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/session-core.ts

@@ -18,6 +18,7 @@ import type { ToolResultMessage } from "@earendil-works/pi-ai";
 import {
 	needsContinuation,
 	newAnswerResult,
+	newNextMessage,
 	newProblemDismissedMarker,
 	newThinkingMessage,
 	newUserMessage,
@@ -532,6 +533,10 @@ export class SessionModel {
 			// optimistically — the card renders from its details the
 			// moment the button fires.
 			optimistic.push({ ...newThinkingMessage(input.problemCallId, input.text), id: localId() });
+		} else if (input.type === "next") {
+			// The move-on signal (owner round 16): the NEXT PROBLEM line
+			// renders the instant the chip/Enter fires.
+			optimistic.push({ ...newNextMessage(), id: localId() });
 		} else if (input.type === "answer") {
 			const tool = pendingCallTool([...this.base, ...this.tail], input.toolCallId) ?? "quiz";
 			optimistic.push({ ...newAnswerResult(input.toolCallId, tool, input.answer), id: localId() });