play whole islands, make home the path itself, draw tutor diagrams, add tedi

- Home is now the island path of every unit with one clear Start button on the
  current island; the six-card dashboard is gone.
- Start opens /nodes/{id}/quiz (4 questions) instead of one-question lessons, so
  an island takes one round instead of ~11. Lessons stay one tap away in the sheet.
- Tutor answers render the backend's validated diagram (plane, number line,
  fraction) as React SVG; function expressions go through a small parser, no eval.
- Tedi, the mobile-preview mascot, joins as the fourth companion with all six moods
  and an onboarding slide.
- Light polish: 3D buttons, header gradients, warmer page background.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/api/index.ts

@@ -75,6 +75,15 @@ export const api = {
   home: () => http.get<T.HomeResponse>('/home'),
   nodeLessons: (nodeId: string) => http.get<T.NodeLessons>(`/nodes/${nodeId}/lessons`),
 
+  /**
+   * آزمونِ جزیره: از هر درسِ جزیره حداکثر یک سوال (پیش‌فرض ۴). ترتیب برای هر
+   * کاربر ثابت است، پس رفرش همان آزمون را می‌دهد.
+   */
+  nodeQuiz: (nodeId: string) => http.get<T.NodeQuiz>(`/nodes/${nodeId}/quiz`),
+  /** پایانِ آزمون، جزیره را با هر نمره‌ای تمام می‌کند و جزیره‌ی بعدی را باز. */
+  nodeQuizComplete: (nodeId: string, result: { correctCount: number; totalQuestions: number }, idempotencyKey?: string) =>
+    http.create<T.NodeQuizComplete>(`/nodes/${nodeId}/quiz/complete`, result, { idempotencyKey }),
+
   lesson: {
     intro: (lessonId: number) => http.get<T.LessonIntro>(`/lessons/${lessonId}/intro`),
     questions: (lessonId: number) =>

src/api/types.ts

@@ -121,6 +121,31 @@ export interface Question {
   options: QuestionOption[];
 }
 
+export interface NodeQuizQuestion extends Question {
+  lessonId: string;
+  lessonTitle: string;
+}
+
+export interface NodeQuiz {
+  nodeId: string;
+  nodeTitle: string;
+  unitTitle: string;
+  /** ممکن است از requested کمتر باشد (جزیره‌ی کم‌سوال). */
+  questionCount: number;
+  requested: number;
+  questions: NodeQuizQuestion[];
+}
+
+export interface NodeQuizComplete {
+  nodeId: string;
+  stars: number;
+  xpEarned: number;
+  coinsEarned: number;
+  /** جزیره‌ی بعدی که حالا باز است؛ null یعنی آخرینِ پایه بود. */
+  nextNodeId: string | null;
+  stats: HomeStats;
+}
+
 export interface AnswerResult {
   correct: boolean;
   correctOptionId: string;
@@ -184,14 +209,36 @@ export interface AskDone {
   suggestedFollowUps: string[];
   remainingQuota: number;
   usedChunks: UsedChunk[];
+  diagram?: Diagram | null;
 }
 
 export interface ConversationMessage {
   messageId: string;
   role: 'user' | 'assistant' | string;
   text: string;
+  diagram?: Diagram | null;
 }
 
+/* ─── شکلِ پاسخِ دستیار (بک‌اند: rag/services/diagram.py) ─────────────────── */
+
+export type DiagramRef = string | [number, number];
+export type DiagramPointDef = [number, number] | { polar: [number, number]; from?: DiagramRef };
+
+export type DiagramItem =
+  | { type: 'circle'; center: DiagramRef; r: number; label?: string }
+  | { type: 'segment' | 'arrow'; from: DiagramRef; to: DiagramRef; label?: string }
+  | { type: 'line'; through: [DiagramRef, DiagramRef]; label?: string }
+  | { type: 'angle' | 'rightAngle'; vertex: DiagramRef; from: DiagramRef; to: DiagramRef; label?: string }
+  | { type: 'polygon'; points: DiagramRef[]; label?: string }
+  | { type: 'point'; point: DiagramRef; label?: string }
+  | { type: 'function'; expr: string; from: number; to: number; label?: string }
+  | { type: 'text'; at: [number, number]; text: string };
+
+export type Diagram =
+  | { kind: 'plane'; title: string; axes: boolean; points: Record<string, DiagramPointDef>; items: DiagramItem[] }
+  | { kind: 'numberline'; title: string; min: number; max: number; points: { at: number; label: string }[]; jumps: { from: number; to: number; label: string }[] }
+  | { kind: 'fraction'; title: string; shape: 'circle' | 'rect'; parts: number; shaded: number };
+
 export interface NotificationItem {
   id: number;
   type: string;