free-recall explain tool: the quizzing-mechanic switch (owner 2026-09-27)

Sycophancy mitigation as a structural commitment: the model writes its
full correctAnswer (plus explanation, in that order) BEFORE the learner
sees the question; the commitment rides the persisted call args, is
revealed on submit, and grades his free text in the model's next reply —
the client never grades free recall.

- tools.explain setting (segmented 'Quizzing — Multiple choice | Free
  recall' in Agent settings' Tools group): free arms explain and drops
  quiz for BOTH agents (prober variant carries no nodeId, same pattern
  as the probe quiz); mechanics keys never pass filterEnabledTools —
  quiz stays unwritable (the 2026-09-19 wedge ruling stands)
- doctrine lives pi-natively in the tool descriptions (owner ruling —
  no conditional system-prompt chunks): explain carries the commitment
  rule; the MC option-building craft moved out of the prompt into the
  quiz description; shared/20-question-tools.md slims to the
  quiz-agnostic core
- display seams: parseExplainInput (LaTeX-debris restoration included),
  dock text-mode with an 'I don't know' row (kbd row 0), AnsweredCard
  reveal (The answer / Why, no verdict chips), [Explain answer] format
- phases/plan seams recognize both quizzing tools' nodeId tags; explain
  answers deliberately feed no ledger evidence (no client grading to
  key on — a future ruling can parse the model's grade)

1049/1049 tests, typecheck/lint/build green.

tests/settings-pure.test.ts

@@ -14,6 +14,7 @@ import {
 	composeSearchEngine,
 	composeSlotModel,
 	composeTool,
+	composeQuizMechanics,
 	researchToolUnavailable,
 	sectionedSegments,
 } from "../components/settings/agent-section.tsx";
@@ -388,3 +389,19 @@ describe("sectionedSegments — the prompts overhaul (2026-09-26)", () => {
 		assert.equal(PROMPT_IN_USE_HINT, "Your version is in use");
 	});
 });
+
+// ─── the quizzing-mechanics segmented control (owner 2026-09-27) ───────────
+
+describe("composeQuizMechanics (the segmented control's write)", () => {
+	it("free recall writes explain:true; multiple choice writes explain:false — nothing else moves", () => {
+		const before: AgentSettings = { tools: { research: false }, prompts: { teacher: true } } as AgentSettings;
+		const free = composeQuizMechanics(before, "free");
+		assert.equal(free.tools?.explain, true);
+		const choice = composeQuizMechanics(before, "choice");
+		assert.equal(choice.tools?.explain, false);
+		for (const after of [free, choice]) {
+			assert.equal(after.tools?.research, false, "the research toggle carries verbatim");
+			assert.deepEqual(after.prompts, before.prompts, "the prompts map carries verbatim");
+		}
+	});
+});