diff --git a/src/beaver_gateway/backends/claude_sdk.py b/src/beaver_gateway/backends/claude_sdk.py
index facc3ea..2f3ee4d 100644
--- a/src/beaver_gateway/backends/claude_sdk.py
+++ b/src/beaver_gateway/backends/claude_sdk.py
@@ -111,6 +111,7 @@ warnings.filterwarnings("ignore", category=CanUseToolShadowedWarning)
 ASK_TOOL = "AskUserQuestion"
 
 __all__ = [
+    "ORIGIN_HEADER",
     "AuditSink",
     "ClaudeSdkBackend",
     "RunnerConfig",
@@ -120,6 +121,9 @@ __all__ = [
     "fingerprint",
 ]
 
+ORIGIN_HEADER = "X-Conversation-Origin"
+"""Rides on every exposed MCP request; the gateway proxy passes it upstream."""
+
 ENV_KEEP: tuple[str, ...] = (
     "PATH",
     "HOME",
@@ -724,7 +728,14 @@ class ClaudeSdkBackend:
         system_prompt = (
             prompt_assembly.assemble(sources) if sources else agent.system_prompt
         )
-        servers: dict[str, Any] = dict(self._servers) if spec.tools else {}
+        servers: dict[str, Any] = (
+            {
+                name: {**server, "headers": {ORIGIN_HEADER: key}}
+                for name, server in self._servers.items()
+            }
+            if spec.tools
+            else {}
+        )
         gateway = (
             self._tool_server(key, spec.kind)
             if spec.tools and self._tool_server is not None and agent.gateway_tools
diff --git a/src/beaver_gateway/conversations/spawning.py b/src/beaver_gateway/conversations/spawning.py
index 828cddd..71521c6 100644
--- a/src/beaver_gateway/conversations/spawning.py
+++ b/src/beaver_gateway/conversations/spawning.py
@@ -148,8 +148,7 @@ class Spawning(Messaging):
         )
         if result.text.strip():
             await self.inject(parent, result.text, urgency="normal", origin="merge")
-        await self.set_status(conv, "merged")
-        await self.mark_closed(conv)
+        await self.mark_closed(await self.set_status(conv, "merged"))
         self._bus.publish(
             "conversation.merged",
             conversation_id=conv.external_id,
diff --git a/src/beaver_gateway/frontends/telegram/frontend.py b/src/beaver_gateway/frontends/telegram/frontend.py
index a8f0c94..2893483 100644
--- a/src/beaver_gateway/frontends/telegram/frontend.py
+++ b/src/beaver_gateway/frontends/telegram/frontend.py
@@ -268,7 +268,10 @@ class TelegramFrontend(Frontend):
         )
 
     async def mark_closed(self, conv: Conversation) -> bool:
-        return await self.mark_topic(conv)
+        merged = conv.status == "merged"
+        return await self.mark_topic(
+            conv, self.texts.closed_prefix if merged else self.texts.idle_prefix
+        )
 
     async def mark_topic(self, conv: Conversation, prefix: str | None = None) -> bool:
         """Rename the topic; closeForumTopic does not exist in private chats."""
@@ -279,10 +282,7 @@ class TelegramFrontend(Frontend):
         name = self._topic_names.get(target[1]) or conv.title or self.texts.branch
         if name.startswith(prefix):
             return True
-        await self.bot.edit_forum_topic(
-            target[0], target[1], name=f"{prefix}{name}"[:128]
-        )
-        self._topic_names[target[1]] = f"{prefix}{name}"
+        await self._rename(target[1], f"{prefix}{self._unmarked(name)}")
         return True
 
     def file_note(self) -> str:
@@ -462,6 +462,36 @@ class TelegramFrontend(Frontend):
             attachments=attachments,
         )
 
