fix(rectification): persist refresh attempts and map collect focus kinds (BUG-656/657/658)

Empty engine refresh now records an already_answered attempt so GET can leave wait-to-narrow; collect kinds map onto the table CHECK; remaining candidates drive probe refresh.

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

frontend/src/lib/rectification-agentic/core/types.ts

@@ -125,6 +125,15 @@ export type RoundTrace = Readonly<{
   kind: "informative" | "low_information" | "tie_break";
 }>;
 
+export type RefreshAttemptResult = "no_new_probes" | "new_probes";
+
+export type RefreshAttempt = Readonly<{
+  candidate_set_id: string;
+  answer_count: number;
+  result: RefreshAttemptResult;
+  at: string;
+}>;
+
 export type InferenceState = Readonly<{
   algorithm_version: typeof INFERENCE_ALGORITHM_VERSION;
   candidate_set_id: string;
@@ -145,6 +154,8 @@ export type InferenceState = Readonly<{
   holdout_passed?: boolean | null;
   refresh_count?: number;
   refresh_answer_count?: number;
+  refresh_attempts?: readonly RefreshAttempt[];
+  targeted_collect_status?: "asked" | "skipped";
   transitions?: readonly Readonly<{
     layer: string;
     at: string;