Wave-5 refinement round 2 (owner's batch)

- Home view: StatsBar under the composer (model+thinking control) — the
  DOCK geometry matches the chat view (max-w-[46rem] px-4) so nothing
  shifts when a session starts; pre-chat selection persists via deferred
  save (ModelControl chatId-empty) + PUT after POST /api/chats.
- Answer marks (✓/✗): same visual size as row text, vertically centered;
  colored green-500/red-500 matching the verdict chips.
- All user-typed inputs (composer, question-dock text/thinking/Other,
  answered-card 'your thinking' and free-text records) now render
  Source Sans 3 via the font-prose utility. Placeholders inherit the
  family via the element.
- Answered-card explanation: markdown wrapper made truly inline so the
  'Why:' label + the paragraph sit on one line — removes the oversized
  leading gap.

components/answered-card.tsx

@@ -58,7 +58,17 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 								)}
 							>
 								{isQuiz && (
-									<span className="w-4 shrink-0">
+									<span
+										aria-hidden
+										className={cn(
+											// Same visual size as the row text, vertically centered,
+											// colored like the verdict chips (owner).
+											"flex size-4 shrink-0 items-center justify-center text-sm font-semibold leading-none",
+											sel && key && "text-green-500",
+											sel && !key && "text-red-500",
+											!sel && key && "text-green-500",
+										)}
+									>
 										{sel && key && "✓"}
 										{sel && !key && "✗"}
 										{!sel && key && "✓"}
@@ -84,7 +94,7 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 				</div>
 			)}
 
-			{answer.text && <div className="mt-2 whitespace-pre-wrap text-sm">“{answer.text}”</div>}
+			{answer.text && <div className="font-prose mt-2 whitespace-pre-wrap text-sm">“{answer.text}”</div>}
 			{answer.dontKnow && isQuiz && <div className="mt-2 text-sm text-muted-foreground">Answered “I don't know”.</div>}
 
 			{answer.note && (
@@ -92,14 +102,16 @@ export function AnsweredCard({ answer }: { answer: QuestionAnswerData }) {
 					<span className="mb-0.5 block text-xxs font-medium uppercase tracking-wide text-muted-foreground">
 						Your thinking
 					</span>
-					<span className="block whitespace-pre-wrap text-sm text-foreground/90">{answer.note}</span>
+					<span className="font-prose block whitespace-pre-wrap text-sm text-foreground/90">{answer.note}</span>
 				</div>
 			)}
 
 			{isQuiz && answer.explanation && (
 				<div className="mt-3 rounded-lg bg-muted px-3 py-2 text-sm text-muted-foreground">
 					<span className="font-medium text-foreground">Why: </span>
-					<MessageResponse className="inline">{answer.explanation}</MessageResponse>
+					{/* The markdown wrapper must go truly inline — a block <p> after the
+								   "Why:" label created the oversized leading gap (owner's fix list). */}
+								<MessageResponse className="inline [&_p]:inline [&_p]:m-0">{answer.explanation}</MessageResponse>
 				</div>
 			)}
 		</div>

components/composer.tsx

@@ -59,7 +59,7 @@ export function Composer({
 				placeholder="Ask, answer, or steer the lesson…"
 				autoFocus={autoFocus}
 				rows={1}
-				className="field-sizing-content max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground"
+				className="field-sizing-content font-prose max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground"
 			/>
 			{verdict && !busy ? (
 				// The plan verdict (docs/probe-teach-split.md §4): accept

components/home.tsx

@@ -5,6 +5,8 @@ import { useRouter } from "next/navigation";
 import { CornerDownLeftIcon } from "lucide-react";
 import { GraphView } from "@/components/graph-view";
 import { SidebarToggle } from "@/components/sidebar";
+import { StatsBar } from "@/components/stats-bar";
+import type { ChatSettings, TurnUsage } from "@/src/core";
 
