diff --git a/server/src/__tests__/cross-issue-influence-limit.test.ts b/server/src/__tests__/cross-issue-influence-limit.test.ts
index 551957c32ac..c4fff2fd10a 100644
--- a/server/src/__tests__/cross-issue-influence-limit.test.ts
+++ b/server/src/__tests__/cross-issue-influence-limit.test.ts
@@ -198,7 +198,11 @@ describe("cross-issue influence limit rollout", () => {
     expect(fake.inserted).toEqual([]);
   });
 
-  it("fails closed when the persisted run has no source issue", async () => {
+  it("counts writes from an unscoped run instead of rejecting them", async () => {
+    // A timer heartbeat with no checked-out issue has no source issue: every
+    // write it makes is cross-issue by definition. The persisted run row is
+    // still the attribution anchor, so the write spends the cap rather than
+    // failing as run-less.
     const fake = counterDb(0, { contextSnapshot: {} });
 
     await expect(observeCrossIssueInfluence(fake.db as never, {
@@ -207,10 +211,31 @@ describe("cross-issue influence limit rollout", () => {
       agentId: "33333333-3333-4333-8333-333333333333",
       targetIssueId: "55555555-5555-4555-8555-555555555555",
       kind: "update",
-    })).rejects.toMatchObject({
-      status: 403,
-      details: { code: "cross_issue_influence_run_context_required" },
+    })).resolves.toMatchObject({ count: 1, allowed: true });
+    expect(fake.inserted).toEqual([
+      expect.objectContaining({
+        action: "issue.cross_issue_influence_observed",
+        details: expect.objectContaining({ sourceIssueId: null }),
+      }),
+    ]);
+  });
+
+  it("still caps an unscoped run once its budget is spent", async () => {
+    const fake = counterDb(CROSS_ISSUE_INFLUENCE_LIMIT, { contextSnapshot: {} });
+
+    await expect(observeCrossIssueInfluence(fake.db as never, {
+      companyId: "22222222-2222-4222-8222-222222222222",
+      runId: "11111111-1111-4111-8111-111111111111",
+      agentId: "33333333-3333-4333-8333-333333333333",
+      targetIssueId: "55555555-5555-4555-8555-555555555555",
+      kind: "comment",
+      now: CROSS_ISSUE_INFLUENCE_ENFORCE_AT,
+    })).resolves.toMatchObject({
+      allowed: false,
+      count: CROSS_ISSUE_INFLUENCE_LIMIT + 1,
     });
-    expect(fake.inserted).toEqual([]);
+    expect(fake.inserted).toEqual([
+      expect.objectContaining({ action: "issue.cross_issue_influence_cap_rejected" }),
+    ]);
   });
 });
diff --git a/server/src/services/cross-issue-influence-limit.ts b/server/src/services/cross-issue-influence-limit.ts
index c2c4319a73b..e1ec2c00244 100644
--- a/server/src/services/cross-issue-influence-limit.ts
+++ b/server/src/services/cross-issue-influence-limit.ts
@@ -109,11 +109,16 @@ export async function observeCrossIssueInfluence(
       throw crossIssueInfluenceRunContextError();
     }
 
+    // An unscoped run (timer heartbeat with no checked-out issue) has no source
+    // issue, so every issue write it makes is cross-issue by definition and
+    // spends the cap. The locked run row above is the attribution anchor;
+    // rejecting these writes as run-less left live heartbeat runs unable to
+    // comment or update any task at all.
     const sourceIssueId = readRunSourceIssueId(run.contextSnapshot);
-    if (!sourceIssueId) throw crossIssueInfluenceRunContextError();
     if (
-      sourceIssueId === input.targetIssueId ||
-      (input.targetIssueIdentifier && sourceIssueId.toUpperCase() === input.targetIssueIdentifier.toUpperCase())
+      sourceIssueId !== null &&
+      (sourceIssueId === input.targetIssueId ||
+        (input.targetIssueIdentifier && sourceIssueId.toUpperCase() === input.targetIssueIdentifier.toUpperCase()))
     ) {
       return null;
     }