diff --git a/components/ai-elements/message.tsx b/components/ai-elements/message.tsx
index 96f47e1..e4b533b 100644
--- a/components/ai-elements/message.tsx
+++ b/components/ai-elements/message.tsx
@@ -331,10 +331,10 @@ export type MessageResponseProps = ComponentProps<typeof Streamdown>;
 // streamdown@2.5 expects shiki@4 types. Both work at runtime (each ships its
 // own highlighter); the cast papers over the .d.ts mismatch.
 //
-// singleDollarTextMath: false — a bare $ is ALWAYS literal currency (the
-// teacher-prompt contract). Inline math arrives as \(...\) and display math
-// as \[...\]; transformMathDelimiters (below) rewrites both to the
-// two-dollar forms remark-math still parses. $ can never start math.
+// Standard dollar authoring (owner, 2026-10-12): $...$ inline, $$ fenced
+// on separate lines for display. transformMathDelimiters stays as the
+// compatibility reader for old \(...\)/\[...\] content; its two-dollar
+// output remains valid alongside native single-dollar math.
 //
 // remark-breaks rides in the cjk plugin's remarkPluginsAfter slot (public
 // PluginConfig API): Streamdown's bare `remarkPlugins` PROP would REPLACE the
@@ -352,16 +352,14 @@ export const streamdownPlugins = {
     remarkPluginsAfter: [...cjk.remarkPluginsAfter, remarkBreaks],
   },
   code,
-  math: createMathPlugin({ singleDollarTextMath: false }),
+  math: createMathPlugin({ singleDollarTextMath: true }),
 } as unknown as PluginConfig;
 
 export const MessageResponse = memo(
   ({ className, children, ...props }: MessageResponseProps) => {
-    // Delimiter preprocessing is a single linear scan (no markdown parsing)
-    // — cheap enough for the render path of this children-memoized
-    // component. Unbalanced delimiters pass through untouched, so mid-stream
-    // chunks render literally until the closing delimiter arrives and the
-    // full text is re-transformed.
+    // Legacy backslash delimiters are converted in a single linear scan;
+    // native dollar math passes through to Streamdown unchanged. Incomplete
+    // legacy spans are left for a later render when their closer arrives.
     const content =
       typeof children === "string"
         ? transformMathDelimiters(children)
diff --git a/components/answered-card.tsx b/components/answered-card.tsx
index b3f2319..f281e33 100644
--- a/components/answered-card.tsx
+++ b/components/answered-card.tsx
@@ -7,6 +7,7 @@ import { ThinkingBlock } from "@/components/thinking-block";
 import { cn } from "@/lib/utils";
 import { MessageResponse } from "@/components/ai-elements/message";
 import type { QuestionAnswerData } from "@/src/core";
+import { parseAskInput, parseQuizInput } from "@/src/core";
 
 /**
  * Static rendering of an answered question (tool part in `output-available`).
@@ -18,7 +19,7 @@ import type { QuestionAnswerData } from "@/src/core";
  * client — the card reveals his answer, the committed correct answer, and
  * the explanation, with NO verdict chips (owner ruling 2026-09-27).
  */
-export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
+export function AnsweredCard({ answer, input }: { answer: QuestionAnswerData; input?: unknown }) {
 	const [whyOpen, setWhyOpen] = useState(false); // the tucked explanation (predictions, owner 2026-10-03)
 	if (answer.dismissed) {
 		return (
@@ -32,6 +33,15 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 	const isExplain = answer.kind === "explain";
 	const selectedIdx = new Set(answer.answers.map((a) => a.index));
 	const correctIdx = new Set(answer.correctIndices ?? []);
+	// The question's own context rides the ORIGINAL CALL, not the answer
+	// snapshot (owner, 2026-10-12): the details line — and, for ask
+	// questions, option descriptions — re-render from the persisted
+	// arguments, so every existing transcript shows them too. The lean
+	// snapshot (what the model sees, compactAnswerForModel) is untouched;
+	// any parse failure or absent input renders exactly the older card.
+	const askInput = answer.kind === "ask" ? parseAskInput(input) : undefined;
+	const parsedDetails = askInput?.details ?? (answer.kind === "quiz" ? parseQuizInput(input)?.details : undefined);
+	const descByIndex = new Map((askInput?.options ?? []).map((o, i) => [i + 1, o.description]));
 
 	return (
 		<>
@@ -78,6 +88,13 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 			<div className="mb-3 font-medium">
 				<MessageResponse>{answer.questionText}</MessageResponse>
 			</div>
+			{parsedDetails && (
+				// The details line, same paint as the pending dock (owner,
+				// 2026-10-12): full markdown, LaTeX included.
+				<div className="mb-3 text-sm text-muted-foreground">
+					<MessageResponse>{parsedDetails}</MessageResponse>
+				</div>
+			)}
 
 			{((answer.options?.length ?? 0) > 0 || answer.other) && (
 				<div className="flex flex-col gap-1.5 text-sm">
@@ -115,6 +132,14 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 								)}
 								<span className={cn(!sel && "text-muted-foreground")}>
 									<MessageResponse>{opt.label}</MessageResponse>
+									{descByIndex.get(opt.index) && (
+										// Ask-option subtext (owner, 2026-10-12): same markdown path
+										// as the pending dock — LaTeX included. Quiz options carry
+										// none (owner ruling 2026-09-26); the map stays empty for them.
+										<MessageResponse className="lh-prose block text-xs text-muted-foreground">
+											{descByIndex.get(opt.index)}
+										</MessageResponse>
+									)}
 								</span>
 							</div>
 						);
diff --git a/components/chat.tsx b/components/chat.tsx
index dc677bc..7746ee1 100644
--- a/components/chat.tsx
+++ b/components/chat.tsx
@@ -1487,7 +1487,9 @@ export function Chat({
 														// Pending/streaming questions live in the dock, not the
 														// transcript; answered ones render as graded records.
 														if (part.state === "output-available") {
-															return <AnsweredCard key={pi} answer={part.output as QuestionAnswerData} />;
+															return (
+																<AnsweredCard key={pi} answer={part.output as QuestionAnswerData} input={part.input} />
+															);
 														}
 														return null;
 													}
diff --git a/components/question-dock.tsx b/components/question-dock.tsx
index 6981e17..661c18b 100644
--- a/components/question-dock.tsx
+++ b/components/question-dock.tsx
@@ -9,7 +9,6 @@ import { MessageResponse } from "@/components/ai-elements/message";
 import { cn } from "@/lib/utils";
 import {
 	buildAnswer,
-	coerceCorrectAnswer,
 	normalizeQuizType,
 	CONFIDENCE_STOPS,
 	DEFAULT_CONFIDENCE_INDEX,
@@ -170,7 +169,7 @@ function teaserText(q: string): string {
 	return q
 		.replace(/\\\(([\s\S]*?)\\\)/g, "$1") // \(...\) inline math
 		.replace(/\\\[([\s\S]*?)\\\]/g, "$1") // \[...\] display math
-		.replace(/\$\$?([^$]*)\$\$?/g, "$1") // legacy $...$ (pre-switch sessions)
+		.replace(/\$\$?([^$]*)\$\$?/g, "$1") // standard $...$/$$...$$ math
 		.replace(/\\frac\{([^{}]*)\}\{([^{}]*)\}/g, "$1/$2")
 		.replace(/\\([a-zA-Z]+)/g, "$1")
 		.replace(/[{}]/g, "")
@@ -293,7 +292,7 @@ function QuestionDockForm({
 			createdAt: new Date().toISOString(),
 		};
 		if (quizInput) {
-			const resolved = resolveCorrect(coerceCorrectAnswer(quizInput.correctAnswer), ordered);
+			const resolved = resolveCorrect(quizInput.correctAnswer, ordered);
 			if (resolved.error) console.error("[quiz] correctAnswer did not resolve:", resolved.error);
 			q.correctIndices = resolved.indices;
 			q.explanation = quizInput.explanation;
@@ -607,8 +606,12 @@ function QuestionDockForm({
 											// the "I don't know" copy stays JetBrains Mono. QUIZ options render
 											// NO description (owner ruling 2026-09-26): the model used them to
 											// telegraph correctness — the schema dropped the field and old
-											// records must not leak either.
-											<span className="lh-prose block text-xs text-muted-foreground">{opt.description}</span>
+											// records must not leak either. Same MessageResponse path as the
+											// label (owner, 2026-10-12): descriptions are full markdown —
+											// LaTeX included — not plain text.
+											<MessageResponse className="lh-prose block text-xs text-muted-foreground">
+												{opt.description}
+											</MessageResponse>
 										)}
 									</span>
 								</button>
diff --git a/docs/vision.md b/docs/vision.md
index 7a98af9..0d9ee74 100644
--- a/docs/vision.md
+++ b/docs/vision.md
@@ -231,6 +231,8 @@ The teacher's context window and attention are precious — it has the lesson to
 
