diff --git a/backend/__tests__/unit/services/webAddressProvenance.test.js b/backend/__tests__/unit/services/webAddressProvenance.test.js
index 13993e1dac..e2d3368e05 100644
--- a/backend/__tests__/unit/services/webAddressProvenance.test.js
+++ b/backend/__tests__/unit/services/webAddressProvenance.test.js
@@ -13,7 +13,7 @@
  */
 
 const {
-  addressKey, addressesIn, addressWasGiven, GivenAddresses,
+  addressKey, addressesIn, addressWasGiven, GivenAddresses, textScanCount,
 } = require('../../../services/webAddressProvenance');
 
 describe('webAddressProvenance', () => {
@@ -144,14 +144,27 @@ describe('webAddressProvenance', () => {
       expect(given.resolve('')).toBeNull();
     });
 
+    // Counted, not timed. This assertion was a 50 ms budget for 1,000 lookups,
+    // which measures the runner as much as the code: it flaked at 62.47 ms on
+    // #1768 and again on #2446 (TASK-347). A rescan is a count, so count it —
+    // ONE rescan fails this now, where the clock needed enough of them to
+    // exceed a budget, and a cold or loaded machine no longer fails it at all.
     test('each text is scanned once: refused attempts against three hostile pages cost no rescan', () => {
       const given = new GivenAddresses();
-      const page = Array.from({ length: 400 }, (_, i) => `https://h${i}.example/p${'!'.repeat(50)}x`).join(' ');
-      [page, page, page].forEach((text) => given.add(text));
+      const address = (i) => `https://h${i}.example/p${'!'.repeat(50)}x`;
+      const page = Array.from({ length: 400 }, (_, i) => address(i)).join(' ');
 
-      const started = process.hrtime.bigint();
-      for (let i = 0; i < 1000; i += 1) given.has(`https://attacker.example/c?d=${i}`);
-      expect(Number(process.hrtime.bigint() - started) / 1e6).toBeLessThan(50);
+      const beforeAdds = textScanCount();
+      [page, page, page].forEach((text) => given.add(text));
+      expect(textScanCount() - beforeAdds).toBe(3);
+
+      const afterAdds = textScanCount();
+      for (let i = 0; i < 1000; i += 1) {
+        expect(given.has(`https://attacker.example/c?d=${i}`)).toBe(false);
+      }
+      // An accepted attempt is a lookup too, so it may not rescan either.
+      expect(given.has(address(7))).toBe(true);
+      expect(textScanCount()).toBe(afterAdds);
     });
   });
 });
diff --git a/backend/services/webAddressProvenance.ts b/backend/services/webAddressProvenance.ts
index e629472f19..827612dcb9 100644
--- a/backend/services/webAddressProvenance.ts
+++ b/backend/services/webAddressProvenance.ts
@@ -75,8 +75,22 @@ const parseAddress = (raw: string): { key: string; url: string } | null => {
 /** The comparable form of one written address, or null when it is not one. */
 export const addressKey = (raw: string): string | null => parseAddress(raw)?.key ?? null;
 
+/**
+ * How many texts have been scanned for addresses, ever, in this process.
+ *
+ * Instrumentation, not behaviour: the no-rescan guarantee below ("each given
+ * text is scanned once, and a refused attempt costs no rescan") used to be
+ * asserted with a wall clock, which measures the shared CI runner as much as
+ * the code and flaked at 62 ms against a 50 ms budget (TASK-347). A rescan is
+ * a count, so count it: one rescan fails the test, and a slow machine does
+ * not. Monotonic and never read by anything here.
+ */
+let textScans = 0;
+export const textScanCount = (): number => textScans;
+
 /** Every address written in `text`, keyed by its comparable form, first writing kept. */
 const writtenAddresses = (text: string): Map<string, string> => {
+  textScans += 1;
   const found = new Map<string, string>();
   for (const token of String(text || '').split(TOKEN_SEPARATORS)) {
     if (!token.includes('.')) continue;