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.

src/core/contracts/plan.ts

@@ -85,7 +85,9 @@ export function derivePlanStatuses(tree: PlanTree, messages: readonly PartsCarri
 	// duplicates collapsed (several checks on one node = one stay on it)
 	for (const m of messages) {
 		for (const part of m.parts) {
-			if (part.type !== "tool-quiz") continue;
+			// Either quizzing tool (quiz/explain) tags position — the mechanic
+			// is a settings switch; the fold recognizes both (owner 2026-09-27).
+			if (part.type !== "tool-quiz" && part.type !== "tool-explain") continue;
 			const nodeId = (part.input as { nodeId?: unknown } | undefined)?.nodeId;
 			if (typeof nodeId !== "string" || !ids.has(nodeId)) continue; // untagged/unknown — moves nothing
 			if (runs.at(-1) !== nodeId) runs.push(nodeId);
@@ -130,7 +132,7 @@ export function derivePlanStatusesLh(tree: PlanTree, messages: readonly LhMessag
 		const content = (m as { content?: unknown }).content;
 		if (!Array.isArray(content)) continue;
 		for (const block of content as Array<{ type?: string; name?: string; arguments?: unknown }>) {
-			if (block.type !== "toolCall" || block.name !== "quiz") continue;
+			if (block.type !== "toolCall" || (block.name !== "quiz" && block.name !== "explain")) continue;
 			const nodeId = (block.arguments as { nodeId?: unknown } | undefined)?.nodeId;
 			if (typeof nodeId !== "string" || !ids.has(nodeId)) continue;
 			if (runs.at(-1) !== nodeId) runs.push(nodeId);