 ## 3. Presentation layer (noted, not yet scheduled)
 
+**Current math authoring contract (2026-10-12):** standard `$...$` inline and `$$...$$` on separate lines for display. This supersedes the currency-only dollar rule below; correctly formed backslash-delimited content remains readable. Existing JSON-escape restoration also recognizes the new delimiters, with its recovery rules unchanged. Additional examples, math validation, over-escaping repairs, and transport redesign are deferred. The original W3 decisions below are historical.
+
 - **LaTeX delimiters: switch to the ChatGPT convention.** Inline math `\(...\)`, display math `\[...\]`. The single `$` is retired from math duty and reserved for currency (ending the dollar-sign hazard for good, on both teacher output and eventually user input). Technical path: preprocess `\(...\)`/`\[...\]` → remark-math-compatible form (or a dedicated micromark extension), plus a system-prompt update. The old `$`/`$$` contract dies with this change.
 - **Line breaks bug:** lesson text loses single line breaks (markdown semantics collapse them — likely fix: `remark-breaks`, or prompt-level blank-line discipline; verify and fix).
 - **Lesson-content formatting:** richer, more structured presentation of teaching blocks (headings, callouts, worked examples) — direction noted, specifics TBD.
diff --git a/src/agent/prompt-segments.ts b/src/agent/prompt-segments.ts
index 57f964a..5d8cc5a 100644
--- a/src/agent/prompt-segments.ts
+++ b/src/agent/prompt-segments.ts
@@ -70,7 +70,7 @@ export function listSourceSegments(agent: PromptAgent): Array<{ path: string; sh
 	// file mechanics stay out (the doctrine contradicts them; 00-base.md
 	// plays the base role), but the FORMATTING guide composes for every
 	// agent (owner, 2026-10-04 late): LaTeX delimiters and markdown apply
-	// in all settings — practice must write \(...\)/\[...\] too.
+	// in all settings — practice shares the $...$/$$...$$ authoring contract.
 	const segments: Array<{ path: string; shared: boolean; file: string }> = agent === "practice" ? [] : [
 		{ path: "system-prompt.md", shared: true, file: PATHS.teacherPrompt },
 	];
diff --git a/src/agent/prompts/shared/20-question-tools.md b/src/agent/prompts/shared/20-question-tools.md
index d5e6e75..df6888c 100644
--- a/src/agent/prompts/shared/20-question-tools.md
+++ b/src/agent/prompts/shared/20-question-tools.md
@@ -7,7 +7,7 @@ Two instruments. The quiz tool (its exact name depends on the quizzing mechanic
 Applies to every graded question you ask, whatever its role:
 
 - Multiple choice carries a separate `explanation` (why the correct option is correct, written BEFORE `correctAnswer`: reason it out first, then commit). Free recall has ONE field — `correctAnswer`, the committed answer with its reasoning inside.
-- **LaTeX everywhere.** Every question field renders markdown and LaTeX — the question text, every option, every explanation. Anything expressible as math goes in math: formulas, symbols, even single variables (`\(x\)`, `\(\alpha\)`). Plain-text math in a question is a craft failure; `\(...\)` and `\[...\]` are the only delimiters (never `$`).
+- **LaTeX everywhere.** Every question field renders markdown and LaTeX — the question text, every option, every explanation. Anything expressible as math goes in math: formulas, symbols, even single variables (`$x$`, `$\alpha$`). Plain-text math in a question is a craft failure; use `$...$` for inline math and `$$...$$` on separate lines for display math.
 - **The option craft.** The giveaway is never the distractors' wrongness, it's asymmetry: the correct option carrying its reasoning while the others are bare, or key-term bolding that flags it. Build evenness in: (1) every option is a bare claim — zero "why" in any of them; all reasoning goes in the explanation, shown only after he answers; (2) write the correct claim first, then mutate it into each distractor — what would someone holding a specific misconception claim? Same skeleton, same grain, same register; (3) each distractor is a real, BELIEVABLE error — the answer he would actually give under a specific wrong model, wrong on knowledge, never obviously wrong on sight. An option a cold reader eliminates instantly is a wasted option: his pick is diagnostic only when the wrong model is what selects it; (4) no asymmetric bolding. If you can tell the right one cold without knowing the material, regenerate — don't patch.
 - **Free-recall grading.** Grade his words strictly against the committed answer; never mark a wrong answer right to be kind — a near-miss is partial understanding: name exactly what he got and what he missed. If he genuinely doesn't know, he says so in his own words — that is a genuine gap, not a wrong answer.
 
diff --git a/src/agent/prompts/shared/40-formatting.md b/src/agent/prompts/shared/40-formatting.md
index c331e20..22499d4 100644
--- a/src/agent/prompts/shared/40-formatting.md
+++ b/src/agent/prompts/shared/40-formatting.md
@@ -2,6 +2,6 @@
 
 Everything you write — every message, every quiz question, every quiz option and explanation — renders as markdown to him, and the full set is available: headings, lists, tables, fenced code, inline code, bold, mermaid diagrams. Use it maximally when it fits — the default is a structured document, not a wall of prose. Headings for the sections a message naturally has; lists and tables for anything enumerable or comparative; code blocks for anything literal. Structure is not decoration — it makes the content readable at a glance — and when in doubt, structure it.
 
-- Math: anything expressible in LaTeX goes in LaTeX — formulas, symbols, even single variables — everywhere text renders, and that means EVERY field: prose, quiz questions, quiz options, explanations, problem statements, answers. Inline `\(f(x)\)`, display `\[` fenced on its own lines. NEVER `$` or `$$` — a bare `$` is literal currency here; `\(...\)` and `\[...\]` are the only delimiters that render.
+- Math: anything expressible in LaTeX goes in LaTeX — formulas, symbols, even single variables — everywhere text renders, and that means EVERY field: prose, quiz questions, quiz options, explanations, problem statements, answers. Inline `$f(x)$`, display `$$` fenced on its own lines. Use `$...$` for inline math and `$$...$$` on separate lines for display math. In JSON strings (tool arguments), use `\\` for LaTeX command backslashes, `\\\\` for TeX row breaks, and `\n` for newlines.
 - Key ideas: a GitHub-style `> [!IMPORTANT]` callout renders as a distinct outlined block — the one emphasis device for load-bearing ideas. Use it sparingly: an unconditional truth as it's laid down, a payoff when it lands, a definition the whole chain hinges on. Everything else stays in prose — if everything is boxed, nothing is.
 - Diagrams: ```mermaid fenced blocks render as real diagrams — reach for one whenever structure, flow, or relationships are the point; a good diagram beats three paragraphs. Node labels with spaces or symbols must use quoted bracket form (`B["u = x^3"]`).
diff --git a/src/agent/tools.ts b/src/agent/tools.ts
index d1c8357..a9cc81b 100644
--- a/src/agent/tools.ts
+++ b/src/agent/tools.ts
@@ -106,12 +106,42 @@ export const askUserQuestionTool: AgentTool<typeof askInputSchema> = {
 // quiz variants): duplicates stay honest by sharing SCHEMA ATOMS
 // (question-core) + PROMPT CHUNKS, and each tool declares only its
 // mechanical delta.
+//
+// ONE sanctioned exception (owner, 2026-10-12): each quiz tool's
+// description ends with a COMPLETE example call — compact, phase-correct
+// (probe carries no phase metadata; quiz leads with type+nodeId), doubling
+// as the JSON-escaping exemplar (LaTeX backslashes double inside JSON
+// strings). Placement ruling: WITH THE TOOL, beside its exact schema — a
+// shared-prompt example is phase-ambiguous (the models fumbled exactly
+// these metadata fields), per-agent prompt copies would drift. Serialized
+// from ONE canonical body so the variants cannot disagree; craft doctrine
+// stays in the prompts.
+
+/** The canonical example body (owner-approved content, 2026-10-12): a
+ *  compact applied question whose fields exercise the escaping hazards —
+ *  braced commands (\frac, \cos), inline and display math, newlines —
+ *  while doubling as an exemplar of good craft: uniform options, stable
+ *  values, reasoning (explanation) committed before correctAnswer.
+ *  JSON.stringify renders the wire text, so the escaping the model sees
+ *  is by construction the correct one. Exported for the description pins. */
+export const quizExampleBody = {
+	question: "A signal is $y=\\sin(2x)$ and $\\frac{dx}{dt}=3$. What is $\\frac{dy}{dt}$?",
+	options: [
+		{ label: "$6\\cos(2x)$", value: "a" },
+		{ label: "$2\\cos(2x)$", value: "b" },
+		{ label: "$3\\cos(2x)$", value: "c" },
+	],
+	explanation:
+		"The phase changes twice as fast as $x$; multiply by the sine's slope:\n$$\n\\frac{dy}{dt}=\\cos(2x)\\cdot2\\cdot3=6\\cos(2x)\n$$",
+	correctAnswer: "a",
+};
 
