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>

CLAUDE.md

@@ -204,7 +204,7 @@ Codeman is a Claude Code session manager with web interface and autonomous Ralph
 
 **Run launch synchronization**: the Run entrypoint holds an in-flight lock and disables `#runBtn` for the whole launch (≥500ms), so a double click cannot create duplicate sessions with the same `w<n>-<case>` name. `_ensureCreatedSessionVisible()` runs before `selectSession()`, and `_onSessionCreated()` stays an idempotent upsert, so POST-first and SSE-first ordering both produce exactly one rendered tab. → [architecture-invariants#run-launch-synchronization](docs/architecture-invariants.md#run-launch-synchronization)
 
-**Session lineage lines** (tab → tab it spawned, `sessionLineageLines`, per-device, desktop default ON): a create request may name the session that spawned it, as a `parentSessionId` body field on `POST /api/sessions` / `POST /api/quick-start` or the `X-Codeman-Parent-Session` header (the agent skill sets that once on its shared curl invocation, so every spawn recipe carries it). `resolveParentSessionId()` (route-helpers.ts) **resolves rather than trusts** it: exact id, else a UNIQUE ≥8-char prefix (ids reach agents truncated), it must be a live session the caller can see AND carry the same owner, and **anything unresolvable is DROPPED, never a 400** — a cosmetic field must not be able to fail a worker spawn. It rides `toState()` into `session_created`, so there is no new SSE event. ⚠️ Rendering is an ADDITIONAL LAYER on the existing SVG pass (`_appendLineageConnectionLines` called at the tail of `_updateConnectionLinesImmediate()`, exactly like ultracode), sharing one batched read→write reflow and the `tab:<id>` rect cache; geometry is pure in `computeLineagePath()` (constants.js). ⚠️ **Desktop only**: the overlay is `z-index: 999` and the desktop header is 100 (arcs paint over it, which is what lets them touch tab bottoms), but under 1024px mobile.css makes the header `fixed; z-index: 1200` and would bury them. ⚠️ Paths carry `data-agent-id="lineage:<childId>"` because that is what `_applyLineEntrances()` queries — that one attribute is what gives them the entrance animation and its negative-`animation-delay` resume across `svg.innerHTML=''`. ⚠️ `.session-tabs` is `overflow-x: auto`, so a scrolled-out tab still HAS a rect (over the logo); edges with an endpoint outside the strip are skipped, and a passive `scroll` listener re-anchors the rest.
+**Session lineage lines** (tab → tab it spawned, `sessionLineageLines`, per-device, desktop default ON): a create request may name the session that spawned it, as a `parentSessionId` body field on `POST /api/sessions` / `POST /api/quick-start` or the `X-Codeman-Parent-Session` header (the agent skill sets that once on its shared curl invocation, so every spawn recipe carries it). `resolveParentSessionId()` (route-helpers.ts) **resolves rather than trusts** it: exact id, else a UNIQUE ≥8-char prefix (ids reach agents truncated), it must be a live session the caller can see AND carry the same owner, and **anything unresolvable is DROPPED, never a 400** — a cosmetic field must not be able to fail a worker spawn. It rides `toState()` into `session_created`, so there is no new SSE event. ⚠️ Rendering is an ADDITIONAL LAYER on the existing SVG pass (`_appendLineageConnectionLines` called at the tail of `_updateConnectionLinesImmediate()`, exactly like ultracode), sharing one batched read→write reflow and the `tab:<id>` rect cache; geometry is pure in `computeLineagePath()` (constants.js). ⚠️ **ONE shape, and the second one was the bug**: every pair (flat strip or wrapped) gets a U-bridge hanging below the strip, anchored on both tabs' BOTTOM edges. A wrapped strip used to get a parent-bottom → child-TOP bezier with a ~14px row gap to bend in, which drew a flat line hidden in the gap with siblings overprinting; the dip is also clamped at 104px rather than 44, since a skill worker lands at the END of the strip where the old cap flattened the arc into a straight thread. ⚠️ **Desktop only**: the overlay is `z-index: 999` and the desktop header is 100 (arcs paint over it, which is what lets them touch tab bottoms), but under 1024px mobile.css makes the header `fixed; z-index: 1200` and would bury them. ⚠️ Paths carry `data-agent-id="lineage:<childId>"` because that is what `_applyLineEntrances()` queries — that one attribute is what gives them the entrance animation and its negative-`animation-delay` resume across `svg.innerHTML=''`. ⚠️ `.session-tabs` is `overflow-x: auto`, so a scrolled-out tab still HAS a rect (over the logo); edges with an endpoint outside the strip are skipped, and a passive `scroll` listener re-anchors the rest.
 
 **Unified session list**: `GET /api/sessions/unified` merges live sessions, persisted state, lifecycle-log history, and Claude transcript files into one deduped list (pure core in `src/services/unified-session-service.ts`). Transcript rows fold into their owning session via a `claudeSessionId → Codeman id` alias map, so resumed and `/clear`-respawned sessions do not appear twice. No terminal buffers in the response, unlike `/api/sessions`. Backs the Cmd+K Session Manager, plus pinning and cross-device tab order (`PUT /api/session-order`; pure merge helpers in `src/session-order.ts`, pushing device wins and server-only ids are never dropped). → [architecture-invariants#unified-session-list-and-session-manager](docs/architecture-invariants.md#unified-session-list-and-session-manager)