fix(gateway): guard live probe schedule timestamps

src/gateway/live-agent-probes.test.ts

@@ -1,4 +1,4 @@
-import { describe, expect, it } from "vitest";
+import { describe, expect, it, vi } from "vitest";
 import {
   assertCronJobMatches,
   assertLiveImageProbeReply,
@@ -73,6 +73,22 @@ describe("live-agent-probes", () => {
     expect(args.job?.sessionKey).toBe("agent:codex:acp:test");
   });
 
+  it("builds a cron probe spec when the process clock is outside the Date range", () => {
+    const dateNowSpy = vi.spyOn(Date, "now").mockReturnValue(8_640_000_000_000_001);
+
+    try {
+      const spec = createLiveCronProbeSpec();
+      const args = JSON.parse(spec.argsJson) as {
+        job?: { schedule?: { at?: string } };
+      };
+
+      expect(spec.at).toBe("1970-01-01T00:00:00.000Z");
+      expect(args.job?.schedule?.at).toBe("1970-01-01T00:00:00.000Z");
+    } finally {
+      dateNowSpy.mockRestore();
+    }
+  });
+
   it("validates cron cli job shape for the shared live probe", () => {
     expect(
       assertCronJobMatches({

src/gateway/live-agent-probes.ts

@@ -1,9 +1,14 @@
 import { execFile } from "node:child_process";
 import { randomBytes } from "node:crypto";
 import { promisify } from "node:util";
+import {
+  resolveExpiresAtMsFromDurationSeconds,
+  resolveTimestampMsToIsoString,
+} from "../shared/number-coercion.js";
 import { normalizeOptionalLowercaseString } from "../shared/string-coerce.js";
 
 const execFileAsync = promisify(execFile);
+const LIVE_CRON_PROBE_DELAY_SECONDS = 7 * 24 * 60 * 60;
 
 type CronListCliResult = {
   jobs?: Array<{
@@ -64,7 +69,9 @@ export function createLiveCronProbeSpec(
   const normalizedNonce = normalizeOptionalLowercaseString(nonce) ?? "";
   const name = `live-mcp-${normalizedNonce}`;
   const message = `probe-${normalizedNonce}`;
-  const at = new Date(Date.now() + 7 * 24 * 60 * 60 * 1000).toISOString();
+  const at = resolveTimestampMsToIsoString(
+    resolveExpiresAtMsFromDurationSeconds(LIVE_CRON_PROBE_DELAY_SECONDS) ?? Date.now(),
+  );
   const argsJson = JSON.stringify({
     action: "add",
     job: {