diff --git a/WORK-RECORDS.md b/WORK-RECORDS.md
index 80a76cd..886ef04 100644
--- a/WORK-RECORDS.md
+++ b/WORK-RECORDS.md
@@ -105,9 +105,9 @@
 | task | SAND-WP-0012-T04 | done | — | workplans/SAND-WP-0012-packer-orchestration.md |
 | task | SAND-WP-0012-T05 | done | — | workplans/SAND-WP-0012-packer-orchestration.md |
 | task | SAND-WP-0012-T06 | done | — | workplans/SAND-WP-0012-packer-orchestration.md |
-| task | SAND-WP-0013-T01 | todo | — | workplans/SAND-WP-0013-bwrap-extension.md |
-| task | SAND-WP-0013-T02 | todo | — | workplans/SAND-WP-0013-bwrap-extension.md |
-| task | SAND-WP-0013-T03 | todo | — | workplans/SAND-WP-0013-bwrap-extension.md |
+| task | SAND-WP-0013-T01 | done | — | workplans/SAND-WP-0013-bwrap-extension.md |
+| task | SAND-WP-0013-T02 | done | — | workplans/SAND-WP-0013-bwrap-extension.md |
+| task | SAND-WP-0013-T03 | done | — | workplans/SAND-WP-0013-bwrap-extension.md |
 | task | SAND-WP-0013-T04 | todo | — | workplans/SAND-WP-0013-bwrap-extension.md |
-| task | SAND-WP-0013-T05 | todo | — | workplans/SAND-WP-0013-bwrap-extension.md |
-| task | SAND-WP-0013-T06 | todo | — | workplans/SAND-WP-0013-bwrap-extension.md |
+| task | SAND-WP-0013-T05 | done | — | workplans/SAND-WP-0013-bwrap-extension.md |
+| task | SAND-WP-0013-T06 | done | — | workplans/SAND-WP-0013-bwrap-extension.md |
diff --git a/docs/integrations/glas-harness.md b/docs/integrations/glas-harness.md
index f98a74e..6860bb8 100644
--- a/docs/integrations/glas-harness.md
+++ b/docs/integrations/glas-harness.md
@@ -22,6 +22,23 @@ sandboxer create \
 | `reachability.remote_dir` | sand-boxer | Workspace root on remote host |
 | `state` | sand-boxer | Lifecycle state (`ready`, etc.) |
 
+## Two reachability modes
+
+Not every sandbox has an SSH hop. `ext.compose-ssh` / `ext.vm-packer`
+always run remote and populate `reachability.ssh` + `reachability.
+remote_dir`; glas-harness execs tools over that SSH channel. `ext.bwrap`
+(SAND-WP-0013) runs same-host and never populates `reachability.ssh` —
+instead it populates `reachability.pid` (the placeholder process holding
+the bwrap namespaces) and `reachability.workspace_dir`. glas-harness
+execs tools by entering that pid's namespaces directly
+(`nsenter --target <pid> --mount --pid --net --uts --ipc -- <cmd>`, no
+tunnel needed) rather than opening an SSH channel. `reachability/enrich.
+build_reachability_report()` returns both an `ssh_one_liner` and a
+`local_exec_hint`; exactly one is non-null depending on which mode the
+resolved extension uses. Consumers should branch on which field is
+populated, not on profile id, since routing can fall back between
+extensions.
+
 ## Ownership
 
 | Concern | Owner |
diff --git a/src/sandboxer/models.py b/src/sandboxer/models.py
index c4922a1..688414f 100644
--- a/src/sandboxer/models.py
+++ b/src/sandboxer/models.py
@@ -156,6 +156,11 @@ class Reachability(BaseModel):
     tunnel: str | None = None
     tunnel_via: str | None = None
     identity: str | None = None
+    # Local (no-SSH-hop) descriptor — populated for same-host extensions
+    # like ext.bwrap. A consumer execs into the sandbox directly
+    # (e.g. `nsenter --target <pid> ...`) rather than over SSH.
+    pid: str | None = None
+    workspace_dir: str | None = None
 
 
 class SandboxStatus(BaseModel):
diff --git a/src/sandboxer/reachability/enrich.py b/src/sandboxer/reachability/enrich.py
index 6fde9ed..89a1efe 100644
--- a/src/sandboxer/reachability/enrich.py
+++ b/src/sandboxer/reachability/enrich.py
@@ -19,6 +19,11 @@ def enrich_reachability(
     enriched = dict(reach)
     spec = profile.reachability
 
