fix(rectification): feed cluster span into confirmation-gate refresh paths

Representative minutes still undercounted width on dossier refresh and parsed snapshots even after the engine used cluster coverage.

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

frontend/src/lib/rectification-agentic/v9/decision-from-dossier.ts

@@ -96,6 +96,10 @@ export type DecisionDossier = Readonly<{
       relativeSupport?: number;
       posterior_score?: number;
       tiedMinuteCount?: number;
+      clusterStart?: string;
+      clusterEnd?: string;
+      cluster_start?: string;
+      cluster_end?: string;
     }>[];
     representativeTime?: string | null;
     evidenceLedgerFingerprint?: string | null;
@@ -667,6 +671,12 @@ export function decideFromDossier(
       time: candidate.time,
       rank: candidate.rank ?? Number.MAX_SAFE_INTEGER,
       tiedMinuteCount: candidate.tiedMinuteCount ?? Number.MAX_SAFE_INTEGER,
+      ...(candidate.clusterStart ?? candidate.cluster_start
+        ? { clusterStart: candidate.clusterStart ?? candidate.cluster_start }
+        : {}),
+      ...(candidate.clusterEnd ?? candidate.cluster_end
+        ? { clusterEnd: candidate.clusterEnd ?? candidate.cluster_end }
+        : {}),
     })),
     decisionReceipt: latest?.decisionReceipt ?? null,
   });

frontend/src/lib/rectification-agentic/v9/method-followup.ts

@@ -115,7 +115,6 @@ import {
   isEventQualityProbe,
   sameYearProbeAsked,
   SEMANTIC_YEAR_KEY,
-  EXISTENCE_STYLE_OPTIONS,
   type DroppedProbe,
   type ProbeStyleOption,
 } from "./probe-question-contract.ts";

frontend/src/lib/rectification-candidate-result.ts

@@ -44,6 +44,8 @@ export type RectificationCandidate = Readonly<{
   time: string;
   relativeSupport: number;
   tiedMinuteCount: number;
+  clusterStart?: string;
+  clusterEnd?: string;
 }>;
 
 export type RectificationHouseRow = Readonly<{
@@ -329,7 +331,17 @@ export function parseRectificationCandidateResult(value: unknown): Rectification
       || relativeSupport === null || !Number.isInteger(relativeSupport) || relativeSupport < 0 || relativeSupport > 100
       || tiedMinuteCount === null || !Number.isInteger(tiedMinuteCount) || tiedMinuteCount < 1
     ) return null;
-    candidates.push({ candidateId, rank, time: candidateTime, relativeSupport, tiedMinuteCount });
+    const clusterStart = time(candidate.clusterStart ?? candidate.cluster_start);
+    const clusterEnd = time(candidate.clusterEnd ?? candidate.cluster_end);
+    candidates.push({
+      candidateId,
+      rank,
+      time: candidateTime,
+      relativeSupport,
+      tiedMinuteCount,
+      ...(clusterStart ? { clusterStart } : {}),
+      ...(clusterEnd ? { clusterEnd } : {}),
+    });
   }
 
   const receipt = receiptFromSnapshot(snapshot);