 /**
  * Home — the knowledge graph is the main view (placeholder until the graph
@@ -15,6 +17,10 @@ export function Home() {
 	const router = useRouter();
 	const [topic, setTopic] = useState("");
 	const [busy, setBusy] = useState(false);
+	// The model+thinking selection made pre-chat — lifted from the StatsBar's
+	// ModelControl, carried to the chat POST then PUT-on-create (the model
+	// picker defers its save when chatId is empty; see components/model-picker).
+	const [settings, setSettings] = useState<ChatSettings | undefined>(undefined);
 
 	const start = async () => {
 		const t = topic.trim();
@@ -27,6 +33,14 @@ export function Home() {
 				body: JSON.stringify({ title: t }),
 			});
 			const { id } = (await res.json()) as { id: string };
+			if (settings) {
+				// Best-effort persist — the selection was made pre-chat.
+				await fetch(`/api/chats/${id}/settings`, {
+					method: "PUT",
+					headers: { "Content-Type": "application/json" },
+					body: JSON.stringify(settings),
+				}).catch(() => {});
+			}
 			router.push(`/chat/${id}?prompt=${encodeURIComponent(t)}`);
 		} catch {
 			setBusy(false);
@@ -46,7 +60,9 @@ export function Home() {
 
 			{/* New session — same floating blob as the chat composer. */}
 			<div className="pb-4">
-				<div className="mx-auto w-full max-w-3xl px-4">
+				{/* Matches chat.tsx's DOCK geometry (max-w-[46rem] px-4) so nothing
+			    shifts when a session starts (owner). */}
+			<div className="mx-auto w-full max-w-[46rem] px-4">
 					<form
 						className="flex items-end gap-1.5 rounded-2xl border bg-card p-1.5 shadow-lg"
 					onSubmit={(e) => {
@@ -77,6 +93,15 @@ export function Home() {
 						<CornerDownLeftIcon className="size-5" />
 						</button>
 					</form>
+					{/* Same as the chat view's under-composer stats bar (owner) — no
+					    session yet, so money/context fold as "—"; the model +
+					    thinking control still works (deferred save). */}
+					<StatsBar
+						turns={[] as TurnUsage[]}
+						chatId=""
+						settings={settings}
+						onSettingsSaved={setSettings}
+					/>
 				</div>
 			</div>
 		</div>

components/model-picker.tsx

@@ -117,6 +117,13 @@ export function ModelControl({
 	const save = useCallback(
 		async (next: ChatSettings) => {
 			setError(null);
+			// Home view (pre-chat): defer — the selection rides along on the
+			// chat POST and is PUT after creation (onSaved is still lifted).
+			if (!chatId) {
+				onSaved(next);
+				setOpen(null);
+				return;
+			}
 			try {
 				const res = await fetch(`/api/chats/${chatId}/settings`, {
 					method: "PUT",

components/question-dock.tsx

@@ -387,7 +387,7 @@ function QuestionDockForm({
 										setSel((prev) => (prev.otherSelected ? prev : toggleOther(selectMode, prev)));
 									}}
 									placeholder="Type your own answer…"
-									className="w-full min-w-0 flex-1 bg-transparent text-sm outline-none placeholder:text-muted-foreground"
+									className="font-prose w-full min-w-0 flex-1 bg-transparent text-sm outline-none placeholder:text-muted-foreground"
 									onClick={(e) => e.stopPropagation()}
 								/>
 							</div>
@@ -429,7 +429,7 @@ function QuestionDockForm({
 							}}
 							placeholder="Type your answer…"
 							rows={1}
-							className="field-sizing-content max-h-48 min-h-10 w-full resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground"
+							className="field-sizing-content font-prose max-h-48 min-h-10 w-full resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground"
 						/>
 					) : (
 						<textarea
@@ -446,7 +446,7 @@ function QuestionDockForm({
 							placeholder="Why this answer? What are you unsure about? Say as much as you like — the teacher reads all of this."
 							rows={1}
 							className={cn(
-								"field-sizing-content max-h-48 w-full resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground/70",
+								"field-sizing-content font-prose max-h-48 w-full resize-none bg-transparent px-2.5 py-2 text-sm outline-none placeholder:text-muted-foreground/70",
 								// Phase-scaled prominence: teaching invites depth,
 								// probing stays quick.
 								phase === "teach" ? "min-h-[4.5rem]" : "min-h-10",