 /** The quiz mechanics every variant shares; `delta` appends the variant's
  *  own fields (its NAME among them — the probe-phase tools self-reference
- *  as probe/recall, owner 2026-10-09). All mechanics, zero doctrine. */
+ *  as probe/recall, owner 2026-10-09). All mechanics, zero doctrine — plus
+ *  the one sanctioned example (above). */
 function quizDescription(delta: { name: "quiz" | "probe"; nodeId: boolean; types: boolean }): string {
-	return (
+	const base =
 		"Ask the learner a GRADED question with a known correct answer, then instantly grade and give feedback. " +
 		"Unlike ask_user_question (which collects preferences/decisions with no right answer), " +
 		delta.name +
@@ -129,7 +159,17 @@ function quizDescription(delta: { name: "quiz" | "probe"; nodeId: boolean; types
 			: "") +
 		"ONE question per turn: call a single " +
 		delta.name +
-		", then end your turn — his answer determines the next."
+		", then end your turn — his answer determines the next.";
+	// Phase-correct shape: the teach example LEADS with the required pair
+	// (type, nodeId — the 2026-10-09 drop-order ruling); the probe example
+	// carries no phase metadata at all, exactly like the probe schema.
+	const example = delta.nodeId ? { type: "check" as const, nodeId: "chain-rule", ...quizExampleBody } : quizExampleBody;
+	return (
+		base +
+		"\nExample arguments — copy the escaping exactly: inside JSON strings a LaTeX backslash is \\\\ and a newline is \\n.\n```json\n" +
+		JSON.stringify(example, null, 2) +
+		"\n```" +
+		(delta.nodeId ? " The example's nodeId is illustrative — copy an exact id from this session's plan_init." : "")
 	);
 }
 
diff --git a/src/core/math-delims.ts b/src/core/math-delims.ts
index 56592ab..cb700c3 100644
--- a/src/core/math-delims.ts
+++ b/src/core/math-delims.ts
@@ -1,17 +1,15 @@
 /**
- * Math delimiter preprocessing — the \(...\)/\[...\] contract.
+ * Legacy math delimiter preprocessing — the \(...\)/\[...\] reader.
  *
- * The teacher writes inline math as `\(...\)` and display math as `\[...\]`;
- * a bare `$` is ALWAYS literal currency (system-prompt contract). remark-math
- * expects `$...$`/`$$...$$`, so this pure transform rewrites balanced
- * delimiters before the markdown hits Streamdown. Combined with
- * `singleDollarTextMath: false`, the dollar sign can never start math — the
- * currency hazard dies structurally.
+ * Current authoring uses `$...$` inline and `$$...$$` on separate lines for
+ * display (owner, 2026-10-12). This pure transform keeps correctly formed
+ * old backslash-delimited content readable; dollar math passes through to
+ * Streamdown's native parser. Escape restoration below recognizes both
+ * syntaxes while retaining the existing recovery rules.
  *
  * Rules:
- * - `\(...\)` → `$$...$$` (two-dollar inline: with
- *   `singleDollarTextMath: false` this is the only inline math form micromark
- *   still parses), `\[...\]` → `$$\n...\n$$` (block form: flow math).
+ * - `\(...\)` → `$$...$$` (two-dollar inline, still accepted by micromark),
+ *   `\[...\]` → `$$\n...\n$$` (block form: flow math).
  * - An escaped delimiter (`\\(` = literal backslash + paren) is left alone.
  * - Nothing inside fenced code blocks or inline code spans is touched.
  * - Unbalanced delimiters are left untouched: Streamdown streams chunks, and
@@ -196,8 +194,8 @@ export function transformMathDelimiters(markdown: string): string {
 									closeEndsLine(markdown, afterClose) ? "" : "\n\n";
 							out.push(`${padBefore}$$\n${content}\n$$${padAfter}`);
 						} else {
-							// Two-dollar inline: the only inline math form left with
-							// singleDollarTextMath: false (renders inline, not display).
+							// Preserve the legacy reader's two-dollar inline output
+							// (renders inline, not display).
 							out.push(`$$${content}$$`);
 						}
 						i = closeAt + close.length;
@@ -226,9 +224,9 @@ export function transformMathDelimiters(markdown: string): string {
  * control chars can never be legitimate content, so restoring the two-char
  * escape reconstructs the model's intent byte-perfectly. Outside spans the
  * same chars might be real prose (pasted tables, formatted text), so only
- * balanced `\(…\)` / `\[…\]` spans are touched — the same scanner rules as
- * transformMathDelimiters (escaped delimiters are literal, unbalanced
- * delimiters pass through untouched).
+ * balanced math spans are touched. The legacy `\(…\)` / `\[…\]` pass stays
+ * unchanged; the dollar reader adds `$…$` and fenced `$$…$$` recognition,
+ * excluding code and escaped opening dollars. Unbalanced spans pass through.
  *
  * ASYMMETRIC NEWLINE RULE (owner ruling 2026-09-27, Option A): inline spans
  * restore all six debris chars — real newlines/tabs inside INLINE math
@@ -257,6 +255,12 @@ const DEBRIS_RE = /[\b\t\n\v\f\r]/;
 const DISPLAY_DEBRIS_RE = /[\b\t\v\f\r]/;
 
