of overprinting.
-- **Different rows** (`tabs-two-rows` / `tabs-auto-wrap` on desktop): the existing
-  vertical bezier from parent-bottom-center to child-top-center.
+```
+y0 = max(parent.bottom, child.bottom)
+d  = clamp(14 + |x2 - x1| * 0.085, 22, 104) + depth * 8 + |child.bottom - parent.bottom|
+path: M x1 parent.bottom  C x1 y0+d, x2 y0+d, x2 child.bottom
+```
 
-A small `<circle r="3">` at the child end marks direction (an SVG `marker` would need a
+`depth` is the child's index among its siblings, so several children of one parent
+**nest** instead of overprinting.
+
+> **Superseded (2026-08-14): the two shapes this section used to specify.** The dip was
+> `clamp(14 + span * 0.06, 16, 44) + depth * 6`, and a wrapped strip
+> (`tabs-two-rows` / `tabs-auto-wrap`) got its own parent-bottom → child-**top** bezier.
+> Both were tuned against two tabs side by side and failed at the distances the feature
+> is used at:
+>
+> - a skill worker is appended to the **end** of the strip, so the real span is
+>   800-1500px, where a 44px cap is a 33px sag, i.e. a line that reads as straight and
+>   crosses the terminal instead of bracketing under the strip;
+> - and when the strip wraps, parent-bottom (34) to child-top (48) leaves **14px** to
+>   bend in, so the arc was a flat line hidden in the row gap, with siblings drawn on
+>   top of each other. Reported as *"they connect already, but the lines are straight
+>   and not easy visible"*.
+>
+> Anchoring both ends at the tab bottoms and hanging the control points below the
+> **lower** row gives the wrapped case the same bracket as the flat one, and removes the
+> branch. Pinned by `test/session-lineage-lines.test.ts`.
+
+A small `<circle r="3.5">` at the child end marks direction (it breathes to 4.5 while that worker is busy) (an SVG `marker` would need a
 `<defs>` block and fights `stroke-dasharray`).
 
 Each path gets `class="connection-line lineage-line"`, `data-parent-tab`,
@@ -139,8 +159,12 @@ callers are cheap. Needed:
 ### 4.5 Styling
 
 `.connection-line.lineage-line`: violet stroke from a `--lineage-line` token,
-`stroke-width: 2`, `dasharray 4 4`, `opacity: .55`, softer glow than the subagent lines
-so the two layers read as different things. Trap to respect: the skin block nests under
+`stroke-width: 2.5`, `dasharray 5 5`, `opacity: .72` (`.95` while the child works),
+softer than the subagent lines so the two layers read as different things, but the
+contrast comes from a **second, wider glow** rather than more weight, because the first
+cut (2px / `4 4` / `.55` / one 5px glow) disappeared into terminal text on a real 1080p
+desktop. `lineage-flow` marches by two dash cycles, so it moves with the dash array
+(`5 5` → `-20`). Trap to respect: the skin block nests under
 `html:not([data-skin="og"])`, so a bare `.lineage-line` rule inside it would outrank the
 base rule at higher specificity. **Define the color as a token per skin, keep exactly
 one `.lineage-line` rule.** Light skins get a darker stroke.