diff --git a/desktop/src/features/mesh-compute/meshRowModel.test.mjs b/desktop/src/features/mesh-compute/meshRowModel.test.mjs
index cc699bb77..870bdac55 100644
--- a/desktop/src/features/mesh-compute/meshRowModel.test.mjs
+++ b/desktop/src/features/mesh-compute/meshRowModel.test.mjs
@@ -211,3 +211,22 @@ test("an agent that uses the mesh leaves a busy sharer showing activity", () =>
   });
   assert.equal(model.pulse, "activity");
 });
+
+test("an empty mesh offers the action instead of sitting inert", () => {
+  // Nothing to show and nothing happening: without a prompt the row is inert
+  // and unexplained. The action is real -- you can be the first to share -- so
+  // the badge slot carries the word where a figure would go.
+  const model = derive({ snapshot: snapshot() });
+  assert.equal(model.tone, "unknown");
+  assert.equal(model.badge, "Share");
+  assert.match(model.tooltip, /share this computer to start the mesh/);
+});
+
+test("an empty mesh does not throb, and an unfetched one offers nothing", () => {
+  // A community that never uses the mesh would otherwise animate forever;
+  // permanent motion earns nothing but annoyance. And a prompt derived from no
+  // data would appear for one poll then retract, reading as a glitch.
+  assert.equal(derive({ snapshot: snapshot() }).pulse, "none");
+  assert.equal(derive({ snapshot: null }).badge, null);
+  assert.equal(derive({ snapshot: null }).pulse, "none");
+});
diff --git a/desktop/src/features/mesh-compute/meshRowModel.ts b/desktop/src/features/mesh-compute/meshRowModel.ts
index c35c61f16..195b4f67c 100644
--- a/desktop/src/features/mesh-compute/meshRowModel.ts
+++ b/desktop/src/features/mesh-compute/meshRowModel.ts
@@ -73,6 +73,9 @@ export type MeshRowModel = {
    * machine is outside the mesh the figure *is* the invitation: a real number
    * argues for joining better than any exhortation, and unlike a nudge there is
    * nothing to dismiss.
+   *
+   * When the mesh is empty there is no figure, so the slot carries the word
+   * "Share" — the row would otherwise be inert with nothing explaining why.
    */
   badge: string | null;
   /**
@@ -179,16 +182,32 @@ export function deriveMeshRowModel({
   // Not participating. The relay snapshot is the only view, and the only thing
   // that distinguishes "there is a mesh to join" from "there is nothing here".
   const count = snapshot?.sharingDeviceCount ?? 0;
-  if (!snapshot || count === 0) {
+  if (!snapshot) {
+    // Not asked yet. No figure, no prompt: a call to action based on no data
+    // would appear for one poll and retract, which reads as a glitch.
     return {
       tone: "unknown",
-      tooltip: snapshot
-        ? "No shared compute in this community yet"
-        : "Checking for shared compute…",
+      tooltip: "Checking for shared compute…",
       badge: null,
       pulse: "none",
     };
   }
+  if (count === 0) {
+    // An empty mesh is the one state with nothing to show and nothing
+    // happening, so without a prompt the row is inert and unexplained. The
+    // action is real — you can be the first to share — so the badge slot
+    // carries the word instead of a figure.
+    //
+    // Static, not throbbing. A community that never uses the mesh would
+    // otherwise animate forever, and permanent motion earns nothing but
+    // annoyance. The invite throb stays reserved for capacity that exists.
+    return {
+      tone: "unknown",
+      tooltip: "No shared compute yet — share this computer to start the mesh",
+      badge: "Share",
+      pulse: "none",
+    };
+  }
   const gb = snapshot.sharedCapacityGb;
   return {
     tone: "available",
diff --git a/desktop/src/features/mesh-compute/ui/SidebarMeshComputeRow.tsx b/desktop/src/features/mesh-compute/ui/SidebarMeshComputeRow.tsx
index a638caf32..86fef77f5 100644
--- a/desktop/src/features/mesh-compute/ui/SidebarMeshComputeRow.tsx
+++ b/desktop/src/features/mesh-compute/ui/SidebarMeshComputeRow.tsx
@@ -7,7 +7,7 @@ import type { MeshRowPulse, MeshRowTone } from "../meshRowModel";
 import { MeshComputePopover } from "./MeshComputePopover";
 
 /**
- * The sidebar Community mesh row.
+ * The sidebar Buzz MeshLLM row.
  *
  * Replaces the ~120px footer card with one menu line beside Inbox and Agents,
  * because front-page sidebar space is premium. The row carries a single signal
@@ -99,7 +99,7 @@ export function SidebarMeshComputeRow({
             </span>
           </span>
           <SidebarMenuLabel className="opacity-80">
-            Community mesh
+            Buzz MeshLLM
           </SidebarMenuLabel>
         </SidebarMenuButton>
       </MeshComputePopover>