+    async def _branch_in_topic(
+        self, topic: int, *, text: str, attachments: list[dict[str, Any]] | None
+    ) -> None:
+        """A fresh topic is named by the first line, a closed one loses its mark."""
+        current = self._topic_names.get(topic)
+        previous = None
+        if current is None:
+            previous = await self.conversations.find_bound(
+                frontend=FRONTEND, external_id=self._ext(topic)
+            )
+        known = current or (previous.title if previous is not None else None)
+        title = (self._unmarked(known) if known else "") or self._title_from(text)
+        await self._branch(topic, title=title, text=text, attachments=attachments)
+        if current == title:
+            return
+        try:
+            await self._rename(topic, title)
+        except TelegramAPIError as exc:
+            _log.warning("topic %s not renamed to %r: %s", topic, title, exc)
+
+    async def _rename(self, topic: int, name: str) -> None:
+        name = name[:128]
+        await self.bot.edit_forum_topic(self.chat_id, topic, name=name)
+        self._topic_names[topic] = name
+
+    def _unmarked(self, name: str) -> str:
+        for prefix in (self.texts.closed_prefix, self.texts.idle_prefix):
+            name = name.removeprefix(prefix)
+        return name
+
     async def _handle(self, update: Update) -> None:
         if update.message is not None:
             await self._on_message(update.message)
@@ -592,9 +622,8 @@ class TelegramFrontend(Frontend):
             topic = cast("int", thread_id)
             conv = await self._live(topic)
             if conv is None:
-                title = self._topic_names.get(topic) or self._title_from(text)
-                await self._branch(
-                    topic, title=title, text=text, attachments=attachments or None
+                await self._branch_in_topic(
+                    topic, text=text, attachments=attachments or None
                 )
                 return
         pending = self.conversations.pending_question(conv.external_id)
diff --git a/src/beaver_gateway/frontends/telegram/texts.py b/src/beaver_gateway/frontends/telegram/texts.py
index edf2116..3fbfbb4 100644
--- a/src/beaver_gateway/frontends/telegram/texts.py
+++ b/src/beaver_gateway/frontends/telegram/texts.py
@@ -42,6 +42,7 @@ class TelegramTexts:
     help_head: str = "General is the master, any other topic is a branch."
     branch: str = "branch"
     closed_prefix: str = "✅ "
+    idle_prefix: str = "💤 "
     waiting: str = "⏳ thinking"
     thinking: str = "🤔 thinking"
     writing: str = "✍️ writing"
diff --git a/src/beaver_gateway/jobs/job.py b/src/beaver_gateway/jobs/job.py
index 0b77654..04d162f 100644
--- a/src/beaver_gateway/jobs/job.py
+++ b/src/beaver_gateway/jobs/job.py
@@ -5,7 +5,7 @@ from __future__ import annotations
 import logging
 from dataclasses import dataclass
 from datetime import datetime, timedelta
-from typing import TYPE_CHECKING, Any
+from typing import TYPE_CHECKING, Any, cast
 
 if TYPE_CHECKING:
     from collections.abc import Awaitable, Callable, Coroutine
@@ -73,6 +73,23 @@ class JobRun:
         )
         return True
 
+    async def inject_into(
+        self,
+        public_id: str | None,
+        text: str,
+        *,
+        urgency: Priority = "normal",
+        origin: str | None = None,
+    ) -> bool:
+        """Inject into that conversation, or the master once it is gone or over."""
+        conv = await self.conversations.get(public_id) if public_id else None
+        if conv is None or conv.status != "open":
+            return await self.inject_master(text, urgency=urgency, origin=origin)
+        await self.conversations.inject(
+            conv, text, urgency=urgency, origin=origin or self.job.name
+        )
+        return True
+
     async def spawn_job(
         self,
         *,
@@ -113,6 +130,21 @@ class JobRun:
                 _log.exception("closing idle %s failed", conv.external_id)
         return out
 
