Show directional lineage in agent map

src/renderer/src/components/dashboard-popout/AgentDashboardToolbar.tsx

@@ -48,7 +48,7 @@ type AgentDashboardToolbarProps = {
   showAgentlessWorkspaces?: boolean
   agentlessWorkspaceCount?: number
   onShowAgentlessWorkspacesChange?: (show: boolean) => void
-  /** Map-only: the dashed parent→child dispatch edges. */
+  /** Map-only: the directional parent→child dispatch edges. */
   showOrchestrationLinks?: boolean
   onShowOrchestrationLinksChange?: (show: boolean) => void
   searchInputRef: React.RefObject<HTMLInputElement | null>

src/renderer/src/components/dashboard-popout/AgentMap.test.tsx

@@ -361,11 +361,13 @@ describe('AgentMap', () => {
     expect(workerLink).toHaveClass('agent-map-lineage-link')
     expect(workerLink).toHaveAttribute('data-agent-map-lineage-relation', 'orchestration')
     expect(workerLink).toHaveAttribute('data-parent-pane-key', 'parent')
+    expect(workerLink?.getAttribute('d')?.match(/\bM\b/g)?.length).toBeGreaterThan(1)
     // Why orchestration, not subagent: `nested` is a card, and in-process subagents
     // never become cards — so a grandchild dispatch is still an orchestration edge.
     expect(nestedLink).toHaveClass('agent-map-lineage-link')
     expect(nestedLink).toHaveAttribute('data-agent-map-lineage-relation', 'orchestration')
     expect(nestedLink).toHaveAttribute('data-parent-pane-key', 'child')
+    expect(nestedLink?.getAttribute('d')?.match(/\bM\b/g)?.length).toBeGreaterThan(1)
   })
 
   it('connects spawned workers across worktree rings', () => {

src/renderer/src/components/dashboard-popout/AgentMapScene.tsx

@@ -12,6 +12,7 @@ import type {
 } from './agent-map-layout'
 import { AGENT_MAP_LINEAGE_RELATION, shouldAggregateAgentMapWorktree } from './agent-map-layout'
 import { selectVisibleAgentMapLabels } from './agent-map-label-declutter'
+import { agentMapLineageChevronPath } from './agent-map-lineage-chevron-path'
 import { AgentMapWorktreeLabel } from './AgentMapWorktreeLabel'
 import { AgentMapWorktreeRingNode } from './AgentMapWorktreeRingNode'
 
@@ -60,7 +61,10 @@ function agentLineagePath(parent: AgentMapAgentNode, child: AgentMapAgentNode):
   }
   const unitX = dx / distance
   const unitY = dy / distance
-  return `M ${parent.x + unitX * parent.radius} ${parent.y + unitY * parent.radius} L ${child.x - unitX * child.radius} ${child.y - unitY * child.radius}`
+  return agentMapLineageChevronPath([
+    { x: parent.x + unitX * parent.radius, y: parent.y + unitY * parent.radius },
+    { x: child.x - unitX * child.radius, y: child.y - unitY * child.radius }
+  ])
 }
 
 /** Memoization keeps pointer panning to one SVG viewBox write, not a map rerender. */

src/renderer/src/components/dashboard-popout/AgentMapWorktreeRingNode.tsx

@@ -14,6 +14,7 @@ import type {
   AgentMapWorktreeRing
 } from './agent-map-layout'
 import { AGENT_MAP_LINEAGE_RELATION, shouldAggregateAgentMapWorktree } from './agent-map-layout'
+import { agentMapLineageChevronPath } from './agent-map-lineage-chevron-path'
 import { agentMapWorktreeActiveStatus } from './agent-map-worktree-active-status'
 
 type AgentMapWorktreeRingNodeProps = {
@@ -58,7 +59,12 @@ function lineagePath(parent: AgentMapAgentNode, child: AgentMapAgentNode): strin
   const startY = parent.y + parent.radius * direction
   const endY = child.y - child.radius * direction
   const branchY = (startY + endY) / 2
-  return `M ${parent.x} ${startY} L ${parent.x} ${branchY} L ${child.x} ${branchY} L ${child.x} ${endY}`
+  return agentMapLineageChevronPath([
+    { x: parent.x, y: startY },
+    { x: parent.x, y: branchY },
+    { x: child.x, y: branchY },
+    { x: child.x, y: endY }
+  ])
 }
 
 function agentName(card: DashboardCard): string {

src/renderer/src/components/dashboard-popout/agent-map-lineage-chevron-path.ts

@@ -0,0 +1,66 @@
+export type AgentMapLineagePoint = {
+  x: number
+  y: number
+}
+
+type LineageSegment = {
+  start: AgentMapLineagePoint
+  unitX: number
+  unitY: number
+  length: number
+}
+
+const CHEVRON_SPACING = 8
+const CHEVRON_DEPTH = 3.5
+const CHEVRON_HALF_WIDTH = 2.25
+
+function svgNumber(value: number): number {
+  return Math.round(value * 1_000) / 1_000
+}
+
+export function agentMapLineageChevronPath(points: AgentMapLineagePoint[]): string {
+  const segments: LineageSegment[] = []
+  let totalLength = 0
+  for (let index = 1; index < points.length; index += 1) {
+    const start = points[index - 1]
+    const end = points[index]
+    const dx = end.x - start.x
+    const dy = end.y - start.y
+    const length = Math.hypot(dx, dy)
+    if (length === 0) {
+      continue
+    }
+    segments.push({ start, unitX: dx / length, unitY: dy / length, length })
+    totalLength += length
+  }
+  if (segments.length === 0) {
+    return points[0] ? `M ${svgNumber(points[0].x)} ${svgNumber(points[0].y)}` : ''
+  }
+
+  const chevronCount = Math.max(1, Math.floor(totalLength / CHEVRON_SPACING))
+  const commands: string[] = []
+  let segmentIndex = 0
+  let segmentStartDistance = 0
+  for (let index = 0; index < chevronCount; index += 1) {
+    const distance = (totalLength * (index + 1)) / (chevronCount + 1)
+    while (
+      segmentIndex < segments.length - 1 &&
+      distance > segmentStartDistance + segments[segmentIndex].length
+    ) {
+      segmentStartDistance += segments[segmentIndex].length
+      segmentIndex += 1
+    }
+    const segment = segments[segmentIndex]
+    const offset = distance - segmentStartDistance
+    const tipX = segment.start.x + segment.unitX * offset
+    const tipY = segment.start.y + segment.unitY * offset
+    const backX = tipX - segment.unitX * CHEVRON_DEPTH
+    const backY = tipY - segment.unitY * CHEVRON_DEPTH
+    const perpendicularX = -segment.unitY * CHEVRON_HALF_WIDTH
+    const perpendicularY = segment.unitX * CHEVRON_HALF_WIDTH
+    commands.push(
+      `M ${svgNumber(backX + perpendicularX)} ${svgNumber(backY + perpendicularY)} L ${svgNumber(tipX)} ${svgNumber(tipY)} L ${svgNumber(backX - perpendicularX)} ${svgNumber(backY - perpendicularY)}`
+    )
+  }
+  return commands.join(' ')
+}

src/renderer/src/components/dashboard-popout/agent-map.css

@@ -198,7 +198,6 @@
   fill: none;
   pointer-events: none;
   stroke: color-mix(in srgb, var(--muted-foreground) 42%, transparent);
-  stroke-dasharray: 1 4;
   stroke-linecap: round;
   stroke-linejoin: round;
   stroke-width: 1;