fix(rectification): keep hour-window tail clusters and lock the search window (BUG-623, BUG-624, BUG-625)

Hour windows no longer drop later signature clusters. Credible range uses cluster coverage, and a mid-session spoken birth window gets a fixed reply without calling the model.

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

frontend/src/app/api/rectification/agent/route.ts

@@ -46,6 +46,7 @@ import { persistServerOwnedFocus, openQuestionFromPersistedFocus, isCollectFocus
 import { buildMethodFollowupPlan } from "@/lib/rectification-agentic/v9/method-followup";
 import { isNonConvergingRangeOffer, nonConvergingRangeNarration } from "@/lib/rectification-agentic/core/rectification-decision";
 import { RECTIFICATION_USER_COPY } from "@/lib/rectification-agentic/user-copy";
+import { parseDeclaredBirthWindow } from "@/lib/rectification-agentic/v9/declared-window-utterance";
 import {
   awaitTurnExitBeforeResponse,
   finalizeSuccessfulTurnExit,
@@ -268,6 +269,30 @@ export async function POST(request: Request) {
     );
   }
 
+  if (action === "message" && parseDeclaredBirthWindow(parsed.data.message ?? "")) {
+    try {
+      const narration = RECTIFICATION_USER_COPY.declaredWindowLockedReply;
+      const turn = await persistV9DeterministicTurn(accounting, userId, caseId, {
+        requestId,
+        userMessage: parsed.data.message ?? null,
+        assistantMessage: narration,
+      });
+      return completedMessageResponse(narration, requestId, caseId, turn.turnId);
+    } catch (error) {
+      if (error instanceof RectificationToolServiceError) {
+        const mapped = mapRectificationRpcError(error);
+        return NextResponse.json(
+          { error: mapped.message, message: mapped.message, code: mapped.code },
+          { status: mapped.status },
+        );
+      }
+      return NextResponse.json(
+        { error: "校正回复保存失败", message: "请稍后重试。" },
+        { status: 500 },
+      );
+    }
+  }
+
   const selectedModel = isStructuredChoice
     ? null
     : await resolveSessionLanguageModel(