fix(rectification): stop unwritten-evidence claims and same-cluster dasha false conflicts (BUG-635–640)

Host only says 记下了 after a real write; Mastra schema rejections fail closed. Ledger year keys no longer drop quality probes, dual-dasha agreement is per cluster, width uses cluster span, and public house tables follow the inference minute.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/components/rectification-agentic-chat.tsx

@@ -1498,14 +1498,13 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
     ? currentQuestion.prompt
     : null;
   const resumableCase = caseStatus !== null && isResumableStatus(caseStatus);
-  const liveQuestionOnMessages = messages.some((message) => (
-    message.role === "assistant"
-    && message.state === "settled"
-    && message.question
+  const liveQuestionOnMessages = Boolean(
+    latestSettledAssistant
+    && latestSettledAssistant.question
     && currentQuestion
-    && message.question.focus_id === currentQuestion.focus_id
-    && !questionIsAnswered(message.question)
-  ));
+    && latestSettledAssistant.question.focus_id === currentQuestion.focus_id
+    && !questionIsAnswered(latestSettledAssistant.question),
+  );
   // The gap between a settled turn and its next question has two visible
   // states: `preparing` (one live timeline row, timed refetches) and
   // `unavailable` (copy and a repair button) — never bare copy telling the