Detail card: per-session understanding notes next to the session list

The extractor's per-proposition understanding observations (named-word
scale: solid/shaky/accepted/...) were ledger data since the redesign,
with no surface. This exposes them at read time and shows each
session's note as a small chip on its session row in the node detail
card — the per-session confidence history the user asked for, one
observation per (node, chat), latest wins within a chat.

- GraphSnapshot.nodeObservations: nodeId -> chatId -> note, built in
  graphSnapshot() from observation events (pure read-time join).
- Sessions list rows: link + observation chip.
- Session-relative judgments stay session-scoped: they render next to
  their session, never as node state (the state model stays pending).

components/graph-view.tsx

@@ -625,15 +625,26 @@ export function GraphView() {
 					{selected.chatIds.length > 0 ? (
 						<div className="mt-3 flex flex-col gap-1">
 							<div className="text-xs text-muted-foreground">Sessions</div>
-							{selected.chatIds.map((chatId) => (
-								<Link
-									key={chatId}
-									href={`/chat/${chatId}`}
-									className="truncate rounded-md px-2 py-1 text-sm text-foreground transition-colors hover:bg-accent"
-								>
-									{snapshot?.sessions[chatId] ?? chatId}
-								</Link>
-							))}
+							{selected.chatIds.map((chatId) => {
+								// That session's understanding observation — the
+								// extractor's named-word note (confidence history).
+								const note = snapshot?.nodeObservations?.[selected.node.id]?.[chatId];
+								return (
+									<div key={chatId} className="flex items-center gap-1.5">
+										<Link
+											href={`/chat/${chatId}`}
+											className="min-w-0 flex-1 truncate rounded-md px-2 py-1 text-sm text-foreground transition-colors hover:bg-accent"
+										>
+											{snapshot?.sessions[chatId] ?? chatId}
+										</Link>
+										{note && (
+											<span className="shrink-0 rounded-full border px-2 py-0.5 text-[10px] text-muted-foreground">
+												{note}
+											</span>
+										)}
+									</div>
+								);
+							})}
 						</div>
 					) : (
 						<div className="mt-3 text-xs text-muted-foreground">No sessions recorded.</div>

src/core/contracts/graph.ts

@@ -229,6 +229,11 @@ export interface GraphSnapshot {
 	sessions: Record<string, string>;
 	/** nodeId → chatIds that touched the node (click-through provenance). */
 	nodeSessions: Record<string, string[]>;
+	/** nodeId → chatId → that session's understanding observation (the
+	 *  extractor's per-session named-word note; session-relative data,
+	 *  shown next to the session list — the confidence history). Multiple
+	 *  notes for one (node, chat) collapse to the latest. */
+	nodeObservations: Record<string, Record<string, string>>;
 }
 
 /** Derive a short chat title from the learner's first message (pure).

src/core/graph.ts

@@ -447,5 +447,26 @@ export function graphSnapshot(deps: GraphDeps): GraphSnapshot {
 		if (ids.length > 0) nodeSessions[nodeId] = ids;
 	}
 
-	return { nodes, edges, sessions, nodeSessions };
+	// Understanding observations per (node, chat) — the extractor's
+	// session-relative note (latest wins within a chat). Read-time join for
+	// the detail card: the confidence history next to the session list.
+	const nodeObservations: Record<string, Record<string, string>> = {};
+	const latestObs = new Map<string, { at: string; note: string; index: number }>();
+	events.forEach((event, index) => {
+		if (event.kind !== "observation" || event.nodeId === null) return;
+		if (!event.note) return;
+		const key = `${event.nodeId}\u0000${event.chatId}`;
+		const current = latestObs.get(key);
+		if (!current || event.at > current.at || (event.at === current.at && index > current.index)) {
+			latestObs.set(key, { at: event.at, note: event.note, index });
+		}
+	});
+	for (const [key, { note }] of latestObs) {
+		const sep = key.indexOf("\u0000");
+		const nodeId = key.slice(0, sep);
+		const chatId = key.slice(sep + 1);
+		(nodeObservations[nodeId] ??= {})[chatId] = note;
+	}
+
+	return { nodes, edges, sessions, nodeSessions, nodeObservations };
 }

tests/graph.test.ts

@@ -363,7 +363,7 @@ describe("the merger (mergeFindings)", () => {
 		assert.deepEqual(m, { chatId: chat2.id, sourceId: "q1", graphNodeId: alphaId });
 	});
 
-	it("derives node states and sessions in graphSnapshot", () => {
+	it("derives sessions and per-session understanding observations in graphSnapshot", () => {
 		const snap = graphSnapshot(graphDeps);
 		const idByStatement = new Map(snap.nodes.map((n) => [n.statement, n.id]));
 		// No node-state classes anymore (2026-09-08): the snapshot carries
@@ -378,6 +378,12 @@ describe("the merger (mergeFindings)", () => {
 		);
 		// Gamma was only ever touched by chat1.
 		assert.deepEqual(snap.nodeSessions[idByStatement.get("Gamma application")!], [chat1.id]);
+
+		// Understanding observations: (node → chat → the extractor's note).
+		// Alpha carries chat1's "solid after the check"; chat2's q1 has no note.
+		const alphaObs = snap.nodeObservations[idByStatement.get("Alpha intuition")!] ?? {};
+		assert.equal(alphaObs[chat1.id], "solid after the check");
+		assert.equal(alphaObs[chat2Id], undefined);
 	});
 
 	it("never string-matches without a verdict — an identical statement without linkTo is a NEW node", () => {