 export function restoreMathEscapes(text: string): string {
+	if (!DEBRIS_RE.test(text)) return text;
+	return restoreDollarMathEscapes(restoreLegacyMathEscapes(text));
+}
+
+/** Keep legacy recovery byte-for-byte; only the recognized syntax expands. */
+function restoreLegacyMathEscapes(text: string): string {
 	if (!DEBRIS_RE.test(text)) return text;
 	const out: string[] = [];
 	let i = 0;
@@ -283,3 +287,113 @@ export function restoreMathEscapes(text: string): string {
 	}
 	return out.join("");
 }
+
+function dollarRun(text: string, i: number): number {
+	let count = 0;
+	while (text[i + count] === "$") count += 1;
+	return count;
+}
+
+/** Native math fences start at a line's block position; one-line $$…$$
+ *  remains inline. A flow opener may have metadata, but never another $. */
+function dollarIsDisplay(text: string, i: number, size: number): boolean {
+	if (size < 2 || !displayIsBlockPositioned(text, i)) return false;
+	const end = text.indexOf("\n", i + size);
+	return !text.slice(i + size, end === -1 ? text.length : end).includes("$");
+}
+
+/** Match micromark's delimiter runs: exact size inline, at least the
+ *  opener's size on an otherwise-empty line for display. Inside math,
+ *  backslashes are TeX data, not Markdown escapes for closing dollars. */
+function findDollarClose(
+	text: string,
+	from: number,
+	size: number,
+	isDisplay: boolean,
+): { at: number; after: number } | undefined {
+	if (isDisplay) {
+		let lineEnd = text.indexOf("\n", from);
+		while (lineEnd !== -1) {
+			const start = lineEnd + 1;
+			lineEnd = text.indexOf("\n", start);
+			const line = text.slice(start, lineEnd === -1 ? text.length : lineEnd);
+			const close = /^([ \t]{0,3})(\$+)[ \t]*\r?$/.exec(line);
+			if (close && close[2]!.length >= size) {
+				const at = start + close[1]!.length;
+				return { at, after: at + close[2]!.length };
+			}
+		}
+		return undefined;
+	}
+	for (let j = from; j < text.length;) {
+		if (text[j] !== "$") {
+			j += 1;
+			continue;
+		}
+		const count = dollarRun(text, j);
+		if (count === size) return { at: j, after: j + count };
+		j += count;
+	}
+	return undefined;
+}
+
+/** Dollar recognition only — the same six/five-character repair maps,
+ *  with no over-escaping normalization or mathematical validation. */
+function restoreDollarMathEscapes(text: string): string {
+	if (!DEBRIS_RE.test(text) || !text.includes("$")) return text;
+	const out: string[] = [];
+	let i = 0;
+	while (i < text.length) {
+		if (atLineStart(text, i) && FENCE_OPEN_RE.test(text.slice(i))) {
+			i = copyFencedBlock(text, i, out);
+			continue;
+		}
+		if (text[i] === "`") {
+			const run = backtickRun(text, i);
+			let j = i + run;
+			while (j < text.length) {
+				const nextRun = backtickRun(text, j);
+				if (nextRun === run) break;
+				j += Math.max(nextRun, 1);
+			}
+			const after = j < text.length ? j + run : i + run;
+			out.push(text.slice(i, after));
+			i = after;
+			continue;
+		}
+		// Legacy spans have already received their own inline/display policy.
+		// Do not reinterpret dollars inside them in this second pass.
+		if (text[i] === "\\" && !isEscaped(text, i)) {
+			const next = text[i + 1];
+			if (next === "(" || next === "[") {
+				const closeAt = findClose(text, i + 2, next === "[" ? DISPLAY_CLOSE : INLINE_CLOSE);
+				if (closeAt !== -1) {
+					out.push(text.slice(i, closeAt + 2));
+					i = closeAt + 2;
+					continue;
+				}
+			}
+		}
+		if (text[i] === "$" && !isEscaped(text, i)) {
+			const size = dollarRun(text, i);
+			const isDisplay = dollarIsDisplay(text, i, size);
+			const close = findDollarClose(text, i + size, size, isDisplay);
+			if (close) {
+				const debris = isDisplay ? DISPLAY_DEBRIS_RE : DEBRIS_RE;
+				out.push(
+					text.slice(i, i + size) +
+					text.slice(i + size, close.at).replace(debris, (c) => ESCAPE_DEBRIS[c]!) +
+					text.slice(close.at, close.after),
+				);
+				i = close.after;
+				continue;
+			}
+			out.push(text.slice(i, i + size));
+			i += size;
+			continue;
+		}
+		out.push(text[i]!);
+		i += 1;
+	}
+	return out.join("");
+}
diff --git a/src/core/question-core.ts b/src/core/question-core.ts
index 33e9422..f0b3214 100644
--- a/src/core/question-core.ts
+++ b/src/core/question-core.ts
@@ -116,9 +116,9 @@ export function quizInputProblems(input: {
 }): string[] {
 	const { problems, keys } = optionProblems(input.options);
 
-	// Debris (colons/quotes/whitespace) strips inside coerceCorrectAnswer —
-	// the shared membership seam (boundary, display, grading).
-	const entries = coerceCorrectAnswer(input.correctAnswer);
+	// Preserve exact option keys before trying copy-syntax cleanup — the
+	// same option-aware coercion runs at the display and grading seams.
+	const entries = coerceCorrectAnswer(input.correctAnswer, keys);
 	const unique = [...new Set(entries)];
 	if (unique.length === 0 || unique.some((v) => v.length === 0)) {
 		problems.push("correctAnswer is required — provide the value (or label) of the correct option(s).");
@@ -606,25 +606,34 @@ export function shuffleOptions(options: QuizOption[], rand: () => number = Math.
 
 // ─── quiz grading ───────────────────────────────────────────────────────────
 
-/** The harness sometimes delivers a multi-select correctAnswer array as a
- *  JSON-stringified string because the schema union lists String first.
- *  Every entry carries the MODEL-VALUE DEBRIS STRIP (whitehead,
- *  2026-10-09): glm-5.3 copied option values with the JSON key-value
- *  colon glued on (`[":parmenides"]`); membership comparisons on ALL
- *  three seams (boundary check, display parse, grading) route through
- *  here, so the strip heals new calls AND already-poisoned records. */
-export function coerceCorrectAnswer(correctAnswer: string | string[]): string[] {
-	if (Array.isArray(correctAnswer)) return correctAnswer.map(stripModelValueDebris);
+/** Preserve an exact option key before trying copy-syntax cleanup: a
+ *  label's final period, quotes, or backticks can be CONTENT (calculus
+ *  incident, 2026-10-12), not model debris. The actual option values are
+ *  required so no caller can strip a valid answer before membership.
+ *  Non-matches keep the existing whitehead heal (`[":parmenides"]`) and
+ *  JSON-stringified multi-select coercion. Shared by boundary, display,
+ *  and grading; canonical option keys are never rewritten. */
+export function coerceCorrectAnswer(
+	correctAnswer: string | string[],
+	optionValues: readonly string[],
+): string[] {
+	const clean = (value: string): string => {
+		const trimmed = value.trim();
+		return optionValues.includes(trimmed) ? trimmed : stripModelValueDebris(value);
+	};
+	if (Array.isArray(correctAnswer)) return correctAnswer.map(clean);
 	const trimmed = correctAnswer.trim();
+	// An exact string key can itself look like a JSON array.
+	if (optionValues.includes(trimmed)) return [trimmed];
 	if (trimmed.startsWith("[") && trimmed.endsWith("]")) {
 		try {
 			const parsed = JSON.parse(trimmed);
-			if (Array.isArray(parsed)) return parsed.map((v) => stripModelValueDebris(String(v)));
+			if (Array.isArray(parsed)) return parsed.map((v) => clean(String(v)));
 		} catch {
 			// not valid JSON — treat as a single literal value
 		}
 	}
-	return [stripModelValueDebris(correctAnswer)];
+	return [clean(correctAnswer)];
 }
 
 /** Resolve author-supplied value(s) to 1-based display indices. Keying by
@@ -635,7 +644,7 @@ export function resolveCorrect(
 	options: QuizOption[],
 ): { indices: number[]; error?: string } {
 	if (correctAnswer === undefined) return { indices: [], error: "correctAnswer is required" };
-	const arr = coerceCorrectAnswer(correctAnswer);
+	const arr = coerceCorrectAnswer(correctAnswer, options.map((o) => o.value));
 	if (arr.length === 0) return { indices: [], error: "correctAnswer is required" };
 	const byValue = new Map(options.map((o, i) => [o.value, i + 1]));
 	const indices: number[] = [];
diff --git a/tests/chat-flow.test.ts b/tests/chat-flow.test.ts
index 7837420..ed25fcc 100644
--- a/tests/chat-flow.test.ts
+++ b/tests/chat-flow.test.ts
@@ -35,7 +35,7 @@ import { buildSubagentSteer } from "../src/core/contracts.ts";
 import { abortTurn, runningTurn, settledTurnResponse } from "../src/server/turn-runs.ts";
 import { chatStore } from "../src/store/chats.ts";
 import { jobStore } from "../src/store/jobs.ts";
-import { buildAnswer, coerceCorrectAnswer, dismissedAnswer, normalizeOptions, resolveCorrect, type QuestionData } from "../src/core/question-core.ts";
+import { buildAnswer, dismissedAnswer, normalizeOptions, resolveCorrect, type QuestionData } from "../src/core/question-core.ts";
 import { danglingQuestionOf, endsInDismissal, needsContinuation, newAnswerResult } from "../src/core/native-messages.ts";
 import { projectView } from "../src/core/view.ts";
 import type { PiEngine } from "../src/agent/models.ts";
@@ -113,7 +113,7 @@ function gradedAnswer(input: typeof QUIZ_INPUT, values: string[]) {
 		question: input.question,
 		mode: "single-select",
 		options,
-		correctIndices: resolveCorrect(coerceCorrectAnswer(input.correctAnswer), options).indices,
+		correctIndices: resolveCorrect(input.correctAnswer, options).indices,
 		explanation: input.explanation,
 		createdAt: new Date().toISOString(),
 	};
diff --git a/tests/practice-agents.test.ts b/tests/practice-agents.test.ts
index 932b2fc..f36f857 100644
--- a/tests/practice-agents.test.ts
+++ b/tests/practice-agents.test.ts
@@ -295,8 +295,12 @@ describe("practice prompt composition (own directory + the formatting appendix)"
 
