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.

app/api/homework/route.ts

@@ -1,6 +1,6 @@
 import { z } from "zod";
 
-import { buildHomeworkGuide, extractNotes, makeHomework, notesToText, type PipelineStage } from "@/lib/ai";
+import { buildHomeworkGuide, checkHomework, extractNotes, makeHomework, notesToText, type PipelineStage } from "@/lib/ai";
 import { authErrorMessage, authErrorKind, getServerConfig, resolveAuth, resolveModelName } from "@/lib/config";
 import { friendlyErrorMessage, OllamaError } from "@/lib/ollama";
 import { rejectCrossOrigin, rejectOversizedBody, requestLocale } from "@/lib/http-guard";
@@ -22,6 +22,8 @@ const requestSchema = z.object({
   mode: homeworkModeSchema,
   images: z.array(z.string().min(32).max(MAX_IMAGE_CHARS)).max(16).optional(),
   text: z.string().max(120_000).optional(),
+  /** Mode "check": the student's own attempt at the assignment. */
+  solution: z.string().max(120_000).optional(),
   /** Language of the assignment (usually detected by the vision step). */
   language: z.string().max(60).optional(),
 });
@@ -80,12 +82,15 @@ export async function POST(request: Request) {
     );
   }
 
-  const { mode, images, text, language } = parsed.data;
+  const { mode, images, text, solution, language } = parsed.data;
   const imageList = (images ?? []).map(stripDataUrlPrefix).filter(Boolean);
 
   if (imageList.length === 0 && !text?.trim()) {
     return Response.json({ error: translate(locale, "server.needAssignment") }, { status: 400 });
   }
+  if (mode === "check" && !solution?.trim()) {
+    return Response.json({ error: translate(locale, "server.needSolution") }, { status: 400 });
+  }
 
   const encode = encoder();
   const abort = new AbortController();
@@ -128,7 +133,14 @@ export async function POST(request: Request) {
         send({
           type: "stage",
           stage: "generation",
-          message: translate(locale, mode === "make" ? "homework.loading.writing" : "homework.loading.planning"),
+          message: translate(
+            locale,
+            mode === "make"
+              ? "homework.loading.writing"
+              : mode === "check"
+                ? "homework.loading.checking"
+                : "homework.loading.planning",
+          ),
         });
 
         const meta = {
@@ -138,7 +150,30 @@ export async function POST(request: Request) {
           textModel: resolveModelName(config.textModel, auth.auth.directCloud),
         };
 
-        if (mode === "make") {
+        if (mode === "check") {
+          const result = await checkHomework({
+            model: config.textModel,
+            auth: auth.auth,
+            assignment: assignmentText,
+            solution: solution!.trim(),
+            language: detectedLanguage,
+            signal: abort.signal,
+          });
+          send({
+            type: "homework",
+            homework: {
+              mode: "check",
+              title: result.title,
+              language: result.language || detectedLanguage,
+              verdict: result.verdict,
+              correct: result.correct,
+              wrong: result.wrong,
+              corrected: result.corrected,
+              sourceText: assignmentText,
+            },
+            meta,
+          });
+        } else if (mode === "make") {
           const result = await makeHomework({
             model: config.textModel,
             auth: auth.auth,