graph context: a separate marker message before the first user turn

The map picks no longer glue into the opening prompt as seed text
(owner, 2026-10-04 late). POST /api/chats accepts graphContext
{propositions}; the route resolves the picks against the live graph,
derives the reasoning chains among them (chainsForSelection →
formatChainLine), and writes a graph-context custom marker as
message[0] — before the learner's first user message, in either mode.

- Core: newGraphContextMessage (model-facing content = the
  contextualization framing + proposition lines + chain lines;
  details = the structured pick); toLlmMessages flattens it to a user
  message like every marker, so the model reads it for free.
- View: projects to a user-side data-graph-context part.
- UI: GraphContextCard — minimal, muted, dashed, collapsed by default
  (counts only); expand reveals name — statement rows and the chain
  lines. Same compact-expandable pattern as the practice cards.
- Home: sends graphContext with the creation whenever picks exist;
  the prompt param carries the learner's own words only.

components/chat.tsx

@@ -38,6 +38,7 @@ import type { PlanBlockData } from "@/src/core";
 import { QuestionDock } from "@/components/question-dock";
 import { PracticeDock } from "@/components/practice-dock";
 import { ThinkingCard, type PracticeThinkingData } from "@/components/practice-cards";
+import { GraphContextCard, type GraphContextData } from "@/components/graph-context-card";
 import { TopBar } from "@/components/top-bar";
 import type { ArtifactPartProps, JobRecord, Phase3, QuestionAnswerData, TurnUsage } from "@/src/core";
 import type { LhViewMessage } from "@/src/core";
@@ -1258,6 +1259,13 @@ export function Chat({
 														);
 													case "step-start":
 														return pi > 0 ? <Separator key={pi} className="my-3" /> : null;
+													case "data-graph-context":
+														// The session's map pick (2026-10-04): a minimal
+														// collapsible card — scaffolding above the first
+														// user message, never a bubble.
+														return (
+															<GraphContextCard key={pi} data={part.data as GraphContextData} />
+														);
 													case "data-practice-thinking":
 														// The learner's practice submission (2026-10-04):
 														// user-side — the register (thinking trace /