diff --git a/engine/crates/layerfs-api/tests/operator_history.rs b/engine/crates/layerfs-api/tests/operator_history.rs
index 10b31ccba..7406cff5d 100644
--- a/engine/crates/layerfs-api/tests/operator_history.rs
+++ b/engine/crates/layerfs-api/tests/operator_history.rs
@@ -1,8 +1,9 @@
-//! `backend.store.project.get_history`: the read model's history half, read from the
-//! Store with no daemon, so the dsh project page starts no Sandbox to show a
-//! project. It lists the Branches, their Commits and the Layers, holds no
-//! Workspaces, and `since` its version answers `unchanged` until history
-//! moves. Disposable profile.
+//! `backend.store.project.get_history` and the `snapshot` behind
+//! `sandbox.list_workspaces`: the read model, read from the Store with no
+//! daemon, so the dsh project page starts no Sandbox to show a project. It
+//! lists the Branches, their Commits and the Layers, names the Branches the
+//! Workspaces are mounted on, and `since` its version answers `unchanged`
+//! until what it shows moves. Disposable profile.
 #[path = "support/installed_store.rs"]
 #[allow(dead_code)]
 mod installed;
@@ -11,7 +12,8 @@ mod installed;
 mod support;
 
 use layerfs_bridge::control::{SdkCall, SdkValue};
-use layerfs_store_service::operator;
+use layerfs_history::HistoryName;
+use layerfs_store_service::operator::{self, WorkspaceView};
 use std::fs;
 use support::{write, Fixture};
 
@@ -59,3 +61,57 @@ fn history_is_read_from_the_store_alone() {
     assert_eq!(moved.get("workspaces"), Some(&SdkValue::List(Vec::new())));
     fixture.cleanup();
 }
+
+#[test]
+fn workspaces_name_branches_beyond_the_first_page() {
+    let fixture = Fixture::new("operator-history-branches", |source| {
+        fs::write(source.join("seed.txt"), b"seed\n").unwrap();
+        1
+    });
+    for n in 1..=70 {
+        fixture.fork(&format!("b{n:02}"));
+    }
+    let history = fixture.service.store.history();
+    let installed = HistoryName::new("installed").unwrap();
+    let stack = history
+        .layer_stack_named(&installed)
+        .unwrap()
+        .expect("installed stack")
+        .id;
+    let branch = history
+        .branch_named(stack, &HistoryName::new("b70").unwrap())
+        .unwrap()
+        .expect("b70 exists");
+    let binding = history
+        .branch_snapshot(branch.id)
+        .unwrap()
+        .expect("b70 snapshot");
+    // Move the head after the Workspace's binding was taken, so the answer
+    // also proves it reads the Branch's current head and not the page's.
+    fixture.apply("b70", vec![write("/after-mount.txt", "moved\n")]);
+    let view = WorkspaceView {
+        workspace: "workspace-4".into(),
+        namespace: 4,
+        binding,
+        activity: "idle",
+        mounted: true,
+        directory: Some("/workspaces/4".into()),
+        dirty: None,
+        pending_merge: false,
+        revision: None,
+    };
+    let args = SdkValue::Map(vec![("project".to_owned(), SdkValue::text("installed"))]);
+    let answer = operator::snapshot(&fixture.service.store, &args, &[view]).unwrap();
+    assert_eq!(answer.get("moreBranches"), Some(&SdkValue::Bool(true)));
+    let workspaces = match answer.get("workspaces") {
+        Some(SdkValue::List(items)) => items,
+        other => panic!("workspaces: {other:?}"),
+    };
+    assert_eq!(workspaces.len(), 1);
+    assert_eq!(workspaces[0].get_text("branch"), Some("b70"));
+    assert_eq!(
+        workspaces[0].get("headMovedSinceMount"),
+        Some(&SdkValue::Bool(true))
+    );
+    fixture.cleanup();
+}
diff --git a/engine/crates/layerfs-store-service/src/operator/inspect.rs b/engine/crates/layerfs-store-service/src/operator/inspect.rs
index d04019fcb..9dc541f56 100644
--- a/engine/crates/layerfs-store-service/src/operator/inspect.rs
+++ b/engine/crates/layerfs-store-service/src/operator/inspect.rs
@@ -129,7 +129,7 @@ pub fn snapshot(store: &Arc<Store>, args: &SdkValue, views: &[WorkspaceView]) ->
         .into_iter()
         .filter(|branch| branch.name.as_str() != MAIN)
         .collect::<Vec<_>>();
-    let names = branches
+    let mut names = branches
         .iter()
         .map(|branch| {
             (
@@ -138,6 +138,22 @@ pub fn snapshot(store: &Arc<Store>, args: &SdkValue, views: &[WorkspaceView]) ->
             )
         })
         .collect::<BTreeMap<_, _>>();
+    // The page is bounded, but a Workspace may be mounted on a Branch outside
+    // it. Resolve just those mounted identities, so the listing does not
+    // depend on how many Branches the project has. The page still reports
+    // `moreBranches`; the Workspace answer needs the name and current head.
+    for view in views {
+        if view.binding.branch.stack != stack.id {
+            continue;
+        }
+        let id = view.binding.branch.id;
+        if names.contains_key(&id) {
+            continue;
+        }
+        if let Some(branch) = store.history().branch(id).map_err(args::history)? {
+            names.insert(id, (branch.name.as_str().to_owned(), branch.head_commit));
+        }
+    }
     let mut spent = 0usize;
     let mut take = |value: SdkValue| {
         spent += cost(&value);