+    if handle.get("workspace_dir"):
+        enriched.setdefault("workspace_dir", handle["workspace_dir"])
+    if handle.get("pid") and enriched.get("endpoint", "").startswith("pid:"):
+        enriched.setdefault("pid", handle["pid"])
+
     if spec.tunnel:
         enriched.setdefault("tunnel_via", spec.tunnel)
     if spec.identity:
@@ -50,6 +55,20 @@ def ssh_one_liner(reach: Reachability) -> str | None:
     return None
 
 
+def local_exec_hint(reach: Reachability) -> str | None:
+    """No-SSH-hop exec hint for same-host extensions (e.g. ext.bwrap).
+
+    Consumers exec directly into the sandbox's namespaces via the
+    placeholder process's pid, rather than opening an SSH channel.
+    """
+    if reach.pid and reach.workspace_dir:
+        return (
+            f"nsenter --target {reach.pid} --mount --pid --net --uts --ipc "
+            f"-- sh -c 'cd {reach.workspace_dir} && exec $SHELL'"
+        )
+    return None
+
+
 def build_reachability_report(status: SandboxStatus) -> dict[str, Any]:
     """Consumer-facing reachability report with ops-bridge pointer."""
     reach = status.reachability
@@ -65,4 +84,5 @@ def build_reachability_report(status: SandboxStatus) -> dict[str, Any]:
     }
     if reach:
         payload["ssh_one_liner"] = ssh_one_liner(reach)
+        payload["local_exec_hint"] = local_exec_hint(reach)
     return payload
\ No newline at end of file
diff --git a/tests/test_bwrap.py b/tests/test_bwrap.py
index b3a73b0..0810945 100644
--- a/tests/test_bwrap.py
+++ b/tests/test_bwrap.py
@@ -164,3 +164,22 @@ def test_supports_snapshots_is_false() -> None:
     assert ext.supports_snapshots() is False
     with pytest.raises(NotImplementedError):
         ext.snapshot({})
+
+
+def test_reachability_local_exec_hint_for_bwrap_handle() -> None:
+    from sandboxer.reachability.enrich import enrich_reachability, local_exec_hint
+    from sandboxer.models import Reachability
+
+    handle = {"pid": "555", "workspace_dir": "/tmp/sandboxer-bwrap/abc", "host": "localhost"}
+    reach = {"host": "localhost", "endpoint": "pid:555"}
+    profile = _profile()
+
+    enriched = enrich_reachability(reach, profile, handle)
+    reachability = Reachability(**enriched)
+
+    assert reachability.pid == "555"
+    assert reachability.workspace_dir == "/tmp/sandboxer-bwrap/abc"
+    assert local_exec_hint(reachability) == (
+        "nsenter --target 555 --mount --pid --net --uts --ipc "
+        "-- sh -c 'cd /tmp/sandboxer-bwrap/abc && exec $SHELL'"
+    )
diff --git a/workplans/SAND-WP-0013-bwrap-extension.md b/workplans/SAND-WP-0013-bwrap-extension.md
index c4b4961..82c6671 100644
--- a/workplans/SAND-WP-0013-bwrap-extension.md
+++ b/workplans/SAND-WP-0013-bwrap-extension.md
@@ -76,7 +76,7 @@ built against the other.
 
 ```task
 id: SAND-WP-0013-T04
-status: todo
+status: done
 priority: high
 state_hub_task_id: "1d8b3e18-d067-4364-89e9-5d5bc5923deb"
 ```