 	it("the SHARED formatting guide composes (owner, 2026-10-04 late): LaTeX delimiters in every setting", () => {
 		const prompt = composeInstructions("practice");
-		// The delimiter law — practice must write \(...\)/\[...\] too.
-		assert.match(prompt, /NEVER `\$` or `\$\$`/);
+		// The standard delimiter law is shared by all three authoring agents.
+		for (const agent of ["practice", "prober", "teacher"] as const) {
+			const instructions = composeInstructions(agent);
+			assert.ok(instructions.includes("Inline `$f(x)$`, display `$$` fenced on its own lines."));
+			assert.ok(!instructions.includes("NEVER `$` or `$$`"));
+		}
 		assert.ok(prompt.indexOf("# The practice session") < prompt.indexOf("## Formatting"), "formatting rides as the appendix");
 	});
 
diff --git a/tests/question-core.test.ts b/tests/question-core.test.ts
index 221f1ea..9ebc3ba 100644
--- a/tests/question-core.test.ts
+++ b/tests/question-core.test.ts
@@ -36,6 +36,7 @@ import {
 	toClientQuestion,
 } from "../src/core/question-core.ts";
 import { toolQuestionKind } from "../src/core/pending.ts";
+import { parseQuizInput } from "../src/core/tool-parts.ts";
 
 // ─── the authoring contract (TypeBox schemas + execute-time refinements) ──
 // Schema-valid ⇔ gradeable: a quiz whose correctAnswer can't be resolved
@@ -249,20 +250,28 @@ describe("shuffleOptions", () => {
 // ─── coerceCorrectAnswer ────────────────────────────────────────────────────
 
 describe("coerceCorrectAnswer", () => {
+	const values = ["mercury", "a", "b"];
+
 	it("wraps a single string", () => {
-		assert.deepEqual(coerceCorrectAnswer("mercury"), ["mercury"]);
+		assert.deepEqual(coerceCorrectAnswer("mercury", values), ["mercury"]);
 	});
 
 	it("passes arrays through", () => {
-		assert.deepEqual(coerceCorrectAnswer(["a", "b"]), ["a", "b"]);
+		assert.deepEqual(coerceCorrectAnswer(["a", "b"], values), ["a", "b"]);
 	});
 
 	it("parses a JSON-stringified multi-select array", () => {
-		assert.deepEqual(coerceCorrectAnswer('["a", "b"]'), ["a", "b"]);
+		assert.deepEqual(coerceCorrectAnswer('["a", "b"]', values), ["a", "b"]);
 	});
 
 	it("leaves a non-JSON bracketed string alone", () => {
-		assert.deepEqual(coerceCorrectAnswer("[not json"), ["[not json"]);
+		assert.deepEqual(coerceCorrectAnswer("[not json", values), ["[not json"]);
+	});
+
+	it("preserves an exact key even when it looks like a JSON array", () => {
+		const key = '["a", "b"]';
+		assert.deepEqual(coerceCorrectAnswer(key, [...values, key]), [key]);
+		assert.deepEqual(coerceCorrectAnswer("[]", ["[]"]), ["[]"]);
 	});
 });
 
@@ -302,6 +311,91 @@ describe("resolveCorrect", () => {
 	});
 });
 
+describe("exact answer membership precedes debris cleanup", () => {
+	it("the calculus label's final period survives boundary, display, shuffle, and grading", () => {
+		const correct = "$f$ need not be differentiable at $a$.";
+		const input = {
+			question: "All partial derivatives of $f$ exist at $a$. Must $f$ be differentiable there?",
+			options: [{ label: "$f$ is differentiable at $a$." }, { label: correct }],
+			explanation: "Existing partial derivatives need not give a linear approximation.",
+			correctAnswer: correct,
+		};
+		const before = JSON.stringify(input);
+		assert.ok(boundaryOk(probeQuizInputSchema, input, quizInputProblems(input)));
+		const parsed = parseQuizInput(input);
+		assert.ok(parsed, "the accepted raw call must also render");
+		assert.equal(parsed.correctAnswer, correct);
+		const options = normalizeOptions(parsed.options).reverse();
+		const resolved = resolveCorrect(parsed.correctAnswer, options);
+		assert.deepEqual(resolved, { indices: [1] });
+		const qd: QuestionData = {
+			id: "calculus-period",
+			kind: "quiz",
+			question: parsed.question,
+			mode: "single-select",
+			options,
+			correctIndices: resolved.indices,
+			explanation: parsed.explanation,
+			createdAt: "2026-10-12T00:00:00Z",
+		};
+		assert.equal(buildAnswer(qd, { values: [correct] }).correct, true);
+		assert.equal(buildAnswer(qd, { values: [input.options[0]!.label] }).correct, false);
+		assert.equal(JSON.stringify(input), before, "raw arguments are never rewritten");
+	});
+
+	it("retains punctuation, quotes, colons, and backticks in exact labels and explicit keys", () => {
+		for (const key of ["value.", "value:", '"value"', "'value'", "`value`", ":value"]) {
+			for (const option of [{ label: key }, { label: "A claim", value: key }]) {
+				const input = {
+					question: "Which claim?",
+					options: [option, { label: "Other", value: "other" }],
+					explanation: "The first claim follows.",
+					correctAnswer: key,
+				};
+				assert.deepEqual(quizInputProblems(input), [], key);
+				assert.ok(parseQuizInput(input), key);
+				assert.deepEqual(resolveCorrect(key, normalizeOptions(input.options)), { indices: [1] }, key);
+			}
+		}
+	});
+
+	it("never redirects an exact punctuated key to a different debris-free option", () => {
+		const keys = ["value", "value.", '"value"', "`value`", ":value"];
+		const options = normalizeOptions(keys.map((value, i) => ({ label: `Claim ${i}`, value })));
+		for (const [i, key] of keys.entries()) {
+			assert.deepEqual(resolveCorrect(key, options), { indices: [i + 1] }, key);
+		}
+		assert.deepEqual(options.map((o) => o.value), keys, "canonical keys stay distinct and untouched");
+	});
+
+	it("preserves exact multi-select entries while still healing non-matching copy debris", () => {
+		const input = {
+			question: "Which claims?",
+			options: [{ label: "First." }, { label: "Second", value: "second" }],
+			explanation: "Both claims follow.",
+			multiSelect: true,
+		};
+		for (const correctAnswer of [["First.", ': "second"'], JSON.stringify(["First.", ': "second"'])]) {
+			assert.deepEqual(quizInputProblems({ ...input, correctAnswer }), []);
+			assert.ok(parseQuizInput({ ...input, correctAnswer }));
+			assert.deepEqual(resolveCorrect(correctAnswer, normalizeOptions(input.options)), { indices: [1, 2] });
+		}
+	});
+
+	it("retains an exact JSON-looking option key across validation and grading", () => {
+		const key = '["a", "b"]';
+		const input = {
+			question: "Which literal?",
+			options: [{ label: key }, { label: "Other" }],
+			explanation: "The first literal is intended.",
+			correctAnswer: key,
+		};
+		assert.deepEqual(quizInputProblems(input), []);
+		assert.ok(parseQuizInput(input));
+		assert.deepEqual(resolveCorrect(key, normalizeOptions(input.options)), { indices: [1] });
+	});
+});
+
 // ─── isCorrect (exact-set match) ────────────────────────────────────────────
 
 describe("isCorrect", () => {
@@ -692,7 +786,7 @@ describe("the quiz role field (predict | check)", () => {
 			question: valid.question,
 			mode: "single-select",
 			options,
-			correctIndices: resolveCorrect(coerceCorrectAnswer(valid.correctAnswer), options).indices,
+			correctIndices: resolveCorrect(valid.correctAnswer, options).indices,
 			explanation: valid.explanation,
 			createdAt: new Date().toISOString(),
 		};
diff --git a/tests/question-tools.test.ts b/tests/question-tools.test.ts
index 38cdadc..aaee97c 100644
--- a/tests/question-tools.test.ts
+++ b/tests/question-tools.test.ts
@@ -21,13 +21,14 @@ import {
 	createTeacherTools,
 	probeQuizTool,
 	probeExplainTool,
+	quizExampleBody,
 	teachExplainToolFor,
 	teachQuizToolFor,
 	type TeacherToolContext,
 } from "../src/agent/tools.ts";
 import { TOGGLEABLE_TOOLS } from "../src/core/pending.ts";
 import { jobStore } from "../src/store/jobs.ts";
-import { probeQuizInputSchema, quizInputObject } from "../src/core/question-core.ts";
+import { probeQuizInputSchema, quizInputObject, quizInputProblems } from "../src/core/question-core.ts";
 import { chatStore } from "../src/store/chats.ts";
 import { PATHS } from "../config.ts";
 
