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/question-core.ts

@@ -1,14 +1,11 @@
 /**
- * question-core — pure logic for quiz/ask questions. No framework imports,
- * no UI: everything here is deterministic and unit-testable.
+ * question-core — the question contract + pure grading logic. No framework
+ * imports, no UI: everything here is deterministic and unit-testable.
  *
- * Used by:
- *   - the TUI quiz extension (extensions/quiz.ts) — blocking terminal UI
- *   - the web app (AI SDK client-side tools) — the browser validates,
- *     shuffles, grades with these functions, then sends the verdict back
- *     as the tool output via addToolOutput
- *
- * The web shape (AI SDK):
+ * The zod schemas below are the tool INPUT contracts (agent/tools declares
+ * the tools against them); the browser validates, shuffles, and grades with
+ * these functions, then sends the verdict back as the tool output via
+ * addToolOutput:
  *   1. The teacher model calls the `quiz` tool (question + options +
  *      correctAnswer + explanation). No server execute → the call lands in
  *      the UI as a typed tool part in `input-available` state.
@@ -20,6 +17,8 @@
  * exited and resumed mid-question for free.
  */
 
+import { z } from "zod";
+
 // ─── shared types ───────────────────────────────────────────────────────────
 
 export interface QuizOption {
@@ -28,6 +27,69 @@ export interface QuizOption {
 	description?: string;
 }
 
+// ─── tool input schemas (the question contract) ─────────────────────────────
+// Parameter names mirror the prompt docs exactly — keep them in sync.
+
+const optionSchema = z.object({
+	label: z.string().describe("Display label for the answer option"),
+	value: z
+		.string()
+		.optional()
+		.describe("Optional machine-readable value returned for the option. Defaults to the label."),
+	description: z.string().optional().describe("Optional extra detail shown below the option"),
+});
+
+export const quizInputSchema = z.object({
+	question: z.string().describe("The single quiz question to ask"),
+	options: z
+		.array(optionSchema)
+		.min(2)
+		.describe(
+			"The answer options (2 or more). Options only — no free-text mode. Never add your own 'I don't know' option.",
+		),
+	correctAnswer: z
+		.union([z.string(), z.array(z.string())])
+		.describe(
+			"The correct answer as the option value(s) — the `value` field of the option you intend. " +
+				"Single-select: one string. Multi-select: an array; the learner is only correct if their selection matches this set exactly.",
+		),
+	explanation: z
+		.string()
+		.describe("Explanation revealed AFTER the learner answers. Always say why the correct answer is correct."),
+	multiSelect: z.boolean().optional().describe("Set true only when more than one option is correct"),
+	details: z.string().optional().describe("Optional extra context or instructions shown under the question"),
+	nodeId: z
+		.string()
+		.optional()
+		.describe(
+			"Optional plan-tree node id this question assesses. Set whenever the question targets a tree node — " +
+				"the outcome feeds the learner's knowledge graph. Omit for ad-hoc probes.",
+		),
+});
+
+export const askInputSchema = z.object({
+	question: z.string().describe("The single question to ask"),
+	mode: z
+		.enum(["single-select", "multi-select", "text"])
+		.optional()
+		.describe(
+			"Answer mode. Omit for single-select when options are given, or text when they are not.",
+		),
+	options: z
+		.array(optionSchema)
+		.min(2)
+		.optional()
+		.describe(
+			"Optional multiple-choice options. Omit for free-form text input. The learner can always choose 'Other' and type a custom answer.",
+		),
+	multiSelect: z.boolean().optional().describe("Set true to allow multiple answers to be selected"),
+	details: z.string().optional().describe("Optional extra context or instructions shown under the question"),
+});
+
+export type QuizToolInput = z.infer<typeof quizInputSchema>;
+export type AskToolInput = z.infer<typeof askInputSchema>;
+
+
 /** A real selected answer, in the order the options were displayed. */
 export interface OptionAnswer {
 	label: string;