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

tests/chat-flow.test.ts

@@ -62,6 +62,7 @@ const QUIZ_INPUT = {
 	],
 	correctAnswer: "Mercury",
 	explanation: "Mercury is the innermost planet.",
+	type: "check",
 	nodeId: "planet-order",
 };
 
@@ -619,6 +620,7 @@ describe("teacher chat flow (scripted model)", () => {
 		// same turn. This pins that whole mechanism (the live Nietzsche bug).
 		const BAD_QUIZ_INPUT = {
 			question: "What is Nietzsche's genealogical claim about religion?",
+			type: "check",
 			nodeId: "genealogy",
 			options: [{ label: "A cultural diagnosis" }, { label: "Atheism as a conclusion" }],
 			correctAnswer: "cultural-diagnosis", // the exact live failure shape: a slug, no match
@@ -695,6 +697,7 @@ describe("teacher chat flow (scripted model)", () => {
 		// question, and the model's retry must become the pending quiz.
 		const STRINGY_QUIZ_INPUT = {
 			question: "Lewis's indexical analysis of 'actual' — which is it?",
+			type: "check",
 			nodeId: "indexicals",
 			options: JSON.stringify([
 				{ label: "Like 'I'", value: "indexical" },