tools: the standard argument heal — every registry, both seams

The whitehead incident (2026-10-09): glm-5.3 emitted quiz type with
quotes baked in ('"predict"') — rejected ten times, byte-identical
retries, the lesson never started — and correctAnswer with the JSON
key-value colon glued on ([':parmenides']). Third GLM wobble incident,
and each prior heal was wired only where its incident landed; this one
landed precisely where the practice heal never reached.

Layer 1 — healEncodedArguments moves to core/argument-heal (the display
seam needs it too — the tool-parts law) with withArgumentHeal +
healToolRecord (agent/tools/heal) wired at EVERY registry: prober,
teacher, practice, bareQuestionTools (it had no prepareArguments at
all), demo-builder, and submit-agent (composing after
healStringifiedArrays; the auditor's extraTools wrapped).

Layer 2 — stripModelValueDebris (core/value-debris): leading/trailing
colons, quotes, backticks, whitespace strip at the MEMBERSHIP seams —
coerceCorrectAnswer (boundary check + display + grading in one),
normalizeQuizType (persisted wobbled records keep their role),
resolveTargetId (copy-syntax on targets).

Layer 3 — schema description hygiene: the quiz type and practice
mode/outcome/rung/missClass values now read as bare words — the quoted
JSON-key style invited quote-copying.

Display mirror — parseQuizInput heals the raw record on read, so a
boundary-healed quiz whose record keeps raw args renders instead of
becoming an invisible pending quiz (learner lockout).

Pins: tests/tool-heal.test.ts (the incident shapes end-to-end through
pi-ai validation, the wiring, the strips, the mirror). The stringy-
options pins flip to boundary-parity per tool-parts' own law; the
chat-flow garbage pin keeps its honest-reject intent with an unhealable
shape. 1471 tests, typecheck, lint green.

src/core/tool-parts.ts

@@ -31,6 +31,7 @@ import { Value } from "typebox/value";
 import type { TSchema } from "typebox";
 import { quizInputBase, quizDisplayInputSchema, askInputSchema, askOptionProblems, quizInputProblems, explainInputBase, explainInputProblems, type AskToolInput, type QuizToolInput, type ExplainToolInput } from "./question-core.ts";
 import { restoreMathEscapes } from "./math-delims.ts";
+import { healEncodedArguments } from "./argument-heal.ts";
 import { probeDoneInputSchema, type ProbeDoneInput } from "./contracts/probe.ts";
 
 /** The pi-boundary parse step, mirrored here (live-smoke fix, 2026-09-26):
@@ -89,7 +90,13 @@ export function parseQuizInput(input: unknown): QuizToolInput | undefined {
 	// dock renders/gates by it (normalizeQuizType at the read seam); old and
 	// probe records carry none. nodeId stays an unknown key Value.Clean
 	// strips, exactly as before.
-	const cleaned = boundaryParse<QuizToolInput>(quizDisplayInputSchema, restoreMathEscapesDeep(input));
+	// The display mirror of the boundary heal (whitehead, 2026-10-09): the
+	// record keeps RAW arguments, so the recorded `type: "\"predict\""`
+	// wobble must heal HERE too or a posed quiz renders invisible (the
+	// tool-parts law). healEncodedArguments is the same pure pass the
+	// boundary's withArgumentHeal runs.
+	const healedInput = healEncodedArguments(restoreMathEscapesDeep(input), quizDisplayInputSchema);
+	const cleaned = boundaryParse<QuizToolInput>(quizDisplayInputSchema, healedInput);
 	if (!cleaned) return undefined;
 	if (quizInputProblems(cleaned).length > 0) return undefined;
 	return cleaned;