Add “Make my homework”, and finish the mobile polish pass

Homework (/homework — entry points in the drawer and on the create screen)

- Assignment intake reuses the study pipeline: pasted text, photos
  (camera/picker, compressed in the browser) and documents (PDF/DOCX/PPTX/
  ODT/text) through lib/image + lib/documents, the same vision step and the
  same language guard. Raw files never leave the device — only text and JPEG
  data URLs reach the server.
- Two large choice cards: “Just make it” returns the finished homework
  (answer only, plain text, copy + make it again); “Explain how to make this
  homework” builds an interactive guide.
- The guide is one step per screen in the study-feed snap layout:
  explanation, three progressive hints (nudge -> hint -> the answer) and an
  optional checkpoint rendered by the existing activity components (graded
  through /api/grade). The last screen assembles the solution from the step
  answers, with a copy button. Checkpoints carry xp 0 so the guide stays free
  of XP/streak chrome.
- Results live in freezmo.homework.v1 with a small history (open/delete);
  “Make it again” re-runs from the stored assignment text (the vision
  transcription when photos were used) — no original files are stored.
- The answer and the guide are written in the assignment's language, never
  translated into the UI language.

Server

- POST /api/homework: NDJSON stage events like /api/generate, the same
  http-guard, auth checked before parsing, and its own RATE_LIMIT_HOMEWORK
  (documented in .env.example + the README table).
- New prompts in lib/prompts.ts and zod schemas in lib/schemas.ts with the
  same single repair retry; TEXT_MODEL for content, VISION_MODEL only for
  photos. New shared client pieces: useNotesIntake, lib/homework store,
  lib/clipboard, and a shared NDJSON reader in lib/client-api.

Also finishing the mobile polish pass from the previous request

- Phone ice scene: the top-left orb moved behind the glass header (it sat
  behind the page heading/subtitle). The settings sheet's scroll cue is now a
  bare chevron inside a content fade (mask) instead of a chip over the status
  banner, and the API key card's note/disclosure/actions are tightened.
- theme-color now follows the in-app theme (SSR metas still fall back to the
  OS preference); apple-mobile-web-app-status-bar-style stays “default”
  because iOS fixes the status-bar text colour at launch.

Verified: 78/78 homework checks (text/photo/PDF, both modes, EN+CS, dark+light,
360/390px, copy, history persistence, storage privacy, API language, axe), plus
the existing suites re-run (mobile 47/47, pixel contrast 0 below AA, i18n 27/27,
desktop regression 72/72). Lint + build clean; service worker freezmo-v6.

lib/ai.ts

@@ -9,9 +9,13 @@ import { needsLanguageRepair } from "./language";
 import {
   buildGenerationUserPrompt,
   buildGradingUserPrompt,
+  buildHomeworkGuideUserPrompt,
+  buildHomeworkMakeUserPrompt,
   buildRepairPrompt,
   GENERATION_SYSTEM_PROMPT,
   GRADING_SYSTEM_PROMPT,
+  HOMEWORK_GUIDE_SYSTEM_PROMPT,
+  HOMEWORK_MAKE_SYSTEM_PROMPT,
   VISION_SYSTEM_PROMPT,
   VISION_USER_INSTRUCTION,
 } from "./prompts";
@@ -19,10 +23,14 @@ import {
   extractedNotesSchema,
   generatedActivitySchema,
   gradeResultSchema,
+  homeworkMakeSchema,
+  homeworkStepSchema,
   type Difficulty,
   type ExtractedNotes,
   type GeneratedActivity,
   type GradeResult,
+  type HomeworkGuide,
+  type HomeworkMake,
 } from "./schemas";
 import { parseJsonLoose } from "./utils";
 import type { OllamaAuth } from "./config";
@@ -391,6 +399,107 @@ export async function gradeShortAnswer(input: {
   return value;
 }
 
