two questions per teaching unit: predict → teach → check (owner 2026-10-03)

The teaching cycle gains its motivation question. The teach quiz schema
now carries a REQUIRED type field — predict (posed before the teaching,
arrives open, the learner predicts the next step) or check (posed after,
arrives collapsed behind the reveal). The prober's quiz stays role-less.

- core: quizInputObject.type union + normalizeQuizType + the reveal law
  as pure quizNeedsReveal; QuestionData.questionType; note → thinking
  rename (legacy reads fold back); readingThinking channel on answers;
  compactAnswerForModel emits thinking / thinkingWhileReading
- tools: descriptions stripped to mechanics — QUIZ_OPTION_CRAFT and
  EXPLAIN_DOCTRINE deleted, doctrine moved to the prompt layer
  (reverses the 2026-09-27 placement, owner 2026-10-03); shared
  quizDescription/explainDescription builders differ only in deltas
- prompts: shared/20-question-tools.md rewritten (option craft,
  transcribed-speech leniency, the two thinking channels); new
  teacher/28-predictions.md (cycle, roles, skip rule, resolution law);
  20-teaching + 30-question-principles scoped to the new taxonomy
- UI: predictions render open with a Prediction eyebrow, verdict shows
  but the explanation tucks behind a toggle; the reading-thinking field
  mounts while a check waits (dictation claims it until reveal);
  answered card separates thinking vs thinking-while-reading blocks

src/core/tool-parts.ts

@@ -29,7 +29,7 @@
 
 import { Value } from "typebox/value";
 import type { TSchema } from "typebox";
-import { quizInputBase, askInputSchema, askOptionProblems, quizInputProblems, explainInputBase, explainInputProblems, type AskToolInput, type QuizToolInput, type ExplainToolInput } from "./question-core.ts";
+import { quizInputBase, quizDisplayInputSchema, askInputSchema, askOptionProblems, quizInputProblems, explainInputBase, explainInputProblems, type AskToolInput, type QuizToolInput, type ExplainToolInput } from "./question-core.ts";
 import { restoreMathEscapes } from "./math-delims.ts";
 import { probeDoneInputSchema, type ProbeDoneInput } from "./contracts/probe.ts";
 
@@ -84,7 +84,12 @@ function restoreMathEscapesDeep(value: unknown): unknown {
 }
 
 export function parseQuizInput(input: unknown): QuizToolInput | undefined {
-	const cleaned = boundaryParse<QuizToolInput>(quizInputBase, restoreMathEscapesDeep(input));
+	// quizDisplayInputSchema (question-core, owner 2026-10-03): base + the
+	// OPTIONAL `type` — new teach-phase records carry predict|check and the
+	// dock renders/gates by it (normalizeQuizType at the read seam); old and
+	// probe records carry none. nodeId stays an unknown key Value.Clean
+	// strips, exactly as before.
+	const cleaned = boundaryParse<QuizToolInput>(quizDisplayInputSchema, restoreMathEscapesDeep(input));
 	if (!cleaned) return undefined;
 	if (quizInputProblems(cleaned).length > 0) return undefined;
 	return cleaned;