Phase 3: Check my work, follow-ups and turn-into-deck

Check my work (third homework mode)
- One model call with its own system prompt marks the student's own
  attempt: verdict, what's right, each issue with why + fix, and the
  corrected version that keeps everything the student got right.
  Unasked-for extras are never errors. The attempt is typed/pasted
  (photos of handwriting are documented as unsupported) and stored in
  the record so Redo re-checks the same work.
- Server: mode "check" + solution on POST /api/homework (zod, 400
  server.needSolution without one) and the same NDJSON stream; new
  checkHomework() pipeline with repair-once validation.

Follow-ups
- New POST /api/homework/refine (plain JSON, RATE_LIMIT_REFINE, zod,
  auth before body): shorter / more detail / explain, plain text back,
  language preserved.
- Shorter + More detail + Original rewrite the finished answer and the
  corrected version in place (FollowUpBar); every guide step has
  Explain step N differently; failed calls say so without losing text.

Turn into a study deck
- Any result hands its content (answer, corrected version or assembled
  guide) to New deck through a one-shot sessionStorage seed with the
  options step pre-filled.

UI
- Phone step 2 gains the third card: tapping it reveals the solution
  field + submit; desktop has three cards and the solution field shows
  with the mode. Homework history labels and share/card previews cover
  the new mode.

Verified: new phase-3 suite 20/20 against a stub Ollama (check payload,
missing-solution 400, refine validation, phone + desktop check flows,
shorter follow-up with restore, guide explain, deck hand-off) plus
regression 74/74, mobile 52/52, declutter 116/116, wizard 80/80,
animation 8/8, native 35/35, phase1 38/38, phase2 43/43, i18n 25/25.
Key parity 734/734. Lint + build clean. SW freezmo-v27.

lib/ai.ts

@@ -9,13 +9,17 @@ import { needsLanguageRepair } from "./language";
 import {
   buildGenerationUserPrompt,
   buildGradingUserPrompt,
+  buildHomeworkCheckUserPrompt,
   buildHomeworkGuideUserPrompt,
   buildHomeworkMakeUserPrompt,
+  buildRefineUserPrompt,
   buildRepairPrompt,
   GENERATION_SYSTEM_PROMPT,
   GRADING_SYSTEM_PROMPT,
+  HOMEWORK_CHECK_SYSTEM_PROMPT,
   HOMEWORK_GUIDE_SYSTEM_PROMPT,
   HOMEWORK_MAKE_SYSTEM_PROMPT,
+  REFINE_SYSTEM_PROMPT,
   VISION_SYSTEM_PROMPT,
   VISION_USER_INSTRUCTION,
 } from "./prompts";
@@ -23,12 +27,14 @@ import {
   extractedNotesSchema,
   generatedActivitySchema,
   gradeResultSchema,
+  homeworkCheckSchema,
   homeworkMakeSchema,
   homeworkStepSchema,
   type Difficulty,
   type ExtractedNotes,
   type GeneratedActivity,
   type GradeResult,
+  type HomeworkCheck,
   type HomeworkGuide,
   type HomeworkMake,
 } from "./schemas";
@@ -502,6 +508,74 @@ export async function buildHomeworkGuide(input: {
   return value;
 }
 
+/* ------------------------------------------------------------------ */
+/* Check my work                                                       */
+/* ------------------------------------------------------------------ */
+
+const HOMEWORK_CHECK_SHAPE_HINT = `{"title":"...","language":"English name of the language used","verdict":"1-2 sentences","correct":["what is right"],"wrong":[{"issue":"...","why":"...","fix":"..."}],"corrected":"the student's solution with every mistake fixed"}`;
+
+/** Mode 3: mark the student's own attempt and hand back a corrected version. */
+export async function checkHomework(input: {
+  model: string;
+  auth: OllamaAuth;
+  assignment: string;
+  solution: string;
+  language?: string;
+  signal?: AbortSignal;
+}): Promise<HomeworkCheck> {
+  const { value } = await runJsonStep<HomeworkCheck>({
+    model: input.model,
+    auth: input.auth,
+    system: HOMEWORK_CHECK_SYSTEM_PROMPT,
+    user: buildHomeworkCheckUserPrompt({
+      assignment: input.assignment,
+      solution: input.solution,
+      language: input.language,
+    }),
+    validate: (parsed) => {
+      const result = homeworkCheckSchema.safeParse(parsed);
+      if (!result.success) return { ok: false, error: summariseZodError(result.error) };
+      if (!result.data.corrected.trim()) return { ok: false, error: "The corrected field is empty." };
+      return { ok: true, value: result.data };
+    },
+    shapeHint: HOMEWORK_CHECK_SHAPE_HINT,
+    label: "Checking the attempt",
+    signal: input.signal,
+    temperature: 0.2,
+  });
+  return value;
+}
+
+/** Follow-ups: rewrite one finished piece (shorter / more detail / explain). */
+export async function refineHomeworkText(input: {
+  model: string;
+  auth: OllamaAuth;
+  instruction: "shorter" | "more" | "explain";
+  text: string;
+  context?: string;
+  signal?: AbortSignal;
+}): Promise<string> {
+  const result = await ollamaChat({
+    model: input.model,
+    auth: input.auth,
+    json: false,
+    signal: input.signal,
+    temperature: 0.4,
+    messages: [
+      { role: "system", content: REFINE_SYSTEM_PROMPT },
+      {
+        role: "user",
+        content: buildRefineUserPrompt({
+          instruction: input.instruction,
+          text: input.text,
+          context: input.context,
+        }),
+      },
+    ],
+  });
+  return result.content.trim();
+}
+
 /* ------------------------------------------------------------------ */
 /* Helpers                                                             */
 /* ------------------------------------------------------------------ */