+/* ------------------------------------------------------------------ */
+/* Make my homework                                                    */
+/* ------------------------------------------------------------------ */
+
+const HOMEWORK_MAKE_SHAPE_HINT = `{"title":"...","language":"English name of the language used","answer":"the finished homework as plain text"}`;
+
+/** Mode 1: the finished homework, with no commentary at all. */
+export async function makeHomework(input: {
+  model: string;
+  auth: OllamaAuth;
+  assignment: string;
+  language?: string;
+  signal?: AbortSignal;
+}): Promise<HomeworkMake> {
+  const { value } = await runJsonStep<HomeworkMake>({
+    model: input.model,
+    auth: input.auth,
+    system: HOMEWORK_MAKE_SYSTEM_PROMPT,
+    user: buildHomeworkMakeUserPrompt({ assignment: input.assignment, language: input.language }),
+    validate: (parsed) => {
+      const result = homeworkMakeSchema.safeParse(parsed);
+      if (!result.success) return { ok: false, error: summariseZodError(result.error) };
+      if (!result.data.answer.trim()) return { ok: false, error: "The answer field is empty." };
+      return { ok: true, value: result.data };
+    },
+    shapeHint: HOMEWORK_MAKE_SHAPE_HINT,
+    label: "Writing the homework",
+    signal: input.signal,
+    temperature: 0.4,
+  });
+  return value;
+}
+
+const HOMEWORK_GUIDE_SHAPE_HINT = `{"title":"...","language":"English name of the language used","steps":[{"title":"...","explanation":"...","hints":["nudge","hint","answer"],"answer":"...","checkpoint":{"type":"multiple_choice","topic":"...","question":"...","options":["...","...","...","..."],"correctIndex":0,"explanation":"..."}}]}`;
+
+/**
+ * Mode 2: the interactive guide. Be forgiving with checkpoints — a step with a
+ * broken checkpoint still ships (the checkpoint is simply dropped), because the
+ * explanation, hints and answer are the valuable part.
+ */
+export async function buildHomeworkGuide(input: {
+  model: string;
+  auth: OllamaAuth;
+  assignment: string;
+  language?: string;
+  signal?: AbortSignal;
+}): Promise<HomeworkGuide> {
+  const { value } = await runJsonStep<HomeworkGuide>({
+    model: input.model,
+    auth: input.auth,
+    system: HOMEWORK_GUIDE_SYSTEM_PROMPT,
+    user: buildHomeworkGuideUserPrompt({ assignment: input.assignment, language: input.language }),
+    validate: (parsed) => {
+      if (!parsed || typeof parsed !== "object") {
+        return { ok: false, error: "Expected a JSON object at the top level." };
+      }
+      const record = parsed as Record<string, unknown>;
+      if (!Array.isArray(record.steps)) {
+        return { ok: false, error: `Missing "steps" array. Expected 3-8 step objects.` };
+      }
+
+      const steps: HomeworkGuide["steps"] = [];
+      const rejected: string[] = [];
+
+      record.steps.slice(0, 12).forEach((raw, index) => {
+        const result = homeworkStepSchema.safeParse(raw);
+        if (!result.success) {
+          rejected.push(`#${index + 1}: ${summariseZodError(result.error)}`);
+          return;
+        }
+        const step = result.data;
+        if (!step.answer.trim() || !step.explanation.trim()) {
+          rejected.push(`#${index + 1}: explanation or answer is empty.`);
+          return;
+        }
+        steps.push({
+          ...step,
+          hints: step.hints.map((hint) => hint.trim()).filter(Boolean).slice(0, 4),
+          checkpoint: step.checkpoint ? sanitiseActivity(step.checkpoint) : undefined,
+        });
+      });
+
+      if (steps.length < 2) {
+        return {
+          ok: false,
+          error: `Only ${steps.length} usable steps were found, at least 2 are needed. Rejected: ${rejected.slice(0, 3).join("; ") || "none"}.`,
+        };
+      }
+
+      const title = typeof record.title === "string" && record.title.trim() ? record.title.trim() : "Homework guide";
+      const language = typeof record.language === "string" && record.language.trim() ? record.language.trim() : undefined;
+      return { ok: true, value: { title, language, steps } };
+    },
+    shapeHint: HOMEWORK_GUIDE_SHAPE_HINT,
+    label: "Building your guide",
+    signal: input.signal,
+    temperature: 0.5,
+  });
+  return value;
+}
+
 /* ------------------------------------------------------------------ */
 /* Helpers                                                             */
 /* ------------------------------------------------------------------ */