@@ -208,6 +209,47 @@ describe("the prober's quiz: no nodeId field at all", () => {
 		assert.equal(Value.Check(probe.parameters, { ...validQuiz, nodeId: "anything" }), true, "no session check to fail");
 	});
 });
+// ─── the description example (owner, 2026-10-12) ─────────────────────────
+
+describe("quiz tool descriptions carry the complete, phase-correct example", () => {
+	it("the canonical body is schema-valid and authoring-clean (never ship a broken exemplar)", () => {
+		assert.deepEqual(quizInputProblems(quizExampleBody), []);
+		assert.equal(Value.Check(probeQuizInputSchema, quizExampleBody), true);
+		const teachExample = { type: "check", nodeId: "chain-rule", ...quizExampleBody };
+		assert.equal(Value.Check(quizInputObject, teachExample), true);
+	});
+
+	it("probe: the serialized body rides the description with correct JSON escaping, no phase metadata", () => {
+		const desc = probeQuizTool.description;
+		assert.ok(
+			desc.includes("```json\n" + JSON.stringify(quizExampleBody, null, 2) + "\n```"),
+			"the example is the exact JSON.stringify of the canonical body",
+		);
+		// The escaping exemplar must be VISIBLE as wire text — the runtime
+		// string carries literal double backslashes, exactly what the model
+		// must type inside JSON.
+		assert.ok(desc.includes("A signal is $y=\\\\sin(2x)$"), "LaTeX command backslash shows doubled");
+		assert.ok(desc.includes("a LaTeX backslash is \\\\ and a newline is \\n"), "the one-line escaping hint");
+		assert.ok(!desc.includes("nodeId"), "probe example carries no phase metadata");
+	});
+
+	it("quiz: the required pair leads the example, with the plan-id caveat", () => {
+		const chatId = newChat("Teacher: description example");
+		const desc = teachQuizToolFor({ chatId, chatStore }).description;
+		const teachExample = { type: "check", nodeId: "chain-rule", ...quizExampleBody };
+		assert.ok(desc.includes("```json\n" + JSON.stringify(teachExample, null, 2) + "\n```"));
+		// The 2026-10-09 drop-order ruling: type+nodeId LEAD the object —
+		// fields generated first get dropped least.
+		assert.ok(
+			/```json\n\{\n {2}"type": "check",\n {2}"nodeId": "chain-rule",/.test(desc),
+			"type and nodeId lead the serialized example",
+		);
+		assert.ok(
+			desc.includes("illustrative — copy an exact id from this session's plan_init"),
+			"the illustrative-nodeId caveat",
+		);
+	});
+});
 // ─── tool availability (2026-09 settings seam) ───────────────────────────────
 
 describe("tool toggles (core/pending.ts + factories)", () => {
diff --git a/tests/render-cards.test.tsx b/tests/render-cards.test.tsx
index 543adee..f473f42 100644
--- a/tests/render-cards.test.tsx
+++ b/tests/render-cards.test.tsx
@@ -25,7 +25,6 @@ import type { JobRecord } from "../src/core/contracts.ts";
 import { AnsweredCard } from "../components/answered-card.tsx";
 import {
 	buildAnswer,
-	coerceCorrectAnswer,
 	normalizeOptions,
 	resolveCorrect,
 	questionNeedsReveal,
@@ -47,7 +46,7 @@ function quizQD(): QuestionData {
 		question: quizInput.question,
 		mode: "single-select",
 		options,
-		correctIndices: resolveCorrect(coerceCorrectAnswer(quizInput.correctAnswer), options).indices,
+		correctIndices: resolveCorrect(quizInput.correctAnswer, options).indices,
 		explanation: quizInput.explanation,
 		createdAt: new Date().toISOString(),
 	};
@@ -342,14 +341,13 @@ describe("render smoke tests", () => {
 });
 
 describe("math rendering (streamdown + KaTeX)", () => {
-	// New delimiter contract (W3): the teacher writes \(...\) / \[...\]; a
-	// bare $ is ALWAYS literal currency (singleDollarTextMath: false kills it
-	// structurally). transformMathDelimiters rewrites both to the two-dollar
-	// forms remark-math still parses. Full coverage: render-markdown.test.tsx.
-	it("renders $...$ as LITERAL text — a $ is never math (the currency fix)", () => {
+	// Standard authoring: $...$ inline and $$ on separate lines for display.
+	// The legacy backslash reader remains for existing content.
+	// Full coverage: render-markdown.test.tsx.
+	it("renders standard $...$ as inline math", () => {
 		const html = renderToStaticMarkup(<MessageResponse>{"The map $f(x) = x^2$ is smooth."}</MessageResponse>);
-		assert.ok(!html.includes("katex"), `$-math must not render, got: ${html.slice(0, 300)}`);
-		assert.match(html, /\$f\(x\) = x\^2\$/, "old-contract math renders verbatim");
+		assert.ok(html.includes("katex"), `$-math must render, got: ${html.slice(0, 300)}`);
+		assert.ok(!html.includes("katex-display"), "single-dollar math is inline");
 	});
 
 	it("renders display math ($$ fenced on own lines — the transform's target form)", () => {
@@ -366,10 +364,8 @@ describe("math rendering (streamdown + KaTeX)", () => {
 		assert.ok(html.includes("katex") && !html.includes("katex-display"), "one-liner should render inline");
 	});
 
-	it("does NOT eat escaped currency (\\$5 stays text — belt and suspenders)", () => {
-		// With singleDollarTextMath: false even a bare $5 can't parse as math;
-		// an escaped \$ is doubly safe. The prompt contract still asks the
-		// teacher to prefer plain "$5" (it renders literally now).
+	it("does NOT eat escaped currency (\\$5 stays text)", () => {
+		// With dollar math enabled, Markdown-escaped dollars remain literal.
 		const html = renderToStaticMarkup(<MessageResponse>{"It costs \\$5 and \\$10 more."}</MessageResponse>);
 		assert.ok(!html.includes("katex"), "escaped currency must not parse as math");
 		assert.match(html, /\$5/);
@@ -377,10 +373,10 @@ describe("math rendering (streamdown + KaTeX)", () => {
 
