Shell/core import law: public API barrels + ESLint enforcement (stage 2)

The shell now imports through exactly two barrels, enforced by
import/no-restricted-paths (npm run lint):

  components/**  ->  "@/src/core"      (pure core API, browser-safe)
  app/**         ->  "@/src/core" + "@/src/server" (server entries)

Zone violations are lint errors with architecture-pointer messages; the
pure-core modules (contracts, question-core, plan-tree, phases, pending,
math-delims, ui-message) may never import agent/server/store.

Supporting moves (direction: IO layers -> core):
- core/index.ts: the core public API barrel
- core/ui-message.ts: moved from src/agent (it was shell-facing all along)
- quiz/ask input zod schemas moved agent/tools -> core/question-core
  (the question contract, alongside the grading logic)
- ChatRecord/ChatSummary moved store/chats -> core/contracts (single schema)
- GraphSnapshot/NodeStateClass moved core/graph -> core/contracts (the
  /api/graph payload IS a contract; the pure renderer needs only these)
- src/server/{chats,graph,jobs}.ts + index.ts: thin server entries for the
  transport layer; GET /api/graph's fold side-effect now lives behind
  graphView() instead of inline in the route

Gates: tsc clean, 190/190 tests, eslint clean (law verified to fire on
store/agent/subpath violations), production build clean.

(Repo repair en route: a git object (app/chat/[id] tree) was missing from
the object store — reconstructed byte-exactly via mktree from its blob;
the broken node_modules that stalled the build was cleanly reinstalled.)

src/core/contracts.ts

@@ -1,12 +1,11 @@
 /**
- * Shared contracts — the single source of truth every workstream codes against.
- * Pure types + protocol docs; no runtime code, no imports (safe everywhere:
- * server, client, tests). See docs/plan.md (waves) and docs/vision.md (§ refs).
- *
- * Owners: orchestrator wrote this file. Workers: do NOT edit it; if a contract
- * looks wrong or is missing something you need, ask the orchestrator.
+ * Shared contracts — the single source of truth every component codes against.
+ * Pure types + protocol docs; no runtime code, type-only imports (safe
+ * everywhere: server, client, tests). See docs/vision.md (§ refs).
  */
 
+import type { UIMessage } from "ai";
+
 // ─── Plan tree (vision §2 "formal plan tree") ────────────────────────────────
 // A session-scoped dependency tree authored by the teacher via plan tools.
 // One substrate with the global graph: tree nodes fold into graph nodes.
@@ -121,6 +120,47 @@ export interface LedgerEvent {
  * events (+ note); quiz parts without nodeId → events with nodeId null.
  */
 
+/** Per-node state class for the home view (vision §1 "Home page") — derived,
+ * never stored: taught if ANY taught event; else the LATEST quiz event decides
+ * (known / missed / dont-know); a node with no events is a candidate. */
+export type NodeStateClass = "taught" | "known" | "missed" | "dont-know" | "candidate";
+
+/** The GET /api/graph payload — everything the home view's PURE renderer needs. */
+export interface GraphSnapshot {
+	nodes: GraphNode[];
+	edges: GraphEdge[];
+	nodeStates: Record<string, NodeStateClass>;
+	/** chatId → title, for every chat that touched the graph. */
+	sessions: Record<string, string>;
+	/** nodeId → chatIds that touched the node (click-through provenance). */
+	nodeSessions: Record<string, string[]>;
+}
+
+// ─── Chat records (the session store's on-disk format) ───────────────────────
+
+/** One persisted session: data/chats/<id>.json. The stored messages are full
+ * AI SDK UIMessages (parts included) — the canonical session record: a
+ * pending quiz is a tool part in `input-available` state, which is exactly
+ * what makes resume-mid-question free. */
+export interface ChatRecord {
+	id: string;
+	title: string;
+	createdAt: string;
+	updatedAt: string;
+	messages: UIMessage[];
+	/** The session's plan tree (vision §2) — written by plan tools via saveTree. */
+	tree?: PlanTree;
+}
+
+/** The list view's shape (messageCount instead of full messages). */
+export interface ChatSummary {
+	id: string;
+	title: string;
+	createdAt: string;
+	updatedAt: string;
+	messageCount: number;
+}
+
 // ─── Async sub-agent jobs (vision §2.5; plan.md Wave 0 protocol) ────────────
 
 export type JobKind = "research" | "demo" | "visual";