fix(rectification): host-fallback empty evidence turns and choice range narration (BUG-633, BUG-634)

Evidence turns that already recorded a batch no longer fail the whole run when the model emits no text; unchanged ranges now name which clock spans lead or lag, and the timeline no longer says 收窄.

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

frontend/tests/rectification-host-fallback.test.ts

@@ -0,0 +1,55 @@
+import assert from "node:assert/strict";
+import { readFileSync } from "node:fs";
+import test from "node:test";
+
+import {
+  composeHostFallbackNarration,
+  publicWriteToolCompleted,
+} from "../src/lib/rectification-agentic/v9/host-fallback.ts";
+
+test("host fallback recap uses only batch return lines", () => {
+  assert.equal(composeHostFallbackNarration(null), null);
+  assert.equal(composeHostFallbackNarration({}), "记下了。");
+  assert.equal(
+    composeHostFallbackNarration({
+      accepted_recaps: [
+        { display_date_label: "2016年9月", event_phrase: "入学" },
+        { display_date_label: "2020年6月", event_phrase: "毕业" },
+      ],
+    }),
+    "记下了：2016年9月 入学、2020年6月 毕业。",
+  );
+  assert.equal(
+    composeHostFallbackNarration({
+      items: [
+        { outcome: "accepted", display_date_label: "2018年7月", event_phrase: "入职" },
+        { outcome: "rejected", display_date_label: "1999年", event_phrase: "不该出现" },
+      ],
+    }),
+    "记下了：2018年7月 入职。",
+  );
+});
+
+test("write-tool completion is limited to batch, set-focus and compare", () => {
+  const none = new Map<string, "completed" | "failed">([
+    ["rectification-read-case", "completed"],
+  ]);
+  assert.equal(publicWriteToolCompleted(none), false);
+  const batch = new Map<string, "completed" | "failed">([
+    ["rectification-record-evidence-batch", "completed"],
+  ]);
+  assert.equal(publicWriteToolCompleted(batch), true);
+  const failedBatch = new Map<string, "completed" | "failed">([
+    ["rectification-record-evidence-batch", "failed"],
+  ]);
+  assert.equal(publicWriteToolCompleted(failedBatch), false);
+});
+
+test("case snapshot receipts expose host_fallback origin from the durable phase", () => {
+  const route = readFileSync(
+    new URL("../src/app/api/rectification/cases/[caseId]/route.ts", import.meta.url),
+    "utf8",
+  );
+  assert.match(route, /answer_origin: "host_fallback"/);
+  assert.match(route, /answer\.host_fallback/);
+});