fix(rectification): label declared birth time as record or estimate (BUG-690)

Hospital records, family estimates and period-only windows now keep distinct copy on the board and range card. Scoring still uses the reported clock as the search-window centre. Hospital minutes outside the current range are stated with the offset and no preference.

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

@@ -73,6 +73,7 @@ import {
   persistedQuestionSurface,
   interviewStopReasonFromSnapshot,
   interviewSessionOutcomeFromSnapshot,
+  birthTimeSourceFromSnapshot,
   type RectificationCaseSnapshotPayload,
 } from "@/lib/rectification-surface-state";
 import { RectificationTimeline } from "@/components/rectification-timeline";
@@ -394,6 +395,7 @@ type CaseSnapshotState = Readonly<{
   stage: RectificationTimelineStage | null;
   interviewStopReason: string | null;
   interviewSessionOutcome: string | null;
+  birthTimeSource: ReturnType<typeof birthTimeSourceFromSnapshot>;
 }>;
 
 function nextUserActionIdFromSnapshot(payload: RectificationCaseSnapshotPayload | null): string | null {
@@ -419,6 +421,7 @@ function caseSnapshotState(payload: RectificationCaseSnapshotPayload | null): Ca
     stage: caseStageFromSnapshot(payload.case?.stage),
     interviewStopReason: interviewStopReasonFromSnapshot(payload),
     interviewSessionOutcome: interviewSessionOutcomeFromSnapshot(payload),
+    birthTimeSource: birthTimeSourceFromSnapshot(payload),
   };
 }
 
@@ -464,6 +467,7 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
   const [nextUserActionId, setNextUserActionId] = useState<string | null>(() => caseSnapshotState(initialSnapshot)?.nextUserActionId ?? null);
   const [interviewStopReason, setInterviewStopReason] = useState<string | null>(() => caseSnapshotState(initialSnapshot)?.interviewStopReason ?? null);
   const [interviewSessionOutcome, setInterviewSessionOutcome] = useState<string | null>(() => caseSnapshotState(initialSnapshot)?.interviewSessionOutcome ?? null);
+  const [birthTimeSource, setBirthTimeSource] = useState(() => caseSnapshotState(initialSnapshot)?.birthTimeSource ?? birthTimeSourceFromSnapshot(initialSnapshot));
   const [caseSnapshotLoaded, setCaseSnapshotLoaded] = useState(initialSnapshot !== null);
   const [questionRetryAttempts, setQuestionRetryAttempts] = useState(0);
   const [questionRepairAttempts, setQuestionRepairAttempts] = useState(0);
@@ -637,6 +641,7 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
     setNextUserActionId(nextActionId || null);
     setInterviewStopReason(interviewStopReasonFromSnapshot(snapshot));
     setInterviewSessionOutcome(interviewSessionOutcomeFromSnapshot(snapshot));
+    setBirthTimeSource(birthTimeSourceFromSnapshot(snapshot));
     setCaseSnapshotLoaded(true);
     if (nextQuestion || nextChoice || acceptedTime || confirmedTime) {
       setQuestionRepairAttempts(0);
@@ -1683,6 +1688,7 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
     <RectificationBoardPeek
       result={candidateResult}
       declaredTime={declaredTime}
+      birthTimeSource={birthTimeSource}
       expanded={boardOpen}
       boardId={boardId}
       onOpen={toggleBoard}
@@ -1988,6 +1994,7 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
       <RectificationBoard
         result={candidateResult}
         declaredTime={declaredTime}
+        birthTimeSource={birthTimeSource}
         savedStatus={savedStatus}
         diff={boardDiff}
         compact={compactBoard}