 	it("quiz cards render math in question, options, and explanation", () => {
 		const mathQuiz = {
-			question: "What is \\(\\frac{dy}{dx}\\) of \\(y = x^2\\)?",
-			options: [{ label: "\\(2x\\)" }, { label: "\\(x^2\\)" }, { label: "\\(x\\)" }],
-			correctAnswer: "\\(2x\\)",
-			explanation: "The power rule gives \\(\\frac{dy}{dx} = 2x\\).",
+			question: "What is $\\frac{dy}{dx}$ of $y = x^2$?",
+			options: [{ label: "$2x$" }, { label: "$x^2$" }, { label: "$x$" }],
+			correctAnswer: "$2x$",
+			explanation: "The power rule gives $\\frac{dy}{dx} = 2x$.",
 		};
 		const pendingHtml = renderDock({ toolName: "quiz", toolCallId: "m1", input: mathQuiz as never });
 		assert.ok(pendingHtml.includes("katex"), "pending dock: question/options math renders");
@@ -392,12 +388,12 @@ describe("math rendering (streamdown + KaTeX)", () => {
 			question: mathQuiz.question,
 			mode: "single-select",
 			options,
-			correctIndices: resolveCorrect(coerceCorrectAnswer(mathQuiz.correctAnswer), options).indices,
+			correctIndices: resolveCorrect(mathQuiz.correctAnswer, options).indices,
 			explanation: mathQuiz.explanation,
 			createdAt: new Date().toISOString(),
 		};
 		const answeredHtml = renderToStaticMarkup(
-			<AnsweredCard answer={buildAnswer(qd, { values: ["\\(2x\\)"] })} />,
+			<AnsweredCard answer={buildAnswer(qd, { values: ["$2x$"] })} />,
 		);
 		assert.ok(answeredHtml.includes("katex"), "answered card: option/explanation math renders");
 	});
@@ -692,3 +688,90 @@ describe("predict vs check rendering", () => {
 		assert.ok(legacyHtml.includes("a 2026-09 answer") || legacyHtml.includes('data-testid="your-thinking-trigger"'), "records from before the rename still render");
 	});
 });
+
+// ─── details + option descriptions render as markdown (owner, 2026-10-12) ──
+
+describe("question context renders as markdown everywhere (owner, 2026-10-12)", () => {
+	it("pending dock: ask option descriptions render LaTeX, not plain text", () => {
+		const html = renderDock({
+			toolName: "ask_user_question",
+			toolCallId: "d1",
+			input: {
+				question: "Which tool?",
+				options: [
+					{ label: "Pencil", description: "Wood around $\\text{Pb}_x\\text{C}$ graphite — the classic $x^2$ choice." },
+					{ label: "Pen" },
+				],
+			} as never,
+		});
+		// The description rides the same MessageResponse path as the label:
+		// KaTeX spans render inside the option subtext.
+		const katexCount = (html.match(/class="katex"/g) ?? []).length;
+		assert.ok(katexCount >= 2, `option description math renders (got ${katexCount})`);
+		assert.ok(!html.includes("$\\text"), "raw dollar delimiters do not leak as visible text");
+	});
+
+	it("settled ask card keeps the details line and option descriptions — retroactively from the persisted call", () => {
+		const input = {
+			question: "Which destination?",
+			details: "Inline $a^2+b^2=c^2$ and display:\n$$\nE = mc^2\n$$",
+			options: [
+				{ label: "Classical", description: "Entropy $H(X)$ first." },
+				{ label: "ML toolkit" },
+			],
+		};
+		const qd: QuestionData = {
+			id: "d2",
+			kind: "ask",
+			question: input.question,
+			mode: "single-select",
+			options: normalizeOptions(input.options),
+			createdAt: new Date().toISOString(),
+		};
+		const answer = buildAnswer(qd, { values: ["Classical"] });
+		const html = renderToStaticMarkup(<AnsweredCard answer={answer} input={input} />);
+		const katexCount = (html.match(/class="katex"/g) ?? []).length;
+		assert.ok(katexCount >= 3, `details (inline+display) + description math render (got ${katexCount})`);
+		assert.match(html, /Entropy/, "the option description text is present");
+		assert.ok(html.includes("katex-display"), "display math in the details line renders");
+	});
+
+	it("settled quiz card keeps the details line; quiz options stay description-less", () => {
+		const input = {
+			question: "Typical sets?",
+			details: "Recall $2^{nH(X)}$ — the asymptotic equipartition bound.",
+			options: [
+				{ label: "$\\approx 2^{nH(X)}$", value: "a" },
+				{ label: "$nH(X)$", value: "b" },
+			],
+			explanation: "AEP.",
+			correctAnswer: "a",
+		};
+		const options = normalizeOptions(input.options);
+		const qd: QuestionData = {
+			id: "d3",
+			kind: "quiz",
+			question: input.question,
+			mode: "single-select",
+			options,
+			correctIndices: resolveCorrect(input.correctAnswer, options).indices,
+			explanation: input.explanation,
+			createdAt: new Date().toISOString(),
+		};
+		const answer = buildAnswer(qd, { values: ["a"] });
+		const html = renderToStaticMarkup(<AnsweredCard answer={answer} input={input} />);
+		const katexCount = (html.match(/class="katex"/g) ?? []).length;
+		assert.ok(katexCount >= 3, `details + option-label math renders (got ${katexCount})`);
+		// Quiz options carry NO description field at all (owner ruling
+		// 2026-09-26) — the desc map is ask-only and stays empty here.
+		assert.ok(!html.includes("lh-prose block text-xs"), "no option-subtext slot on quiz rows");
+	});
+
+	it("legacy settled records (no input prop) render exactly as before", () => {
+		const answer = buildAnswer(askQD(), { values: ["Very"] });
+		const html = renderToStaticMarkup(<AnsweredCard answer={answer} />);
+		assert.match(html, /Very/, "the card renders");
+		assert.equal((html.match(/class="katex"/g) ?? []).length, 0, "no context slot appears from nothing");
+		assert.ok(!html.includes("lh-prose block text-xs"), "no description slot without an ask input");
+	});
+});
diff --git a/tests/render-markdown.test.tsx b/tests/render-markdown.test.tsx
index 7359744..fdbd1d9 100644
--- a/tests/render-markdown.test.tsx
+++ b/tests/render-markdown.test.tsx
@@ -94,7 +94,7 @@ describe("math delimiter transform (pure unit)", () => {
 	});
 });
 
-describe("render — new math contract (streamdown + KaTeX)", () => {
+describe("render — standard dollar math + legacy compatibility (streamdown + KaTeX)", () => {
 	it("renders \\(...\\) as inline KaTeX", () => {
 		const html = render("The map \\(f(x) = x^2\\) is smooth.");
 		assert.ok(html.includes("katex"), `inline math should render, got: ${html.slice(0, 300)}`);
@@ -121,16 +121,29 @@ describe("render — new math contract (streamdown + KaTeX)", () => {
 		assert.equal(items.length, 2, "both list items render");
 	});
 
-	it("renders bare $ as literal currency — the hazard dies structurally", () => {
-		const html = render("It costs $5 and $10 more.");
-		assert.ok(!html.includes("katex"), "currency must never parse as math");
+	it("keeps escaped currency literal", () => {
+		const html = render("It costs \\$5 and \\$10 more.");
+		assert.ok(!html.includes("katex"), "escaped currency must not parse as math");
 		assert.match(html, /\$5 and \$10/);
 	});
 
-	it("renders old-contract $...$ math as literal text (singleDollarTextMath: false)", () => {
+	it("renders standard $...$ math inline", () => {
 		const html = render("The map $f(x) = x^2$ is smooth.");
-		assert.ok(!html.includes("katex"), "$ can never start math");
-		assert.match(html, /\$f\(x\) = x\^2\$/, "the old form renders verbatim");
+		assert.ok(html.includes("katex"), "single-dollar math renders");
+		assert.ok(!html.includes("katex-display"), "single-dollar math is inline");
+	});
+
+	it("renders standard dollar commands and fenced display math", () => {
+		const html = render("The symbol $\\Omega$ appears here.\n\n$$\nS = k_B \\ln \\Omega\n$$");
+		assert.ok(html.includes("katex-display"), "standalone dollar fences render display math");
+		assert.ok(html.includes("Ω"), "the command renders as the Greek symbol");
+		assert.ok(!html.includes("katex-error"), "both formulas are valid");
+	});
+
+	it("keeps dollar examples in inline code and code fences literal", () => {
+		const html = render("Use `$x$` here.\n\n```text\n$$\ny = x^2\n$$\n```");
+		assert.ok(!html.includes("katex"), "code examples are not math");
+		assert.ok(html.includes("$x$"), "inline code retains its delimiters");
 	});
 
 	it("keeps \\(...\\) inside a code fence literal", () => {
diff --git a/tests/tool-heal.test.ts b/tests/tool-heal.test.ts
index 7428e85..e450607 100644
--- a/tests/tool-heal.test.ts
+++ b/tests/tool-heal.test.ts
@@ -34,6 +34,7 @@ import {
 import { parseQuizInput } from "../src/core/tool-parts.ts";
 import { resolveTargetId } from "../src/core/chains.ts";
 import { bareQuestionTools } from "../src/agent/teacher-agent.ts";
+import { probeQuizTool } from "../src/agent/tools.ts";
 
 /** The incident's exact encoding: the value wrapped in literal quotes. */
 function QUOTED(value: string): string {
@@ -126,9 +127,9 @@ describe("the colon shape — correctAnswer with copy-syntax debris", () => {
 		assert.equal(stripModelValueDebris('["x"]'), '["x"]'); // interior quotes are content (JSON-array strings)
 	});
 