+    async def close_quiet(
+        self, *, kind: str = "branch", days: int = 3, limit: int | None = None
+    ) -> list[Conversation]:
+        """Close chats quiet for ``days`` without a digest, their windows marked."""
+        out: list[Conversation] = []
+        for conv in await self.conversations.idle(kind=kind, days=days, limit=limit):
+            if await self.conversations.busy(
+                conv
+            ) or await self.conversations.queue.pending(cast("int", conv.id)):
+                continue
+            row = await self.conversations.close(conv)
+            await self.conversations.mark_closed(row)
+            out.append(row)
+        return out
+
     async def retry_in(self, delay: timedelta) -> None:
         await self.scheduler.trigger(
             self.job, self.payload, delay=delay, trigger=self.trigger
diff --git a/tests/test_claude_sdk_backend.py b/tests/test_claude_sdk_backend.py
index 4920727..f65b7ab 100644
--- a/tests/test_claude_sdk_backend.py
+++ b/tests/test_claude_sdk_backend.py
@@ -250,7 +250,11 @@ async def test_stream_envelope_and_index_rebase(cwd: Path) -> None:
     assert opts.strict_mcp_config is True
     assert opts.permission_mode == "bypassPermissions"
     assert opts.mcp_servers == {
-        "firefly": {"type": "http", "url": "http://127.0.0.1:1/mcp/firefly/"}
+        "firefly": {
+            "type": "http",
+            "url": "http://127.0.0.1:1/mcp/firefly/",
+            "headers": {"X-Conversation-Origin": "conv-1"},
+        }
     }
     assert opts.session_store is not None
     assert opts.resume is None
diff --git a/tests/test_jobrun.py b/tests/test_jobrun.py
new file mode 100644
index 0000000..7a443d2
--- /dev/null
+++ b/tests/test_jobrun.py
@@ -0,0 +1,85 @@
+from datetime import UTC, datetime, timedelta
+from types import SimpleNamespace
+from typing import Any, cast
+
+from test_conversations import StubFrontend, World, world
+
+from beaver_gateway.jobs.job import Job, JobRun
+from beaver_gateway.storage.models import Conversation
+
+__all__ = ["world"]
+
+
+async def _noop(_: JobRun) -> None:
+    return None
+
+
+def _run(world: World) -> JobRun:
+    return JobRun(
+        job=Job("test", _noop),
+        trigger="test",
+        payload={},
+        scheduler=cast("Any", SimpleNamespace(conversations=world.conversations)),
+    )
+
+
+async def _quiet_since(world: World, conv: Conversation, ago: timedelta) -> None:
+    async def apply(row: Conversation) -> None:
+        row.last_activity_at = datetime.now(UTC) - ago
+
+    await world.conversations._update(conv, apply)  # noqa: SLF001
+
+
+async def test_close_quiet_closes_and_marks_only_idle_branches(world: World) -> None:
+    marked: list[tuple[str, str]] = []
+
+    class MarkingFrontend(StubFrontend):
+        async def mark_closed(self, conv: Conversation) -> bool:
+            marked.append((conv.external_id, conv.status))
+            return True
+
+    tg = MarkingFrontend("tg", ("master", "branch"))
+    tg.conversations = world.conversations
+    world.conversations._frontends = [tg]  # noqa: SLF001
+    convs = world.conversations
+    master = await convs.create(kind="master", agent="a", session_id="m")
+    idle = await convs.create(kind="branch", agent="a", parent=master, session_id="1")
+    fresh = await convs.create(kind="branch", agent="a", parent=master, session_id="2")
+    waiting = await convs.create(
+        kind="branch", agent="a", parent=master, session_id="3"
+    )
+    await _quiet_since(world, idle, timedelta(days=4))
+    await _quiet_since(world, fresh, timedelta(days=1))
+    await _quiet_since(world, waiting, timedelta(days=4))
+    await convs.queue.push(
+        conversation_id=cast("int", waiting.id),
+        priority="normal",
+        origin="cron",
+        text="later",
+    )
+
+    closed = await _run(world).close_quiet(kind="branch", days=3)
+
+    assert [c.external_id for c in closed] == [idle.external_id]
+    assert marked == [(idle.external_id, "closed")]
+    assert (await convs.get(fresh.external_id)).status == "open"
+    assert (await convs.get(waiting.external_id)).status == "open"
+
+
+async def test_inject_into_falls_back_to_the_master(world: World) -> None:
+    convs = world.conversations
+    master = await convs.create(kind="master", agent="a", session_id="m")
+    branch = await convs.create(kind="branch", agent="a", parent=master)
+    gone = await convs.create(kind="branch", agent="a", parent=master)
+    await convs.set_status(gone, "closed")
+    run = _run(world)
+
+    assert await run.inject_into(branch.external_id, "to branch", urgency="normal")
