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.

components/chat.tsx

@@ -1115,7 +1115,8 @@ export function Chat({
 															/>
 														);
 													case "tool-quiz":
-													case "tool-ask_user_question": {
+													case "tool-ask_user_question":
+													case "tool-explain": {
 														// Pending/streaming questions live in the dock, not the
 														// transcript; answered ones render as graded records.
 														if (part.state === "output-available") {
@@ -1650,7 +1651,7 @@ function DockOverlay({
 						<div key={mode} className={mode === initialModeRef.current ? undefined : "dock-variant"}>
 							{pending ? (
 								<QuestionDock
-									toolName={pending.tool as "quiz" | "ask_user_question"}
+									toolName={pending.tool as "quiz" | "ask_user_question" | "explain"}
 									toolCallId={pending.toolCallId}
 									input={pending.input as never}
 									expanded={expanded}