diff --git a/web/src/lib/components/GraphBackground.svelte b/web/src/lib/components/GraphBackground.svelte
index 58a8ab1..023b267 100644
--- a/web/src/lib/components/GraphBackground.svelte
+++ b/web/src/lib/components/GraphBackground.svelte
@@ -198,8 +198,14 @@
       const z = (s.z + tg.z) / 2
       const a = project(s.x, s.y!, z)
       const b = project(tg.x, tg.y!, z)
+      const dx = b.x - a.x
+      const dy = b.y - a.y
+      const len = Math.max(Math.hypot(dx, dy), 1)
+      const curve = Math.min(len * 0.15, 40)
+      const mx = (a.x + b.x) / 2 - (dy / len) * curve
+      const my = (a.y + b.y) / 2 + (dx / len) * curve
       ctx.moveTo(a.x, a.y)
-      ctx.lineTo(b.x, b.y)
+      ctx.quadraticCurveTo(mx, my, b.x, b.y)
     }
     ctx.stroke()
 
diff --git a/web/src/lib/components/SessionGraph.svelte b/web/src/lib/components/SessionGraph.svelte
index fb7973c..3f66120 100644
--- a/web/src/lib/components/SessionGraph.svelte
+++ b/web/src/lib/components/SessionGraph.svelte
@@ -11,10 +11,22 @@
     type Simulation
   } from 'd3-force'
   import { fetchGraph, type Entity } from '$lib/api'
-  import { messages } from '$lib/stores/chat'
-  import { touched, healthDiffs } from '$lib/stores/workspace'
+  import type { ChatMessage } from '$lib/stores/chat'
+  import type { TouchedEntity, HealthDiff } from '$lib/stores/workspace'
   import { openEntityWindow, wmState } from '$lib/stores/windows'
 
+  // Prop-driven (not store-imported) so this can render either the main
+  // page's global "current session" data or a floating task window's own
+  // per-session data — see TaskContextPanel.svelte, which supplies both.
+  let { messages, touched, healthDiffs }: { messages: ChatMessage[]; touched: TouchedEntity[]; healthDiffs: HealthDiff[] } = $props()
+
+  // SVG ids are document-global, not scoped to this <svg> — several task
+  // windows can each have their own Scope graph open at once, and without a
+  // per-instance suffix every one of them would define (and reference)
+  // <pattern id="dot-grid">, so only the first in the document would ever
+  // actually paint (the rest resolve to nothing, background reads blank).
+  const dotGridId = `dot-grid-${crypto.randomUUID().slice(0, 8)}`
+
   interface Node extends Entity {
     x?: number
     y?: number
@@ -75,7 +87,7 @@
   // get_health_summary would otherwise dump all 168 entities into the graph).
   const candidateSlugs = $derived.by(() => {
     const out = new Set<string>()
-    for (const m of $messages) {
+    for (const m of messages) {
       collectSlugs(m.text, out)
       for (const t of m.tools) collectSlugs(t.args, out)
     }
@@ -234,15 +246,15 @@
   // object identity fine and this is small (≤12 touched, ≤8 diffs).
   const touchedBySlug = $derived.by(() => {
     const m: Record<string, true> = {}
-    for (const t of $touched) m[t.slug] = true
+    for (const t of touched) m[t.slug] = true
     return m
   })
   const diffBySlug = $derived.by(() => {
     const m: Record<string, { from: string; to: string }> = {}
-    for (const d of $healthDiffs) if (!(d.slug in m)) m[d.slug] = d
+    for (const d of healthDiffs) if (!(d.slug in m)) m[d.slug] = d
     return m
   })
-  const nowTouching = $derived($touched[0] ?? null)
+  const nowTouching = $derived(touched[0] ?? null)
 
   function endpoint(end: string | Node): Node | undefined {
     return typeof end === 'object' ? end : nodes.find((n) => n.slug === end)
@@ -348,28 +360,32 @@
         onpointercancel={onUp}
       >
         <defs>
-          <pattern id="dot-grid" width="12" height="12" patternUnits="userSpaceOnUse">
+          <pattern id={dotGridId} width="12" height="12" patternUnits="userSpaceOnUse">
             <circle cx="2" cy="2" r="0.8" fill="var(--border)" opacity="0.75" />
           </pattern>
         </defs>
-        <rect width={cw} height={ch} fill="url(#dot-grid)" />
+        <rect width={cw} height={ch} fill="url(#{dotGridId})" />
         <g>
           {#each links as link}
             {@const s = endpoint(link.source)}
             {@const t = endpoint(link.target)}
             {#if s?.x != null && t?.x != null && s?.y != null && t?.y != null}
               {@const focus = selected && (s.slug === selected.slug || t.slug === selected.slug)}
-              <line
-                x1={s.x}
-                y1={s.y}
-                x2={t.x}
-                y2={t.y}
+              {@const dx = t.x - s.x}
+              {@const dy = t.y - s.y}
+              {@const len = Math.max(Math.hypot(dx, dy), 1)}
+              {@const curve = Math.min(len * 0.15, 40)}
+              {@const cx = (s.x + t.x) / 2 - (dy / len) * curve}
+              {@const cy = (s.y + t.y) / 2 + (dx / len) * curve}
+              <path
+                d="M {s.x},{s.y} Q {cx},{cy} {t.x},{t.y}"
+                fill="none"
                 stroke="var(--muted-foreground)"
                 stroke-width={focus ? 1.6 : 1}
                 opacity={selected ? (focus ? 0.7 : 0.12) : 0.35}
               >
                 <title>{link.type}</title>
-              </line>
+              </path>
             {/if}
           {/each}
         </g>