math: dollar delimiters end-to-end (exact answers, escaping examples, context rendering)

- switch the math authoring/rendering contract from \(...\)/\[...\] to the
  standard $...$ inline / $$...$$ display: prompts (20-question-tools,
  40-formatting), singleDollarTextMath on the renderer, legacy reader kept,
  and escape-debris recovery extended to dollar spans (mirroring micromark
  delimiter-run rules)
- exact answer membership now precedes debris cleanup in
  coerceCorrectAnswer (calculus incident: an exact sentence-final-period
  label was stripped as model debris, then rejected); option keys are
  passed at the boundary/grading seams, the dock no longer pre-coerces
- a complete, phase-correct JSON-escaping example rides the probe/quiz
  tool descriptions (serialized from one canonical body; quiz leads with
  type+nodeId), plus the one-sentence JSON-escaping rule in 40-formatting
- ask option descriptions render markdown/LaTeX in the pending dock;
  settled cards keep the details line and option descriptions
  retroactively, read from the persisted call arguments (chat passes
  part.input to AnsweredCard)

1566/1566 tests on both navigator configs; typecheck, lint, production
build, standalone packaging, and Electron-runtime smoke all green.

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");
 	});