feat(rectification): stream agent execution and redesign entry routing

Replace the Direct Agentic textStream relay with a durable V9 agent runtime:

- agentic-rectification.ts: short boundary-only system prompt (no gate->scan
  ->score->diagnostics copy); pins skills/jyotish-birth-time-rectification;
  per-action bounded maxSteps (opening/read-only 6, evidence 8, rescore 12,
  accept/confirm 6) with a hard ceiling and repeated-tool-call detection.
- rectification-v9-tools.ts: ten Case-ref tools (read-case, propose/confirm/
  revise-evidence, compare-candidates, read-diagnostics, offer-candidates,
  accept-candidate, confirm-birth-time, close-case). Inputs are minimal refs
  only; RPC-backed evidence ledger, fingerprint cache reuse, receipts, and
  accepted!=confirmed semantics; confirm requires gate + grounded consent.
- /api/rectification/agent: caseId/sessionId/requestId/action/message; exact
  Case<->Session binding verified server-side; client history never overrides
  the durable dossier; pending turn -> completed/failed/retryable; consumes
  result.fullStream and emits allowlisted NDJSON only (reasoning/raw/provider
  metadata/tool payloads/birth data/scores never forwarded); first-turn real
  skill.started/skill.loaded gate with one controlled retry; billing bound to
  rectification:case:{caseId}.
- New forward migration 20260813010000_agentic_rectification_v9_agent_api.sql:
  case dossier/compute, turn finalize, fingerprint-cached candidate persist,
  case-scoped accept, consent-gated confirm, guarded transitions,
  needs_rebaseline profile guard, run_phases receipt table, and the
  rectification_runtime_version feature flag (v9 default, legacy read-only).
- Frontend: homepage/sidebar entry routing now uses the server Case open API
  (openRectificationFromHomepage/openRectificationSession/startNewRectification)
  with exact sessionId/caseId and server-owned shouldStartOpening; CTA driven
  by entry-summary; chat restores from persisted turns, candidate cards from
  the Candidate Snapshot API, activity from real NDJSON + persisted receipts;
  direct durable candidate-accept endpoint for the UI cards.

frontend/src/lib/rectification-entry.ts

@@ -0,0 +1,144 @@
+/**
+ * Client-side rectification entry routing contracts.
+ *
+ * Every disposition decision comes from the server Case open API. The browser
+ * never guesses "resume vs create" from session lists or message counts.
+ */
+
+export type RectificationEntrySummary = Readonly<{
+  hasResumableCase: boolean;
+  hasTerminalCaseWithTime: boolean;
+  latestResumable: Readonly<{
+    caseId: string;
+    status: string;
+    lastActivityAt: string;
+  }> | null;
+  latestTerminal: Readonly<{
+    caseId: string;
+    status: string;
+    hasUsableTime: boolean;
+  }> | null;
+}>;
+
+export type RectificationCardAction = "start" | "resume" | "restart";
+
+export const rectificationEntryLabels: Readonly<Record<RectificationCardAction, string>> = {
+  start: "开始生时校正",
+  resume: "继续上次校正",
+  restart: "再次校正",
+};
+
+export function resolveRectificationEntryAction(
+  summary: RectificationEntrySummary,
+): RectificationCardAction {
+  if (summary.hasResumableCase) return "resume";
+  if (summary.hasTerminalCaseWithTime) return "restart";
+  return "start";
+}
+
+export type OpenRectificationDisposition = "created" | "resumed" | "readonly";
+
+export type OpenRectificationCaseResponse = Readonly<{
+  disposition: OpenRectificationDisposition;
+  caseId: string;
+  sessionId: string;
+  status: string;
+  shouldStartOpening: boolean;
+  skillVersion: string;
+}>;
+
+const RESUMABLE_STATUSES = new Set([
+  "draft",
+  "collecting_evidence",
+  "candidate_ready",
+  "candidate_accepted",
+  "needs_rebaseline",
+  "paused",
+]);
+
+const TERMINAL_STATUSES = new Set([
+  "confirmed",
+  "closed",
+  "abandoned",
+  "superseded",
+]);
+
+export function isResumableRectificationStatus(status: string): boolean {
+  return RESUMABLE_STATUSES.has(status);
+}
+
+export function isTerminalRectificationStatus(status: string): boolean {
+  return TERMINAL_STATUSES.has(status);
+}
+
+export function entrySummaryFromResponse(value: unknown): RectificationEntrySummary {
+  if (!value || typeof value !== "object") {
+    return { hasResumableCase: false, hasTerminalCaseWithTime: false, latestResumable: null, latestTerminal: null };
+  }
+  const row = value as Record<string, unknown>;
+  const latestResumable = row.latest_resumable && typeof row.latest_resumable === "object"
+    ? row.latest_resumable as Record<string, unknown>
+    : null;
+  const latestTerminal = row.latest_terminal && typeof row.latest_terminal === "object"
+    ? row.latest_terminal as Record<string, unknown>
+    : null;
+  return {
+    hasResumableCase: row.has_resumable_case === true,
+    hasTerminalCaseWithTime: row.has_terminal_case_with_time === true,
+    latestResumable: latestResumable && typeof latestResumable.case_id === "string"
+      ? {
+          caseId: latestResumable.case_id,
+          status: String(latestResumable.status ?? ""),
+          lastActivityAt: String(latestResumable.last_activity_at ?? ""),
+        }
+      : null,
+    latestTerminal: latestTerminal && typeof latestTerminal.case_id === "string"
+      ? {
+          caseId: latestTerminal.case_id,
+          status: String(latestTerminal.status ?? ""),
+          hasUsableTime: latestTerminal.has_usable_time === true,
+        }
+      : null,
+  };
+}
+
+export function openResponseFromPayload(value: unknown): OpenRectificationCaseResponse | null {
+  if (!value || typeof value !== "object") return null;
+  const row = value as Record<string, unknown>;
+  const disposition = row.disposition;
+  const caseId = typeof row.caseId === "string" ? row.caseId : "";
+  const sessionId = typeof row.sessionId === "string" ? row.sessionId : "";
+  const status = typeof row.status === "string" ? row.status : "";
+  if (
+    (disposition !== "created" && disposition !== "resumed" && disposition !== "readonly")
+    || !caseId || !sessionId || !status
+  ) {
+    return null;
+  }
+  return {
+    disposition,
+    caseId,
+    sessionId,
+    status,
+    shouldStartOpening: row.shouldStartOpening === true,
+    skillVersion: typeof row.skillVersion === "string" ? row.skillVersion : "",
+  };
+}
+
+export type RectificationEntryOpenIntent = "homepage" | "session" | "new";
+
+/** Build the server open request body; the browser never adds business state. */
+export function openRectificationRequestBody(
+  intent: RectificationEntryOpenIntent,
+  sessionId: string | null,
+): { intent: RectificationEntryOpenIntent; requestId: string; sessionId?: string } {
+  const requestId = globalThis.crypto?.randomUUID?.() ?? fallbackUuid();
+  if (intent === "session" && sessionId) {
+    return { intent, requestId, sessionId };
+  }
+  return { intent, requestId };
+}
+
+function fallbackUuid(): string {
+  return "00000000-0000-4000-8000-000000000000";
+}