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/server/settings-body.ts

@@ -23,7 +23,7 @@ import type {
 	RoleModelOverride,
 } from "../core/settings.ts";
 import { BACKGROUND_MODEL_ROLES, EXTRACTION_CHUNK_TOKENS_FLOOR, MODEL_SLOTS } from "../core/settings.ts";
-import { TOGGLEABLE_TOOLS } from "../core/pending.ts";
+import { WRITABLE_TOOL_KEYS } from "../core/pending.ts";
 
 /** Parsed-or-rejected — `ok: false` carries the 400's error message. */
 export type SettingsBodyResult<T> =
@@ -157,10 +157,11 @@ export function parseAgentSettingsBody(body: unknown): SettingsBodyResult<AgentS
 	if (tools.map) {
 		// Unknown tool keys are rejected at WRITE time (user decision
 		// 2026-09-19): the delta is inert while unread, but once the bridge
-		// honors it a persisted `quiz: false` would genuinely drop the quiz —
-		// and the definitive list is the adjudicated job-tools-only set.
-		// The read-side sanitizer stays lenient for forward-compat.
-		const supported = TOGGLEABLE_TOOLS as readonly string[];
+		// honors it a persisted bogus key would drift. The writable set is
+		// the job tools + the quizzing-mechanics switch (explain, owner
+		// 2026-09-27). The read-side sanitizer stays lenient for
+		// forward-compat.
+		const supported = WRITABLE_TOOL_KEYS as readonly string[];
 		for (const key of Object.keys(tools.map)) {
 			if (!supported.includes(key)) {
 				return { ok: false, error: `unknown tool "${key}" (supported: ${supported.join(", ")})` };