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/tests/rectification-server-focus.test.ts

@@ -5,6 +5,8 @@ import test from "node:test";
 import { buildInferenceState } from "../src/lib/rectification-agentic/core/build-state.ts";
 import {
   COLLECT_FOCUS_RETRY_SUFFIX,
+  FOCUS_TARGET_KIND_CHECK,
+  collectFocusTargetKind,
   openQuestionFromPersistedFocus,
   persistableFocusDomain,
   persistServerOwnedFocus,
@@ -924,3 +926,55 @@ test("frameless precision-stage distinguish is skipped instead of opening GENERI
     GENERIC_COLLECT_QUESTION,
   );
 });
+
+function targetKindCheckFromSql(): string[] {
+  const sql = readFileSync(new URL(
+    "../supabase/migrations/20260814020000_rectification_v10_runtime.sql",
+    import.meta.url,
+  ), "utf8");
+  const match = /target_kind text check \(\s*target_kind is null or target_kind in \(\s*([\s\S]*?)\)\s*\)/.exec(sql);
+  assert.ok(match?.[1], "target_kind CHECK missing");
+  return [...match[1].matchAll(/'([a-z_]+)'/g)].map((item) => item[1]);
+}
+
+test("T1: collect focus kinds map to the table CHECK enum", async () => {
+  const allowed = targetKindCheckFromSql();
+  assert.deepEqual([...FOCUS_TARGET_KIND_CHECK], allowed);
+  const cases: ReadonlyArray<{
+    kind_hint: string;
+    domain: string;
+    collectKind: string;
+  }> = [
+    { kind_hint: "targeted:family", domain: "family", collectKind: "targeted:family" },
+    { kind_hint: "anchor:education_start:2016", domain: "education", collectKind: "anchor:education_start:2016" },
+    { kind_hint: "generic:relationship", domain: "relationship", collectKind: "generic:relationship" },
+  ];
+  for (const item of cases) {
+    const mapped = collectFocusTargetKind({ kind_hint: item.kind_hint, domain: item.domain });
+    assert.ok(mapped && allowed.includes(mapped), `${item.kind_hint} -> ${mapped}`);
+    const accounting = fakeAccounting({
+      set_agentic_rectification_conversation_focus: (_fn, args) => focusRowFromArgs(args),
+    });
+    const persisted = await persistServerOwnedFocus({
+      accounting: accounting.client,
+      userId: USER_ID,
+      caseId: CASE_ID,
+      activeFocus: null,
+      decisionReceipt: null,
+      followup: collectFollowup({
+        domain: item.domain,
+        kind_hint: item.kind_hint,
+        collection_key: item.kind_hint.startsWith("targeted:")
+          ? `collect:targeted:${item.domain}`
+          : undefined,
+      }),
+    });
+    assert.equal(persisted.status, "created", item.kind_hint);
+    assert.ok(
+      persisted.focus?.targetKind && allowed.includes(persisted.focus.targetKind),
+      `${item.kind_hint} wrote ${persisted.focus?.targetKind}`,
+    );
+    assert.equal(persisted.focus?.expectedAnswerSchema.collect_kind, item.collectKind);
+    assert.equal(accounting.calls[0]?.args.p_target_kind, persisted.focus?.targetKind);
+  }
+});