practice: the between-problems pause — conclude ends the turn, the learner's go-ahead paces the stream (round 16)

Owner ruling (2026-10-06): every concluded problem opens a pause. The
agent may speak its closing words about the learner's last thinking
after the conclude result, then ENDS ITS TURN — a system-prompt law
deliberately, per owner correction, NOT tool-level terminate. The next
problem is never posed until the learner explicitly moves on; the pause
is the session's teaching space (repairs, clarifications, follow-ups —
still surgical, never re-teaching).

The move-on signal is a first-class input: { type: "next" } appends a
practice-next marker (content = single-sourced NEXT_PROBLEM_TEXT — the
model's unambiguous go-ahead: pose per the selection rules or wrap if
the arc is complete). Honest 400s: practice sessions only, nothing
active (mid-problem input rides the dock), riding after any pending
dismissal synthesis exactly like text.

The fast path (owner approved: composer-band chip + Enter-on-empty):
- Composer.enterAction gains "next" — Enter on an EMPTY composer in
  the pause fires the signal; typing anything makes Enter a send again;
  busy (steer/stop) outranks the pause.
- The Next chip hovers at the composer band's top-right (pick-pill
  chrome register) whenever the pause is live and a problem has ever
  been posed; the placeholder becomes the hint ("Ask about this
  problem — or press Enter for the next one…", exact);
- the transcript renders the signal as a compact centered NEXT PROBLEM
  line (mono-caps chrome); session-core appends it optimistically.

CONCLUDE_ACK_TEXT rewritten to carry the law; doctrine §VIII gains the
pause law (owner-sanctioned edit #3); 00-base's conclude/dismissal
bullets rewritten + the between-problems section added.

components/composer.tsx

@@ -13,17 +13,26 @@ import { Hint } from "@/components/ui/hint";
  * row padding p-1.5 (6px) = button rounded-[10px] = 25% of the 40px button.
  */
 /** What one Enter press does, in precedence order: stop a busy stream,
- *  otherwise send the message. (The plan-verdict accept branch died
- *  2026-09-26 with the verdict itself.) Pure so the static-render harness
+ *  otherwise send the message, otherwise — practice sessions only — fire
+ *  the next-problem signal while the between-problems pause is live
+ *  (owner round 16: Enter on an EMPTY composer is the go-ahead; typing
+ *  anything makes Enter a send again). Pure so the static-render harness
  *  can pin the decision (key events can't be simulated in
  *  renderToStaticMarkup). */
-export function enterAction(state: { busy: boolean; canSend: boolean }): "stop" | "send" | "none" {
+export function enterAction(state: {
+	busy: boolean;
+	canSend: boolean;
+	/** The between-problems pause is live: practice session, nothing
+	 *  active, no turn/compaction in flight (the caller's fold). */
+	nextProblem?: boolean;
+}): "stop" | "send" | "next" | "none" {
 	// Composer steering (owner arc 2026-10-03): while a turn runs, typed
 	// text makes Enter a STEER (the queue-and-redirect send); Enter with
 	// an empty composer stays the stop shortcut. The button itself keeps
 	// the square — Stop stays one click away at all times.
 	if (state.busy) return state.canSend ? "send" : "stop";
 	if (state.canSend) return "send";
+	if (state.nextProblem) return "next";
 	return "none";
 }
 
@@ -38,6 +47,8 @@ export function Composer({
 	inputRef,
 	onEscape,
 	placeholder = "Ask, answer, or steer the lesson…",
+	nextProblem = false,
+	onNext,
 }: {
 	busy: boolean;
 	value: string;
@@ -56,16 +67,27 @@ export function Composer({
 	 *  active sessions read "Ask, answer, or steer the lesson…"; the fresh
 	 *  new-session page asks the graph view's opening question instead. */
 	placeholder?: string;
+	/** The practice pause is live (owner round 16): Enter on the empty
+	 *  composer fires the next-problem signal instead of doing nothing —
+	 *  the keyboard-first move-on. */
+	nextProblem?: boolean;
+	/** The signal's dispatcher (send({type:"next"})) — the chip and the
+	 *  empty-Enter share it. */
+	onNext?: () => void;
 }) {
+	const act = () => {
+		const action = enterAction({ busy, canSend, nextProblem });
+		if (action === "stop") onStop();
+		else if (action === "send") onSend();
+		else if (action === "next") onNext?.();
+	};
 	return (
 		<form
 			data-testid="composer"
 			className="flex items-end gap-1.5 p-1.5"
 			onSubmit={(e) => {
 				e.preventDefault();
-				const action = enterAction({ busy, canSend });
-				if (action === "stop") onStop();
-				else if (action === "send") onSend();
+				act();
 			}}
 		>
 			<textarea
@@ -88,9 +110,7 @@ export function Composer({
 					// across every input in the app (thinking field, answers).
 					if (e.key === "Enter" && (e.metaKey || e.ctrlKey || !e.shiftKey)) {
 						e.preventDefault();
-						const action = enterAction({ busy, canSend });
-						if (action === "stop") onStop();
-						else if (action === "send") onSend();
+						act();
 					}
 				}}
 				placeholder={placeholder}