-	it("coerceCorrectAnswer strips every entry (boundary check + grading seam)", () => {
-		assert.deepEqual(coerceCorrectAnswer([":parmenides"]), ["parmenides"]);
-		assert.deepEqual(coerceCorrectAnswer(QUOTED("primary-external")), ["primary-external"]);
+	it("coerceCorrectAnswer cleans non-matching entries (boundary check + grading seam)", () => {
+		assert.deepEqual(coerceCorrectAnswer([":parmenides"], ["parmenides"]), ["parmenides"]);
+		assert.deepEqual(coerceCorrectAnswer(QUOTED("primary-external"), ["primary-external"]), ["primary-external"]);
 	});
 
 	it("the incident's exact call passes the semantic boundary (quizInputProblems)", () => {
@@ -153,6 +154,27 @@ describe("the colon shape — correctAnswer with copy-syntax debris", () => {
 	});
 });
 
+describe("the calculus retry loop — an exact answer was incorrectly stripped", () => {
+	it("the real probe tool accepts a label with its sentence-final period", async () => {
+		const input = {
+			question: "Which claim?",
+			options: [{ label: "The claim holds." }, { label: "The claim need not hold." }],
+			explanation: "The premise does not imply the claim.",
+			correctAnswer: "The claim need not hold.",
+		};
+		const validated = validateToolArguments(probeQuizTool, {
+			type: "toolCall",
+			id: "calculus-period",
+			name: "probe",
+			arguments: probeQuizTool.prepareArguments!(input),
+		});
+		assert.equal(validated.correctAnswer, input.correctAnswer);
+		const result = await probeQuizTool.execute("calculus-period", validated);
+		assert.notEqual(result.isError, true, "an already-exact answer must not trigger a retry");
+		assert.equal(result.terminate, true, "the valid question is posed normally");
+	});
+});
+
 describe("the display mirror — raw records heal on read", () => {
 	it("parseQuizInput renders the incident's persisted raw record (no invisible quiz)", () => {
 		const raw = whiteheadQuiz(QUOTED("predict"), [":parmenides"]);
@@ -163,6 +185,6 @@ describe("the display mirror — raw records heal on read", () => {
 		// which strips the recorded wobble to the intended role.
 		assert.equal(normalizeQuizType(parsed?.type), "predict");
 		// The graded answer resolves to the option despite the recorded colon.
-		assert.deepEqual(parsed ? coerceCorrectAnswer(parsed.correctAnswer) : [], ["parmenides"]);
+		assert.deepEqual(parsed ? coerceCorrectAnswer(parsed.correctAnswer, parsed.options.map((o) => o.value ?? o.label)) : [], ["parmenides"]);
 	});
 });
diff --git a/tests/tool-parts.test.ts b/tests/tool-parts.test.ts
index 7b1d7a4..e1482d2 100644
--- a/tests/tool-parts.test.ts
+++ b/tests/tool-parts.test.ts
@@ -12,6 +12,7 @@ import assert from "node:assert/strict";
 import { describe, it } from "node:test";
 import { quizInputProblems } from "../src/core/question-core.ts";
 import { Value } from "typebox/value";
+import { restoreMathEscapes } from "../src/core/math-delims.ts";
 import {
 	parseAskInput,
 	parseProbeDoneInput,
@@ -279,6 +280,89 @@ describe("display-math newline rule (Option A, owner ruling 2026-09-27)", () =>
 	});
 });
 
+describe("dollar-delimiter recognition — existing escape restoration rules", () => {
+	it("restores question, option, and explanation debris in dollar math", () => {
+		const parsed = parseQuizInput({
+			question: "What does $\x0corall x$ mean?",
+			options: [{ label: "$\x0barphi$ holds", value: "yes" }, { label: "No", value: "no" }],
+			correctAnswer: "yes",
+			explanation: "Here $p\to q$ is an implication.",
+		});
+		assert.ok(parsed);
+		assert.equal(parsed.question, "What does $\\forall x$ mean?");
+		assert.equal(parsed.options[0]!.label, "$\\varphi$ holds");
+		assert.equal(parsed.explanation, "Here $p\\to q$ is an implication.");
+	});
+
+	it("keeps the same six-character inline recovery map", () => {
+		for (const [debris, command] of [
+			["\beta", "\\beta"], ["\to", "\\to"], ["\neq", "\\neq"],
+			["\x0barphi", "\\varphi"], ["\x0corall", "\\forall"], ["\rho", "\\rho"],
+		]) {
+			assert.equal(restoreMathEscapes(`$${debris}$`), `$${command}$`);
+		}
+	});
+
+	it("preserves display newlines and real LaTeX row breaks", () => {
+		const math = "Compare:\n$$\n\\begin{aligned}\nx &= 1 \\\\\ny &= 2\n\\end{aligned}\n$$";
+		assert.equal(restoreMathEscapes(math), math);
+	});
+
+	it("restores five display debris characters but keeps newline ambiguity unchanged", () => {
+		for (const [debris, command] of [
+			["\beta", "\\beta"], ["\to", "\\to"], ["\x0barphi", "\\varphi"],
+			["\x0corall", "\\forall"], ["\\left(x \right)", "\\left(x \\right)"],
+		]) {
+			assert.equal(
+				restoreMathEscapes(`Compare:\n$$\n${debris}, p \neq q\n$$`),
+				`Compare:\n$$\n${command}, p \neq q\n$$`,
+			);
+		}
+	});
+
+	it("preserves legacy replacement frequency when a span has multiple debris characters", () => {
+		const body = "p\to q, \rho";
+		const legacy = restoreMathEscapes(`\\(${body}\\)`).slice(2, -2);
+		assert.equal(restoreMathEscapes(`$${body}$`), `$${legacy}$`);
+		assert.equal(legacy, "p\\to q, \rho", "the existing first-match-only behavior is unchanged");
+	});
+
+	it("shares dollar recovery with ask and free-recall fields", () => {
+		const ask = parseAskInput({ question: "Goal?", options: [{ label: "$\x0corall$ rigor" }, { label: "Intuition" }] });
+		assert.ok(ask);
+		assert.equal(ask.options![0]!.label, "$\\forall$ rigor");
+		const explain = parseExplainInput({ question: "Explain $p\to q$", correctAnswer: "$p\neq q$ is different." });
+		assert.ok(explain);
+		assert.equal(explain.question, "Explain $p\\to q$");
+		assert.equal(explain.correctAnswer, "$p\\neq q$ is different.");
+	});
+
+	it("leaves non-math debris, escaped opening dollars, and code examples untouched", () => {
+		const prose = "Pasted:\t\x0cb. \\$\x0corall x$. A good $x$.";
+		assert.equal(restoreMathEscapes(prose), prose);
+		const code = "Literal `$\x0corall x$`.\n\n```text\n$\x0barphi$\n```\n\nReal $\x0corall x$.";
+		assert.equal(restoreMathEscapes(code), code.replace("Real $\x0corall x$", "Real $\\forall x$"));
+	});
+
+	it("leaves unbalanced and mismatched delimiter runs untouched", () => {
+		for (const text of ["$\x0corall", "$$\n\x0corall x\n", "$\x0corall$$", "$$\x0corall$"]) {
+			assert.equal(restoreMathEscapes(text), text);
+		}
+	});
+
+	it("recognizes native inline runs and longer display closing fences", () => {
+		assert.equal(restoreMathEscapes("Inline $$p\neq q$$."), "Inline $$p\\neq q$$.");
+		assert.equal(restoreMathEscapes("$$\n\x0corall x\n$$$"), "$$\n\\forall x\n$$$");
+	});
+
+	it("does not add an over-escaping repair or reprocess legacy spans", () => {
+		const overescaped = "$$\n\\\\Omega\n$$";
+		assert.equal(restoreMathEscapes(overescaped), overescaped);
+		const legacy = "\\[\np $a\neq b$\n\\]";
+		assert.equal(restoreMathEscapes(legacy), legacy);
+	});
+});
+
 // ─── parseExplainInput (free-recall display parse, owner 2026-09-27) ───────
 
 describe("parseExplainInput: the dock's display seam for explain calls", () => {