fix(rectification): persist the next interview after a choice tap

Closing a discriminator used to leave GET without a card after refresh.
Write the next dated question in the same request, skip childhood career
and move probes, and do not continue a read-only turn when that question
is already persisted.

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

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

@@ -2,6 +2,7 @@ import { NextResponse } from "next/server";
 import { z } from "zod";
 import { getRectificationV9Agent, type RectificationAgentAction } from "@/mastra/agentic-rectification";
 import {
+  loadV9CaseCompute,
   loadV9CaseDossier,
   persistV9DeterministicTurn,
   RectificationToolServiceError,
@@ -280,6 +281,8 @@ export async function POST(request: Request) {
         sourceQuote: applied.sourceQuote,
         derivedContext: applied.derivedContext,
         nextAction: applied.nextAction,
+        nextInterviewPersisted: applied.nextInterviewPersisted,
+        nextChoiceReady: applied.nextChoiceReady,
       });
     } catch (error) {
       if (error instanceof RectificationToolServiceError) {
@@ -386,11 +389,19 @@ export async function POST(request: Request) {
             dossier.latestResult,
             dossier.evidence,
           );
+          let birthDate: string | null = null;
+          try {
+            const compute = await loadV9CaseCompute(accounting, userId, caseId);
+            birthDate = String(compute.baselineBirthSnapshot.birth_date ?? "") || null;
+          } catch {
+            // Ranking stays fail-open when compute is unavailable.
+          }
           const plan = buildMethodFollowupPlan({
             evidence: dossier.evidence,
             declinedTopics: dossier.conversationSummary.declinedSkippedTopics,
             sessionOutcome: "discriminate_candidates",
             ...catalog,
+            birthDate,
             candidatesSeparated: false,
           });
           const persisted = await persistServerOwnedFocus({