Retain live history and warn on silent equities feeds

- Keep pausable live snapshots visible while stale
- Surface a connected-but-silent equities warning
- Add coverage for history retention and warning timing

apps/web/app/terminal.test.ts

@@ -5,7 +5,10 @@ import {
   flushPausableTapeData,
   getLiveFeedStatus,
   nextFlowFilterPopoverState,
+  projectPausableTapeState,
   reducePausableTapeData,
+  shouldRetainLiveSnapshotHistory,
+  shouldShowEquitiesSilentFeedWarning,
   toggleFilterValue
 } from "./terminal";
 
@@ -53,6 +56,55 @@ describe("live tape pausable helpers", () => {
     expect(getLiveFeedStatus("connected", 1000, 500, 1601)).toBe("stale");
     expect(getLiveFeedStatus("disconnected", 1000, 500, 1601)).toBe("disconnected");
   });
+
+  it("keeps visible history even when live status is stale", () => {
+    const projected = projectPausableTapeState([makeItem("stale", 7, 1000)], "stale", 2000);
+    expect(projected.items.map((item) => item.trace_id)).toEqual(["stale"]);
+    expect(projected.lastUpdate).toBeNull();
+  });
+
+  it("flags connected equities feeds that stay silent past threshold", () => {
+    expect(
+      shouldShowEquitiesSilentFeedWarning({
+        wsStatus: "connected",
+        equitiesSubscribed: true,
+        connectedAt: 1_000,
+        lastEquitiesEventAt: null,
+        now: 20_000,
+        thresholdMs: 25_000
+      })
+    ).toBe(false);
+
+    expect(
+      shouldShowEquitiesSilentFeedWarning({
+        wsStatus: "connected",
+        equitiesSubscribed: true,
+        connectedAt: 1_000,
+        lastEquitiesEventAt: null,
+        now: 27_000,
+        thresholdMs: 25_000
+      })
+    ).toBe(true);
+
+    expect(
+      shouldShowEquitiesSilentFeedWarning({
+        wsStatus: "connected",
+        equitiesSubscribed: true,
+        connectedAt: 1_000,
+        lastEquitiesEventAt: 20_000,
+        now: 40_000,
+        thresholdMs: 25_000
+      })
+    ).toBe(false);
+  });
+
+  it("retains live history when freshness-gated snapshots are empty", () => {
+    expect(shouldRetainLiveSnapshotHistory("options", true, 0, 3)).toBe(true);
+    expect(shouldRetainLiveSnapshotHistory("equities", true, 0, 2)).toBe(true);
+    expect(shouldRetainLiveSnapshotHistory("alerts", true, 0, 3)).toBe(false);
+    expect(shouldRetainLiveSnapshotHistory("options", true, 1, 3)).toBe(false);
+    expect(shouldRetainLiveSnapshotHistory("options", false, 0, 3)).toBe(false);
+  });
 });
 
 describe("flow filter popup helpers", () => {