+    assert await run.inject_into(gone.external_id, "to closed", urgency="normal")
+    assert await run.inject_into(None, "to nobody", urgency="normal")
+
+    assert [i.text for i in await convs.queue.pending(branch.id)] == ["to branch"]
+    assert [i.text for i in await convs.queue.pending(master.id)] == [
+        "to closed",
+        "to nobody",
+    ]
diff --git a/tests/test_mcp_proxy_headers.py b/tests/test_mcp_proxy_headers.py
new file mode 100644
index 0000000..22b6c7b
--- /dev/null
+++ b/tests/test_mcp_proxy_headers.py
@@ -0,0 +1,69 @@
+from __future__ import annotations
+
+import asyncio
+import contextlib
+import socket
+from typing import TYPE_CHECKING, Any
+
+import pytest
+import uvicorn
+from fastmcp import Client, FastMCP
+from fastmcp.client.transports import StreamableHttpTransport
+from fastmcp.server.dependencies import get_http_headers
+
+from beaver_gateway.backends.claude_sdk import ORIGIN_HEADER
+from beaver_gateway.mcp.internal_app import build_internal_app
+from beaver_gateway.mcp.types import McpServer
+
+if TYPE_CHECKING:
+    from collections.abc import AsyncIterator
+
+
+def _free_port() -> int:
+    with socket.socket() as s:
+        s.bind(("127.0.0.1", 0))
+        return s.getsockname()[1]
+
+
+@contextlib.asynccontextmanager
+async def _serving(app: Any, port: int) -> AsyncIterator[None]:
+    server = uvicorn.Server(
+        uvicorn.Config(app, host="127.0.0.1", port=port, log_level="warning")
+    )
+    task = asyncio.create_task(server.serve())
+    while not server.started:
+        await asyncio.sleep(0.02)
+    try:
+        yield
+    finally:
+        server.should_exit = True
+        await task
+
+
+@pytest.mark.anyio
+async def test_the_origin_header_reaches_the_upstream_mcp() -> None:
+    upstream = FastMCP("upstream")
+
+    @upstream.tool
+    def caller() -> str:
+        return get_http_headers().get(ORIGIN_HEADER.lower(), "")
+
+    up, gateway = _free_port(), _free_port()
+    app, urls, _ = build_internal_app(
+        [McpServer.http(name="t3", url=f"http://127.0.0.1:{up}/mcp")],
+        host="127.0.0.1",
+        port=gateway,
+    )
+    seen = []
+    async with (
+        _serving(upstream.http_app(transport="http", path="/mcp"), up),
+        _serving(app, gateway),
+    ):
+        for conversation in ("conv-a", "conv-b"):
+            transport = StreamableHttpTransport(
+                urls["t3"], headers={ORIGIN_HEADER: conversation}
+            )
+            async with Client(transport) as client:
+                result = await client.call_tool("caller", {})
+                seen.append(result.data)
+    assert seen == ["conv-a", "conv-b"]
diff --git a/tests/test_telegram.py b/tests/test_telegram.py
index 441c83c..8ce8ac7 100644
--- a/tests/test_telegram.py
+++ b/tests/test_telegram.py
@@ -519,10 +519,10 @@ async def test_commands_status_merge_and_new(stack: Stack) -> None:
         frontend="telegram", external_id=f"{USER}/11"
     )
     assert branch.status == "merged"
-    assert stack.bot.topics == ["🦫 General", "edit:11:✅ work"]
+    assert stack.bot.topics == ["🦫 General", "edit:11:work", "edit:11:✅ work"]
     stack.bot.message("/new отчёт")
     await stack.until(lambda: stack.sent_with("in a new topic"), what="new topic")
-    assert stack.bot.topics == ["🦫 General", "edit:11:✅ work", "отчёт"]
+    assert stack.bot.topics[-1] == "отчёт"
     child = await stack.world.conversations.find_bound(
         frontend="telegram", external_id=f"{USER}/902"
     )
@@ -1298,3 +1298,34 @@ def test_a_tool_call_between_progress_updates_starts_a_new_paragraph() -> None:
     )
     feed(_thinking_delta("now writing it back"))
     assert draft.text == "reading the note\n\nnow writing it back"
+
+
+async def test_a_closed_topic_is_marked_asleep_and_wakes_with_a_new_branch(
+    stack: Stack,
+) -> None:
+    stack.bot.message("кухня на неделю\nи ещё строка", thread=12)
+    await stack.until(lambda: stack.sent_with("кухня на неделю"), what="reply")
+    assert stack.bot.topics[-1] == "edit:12:кухня на неделю"
+    branch = await stack.world.conversations.find_bound(
+        frontend="telegram", external_id=f"{USER}/12"
+    )
+    closed = await stack.world.conversations.close(branch)
+    assert await stack.world.conversations.mark_closed(closed)
+    assert stack.bot.topics[-1] == "edit:12:💤 кухня на неделю"
+    stack.tg._topic_names.clear()  # noqa: SLF001
+    stack.bot.message("а в четверг?", thread=12)
+    await stack.until(lambda: stack.sent_with("а в четверг?"), what="new branch")
+    assert stack.bot.topics[-1] == "edit:12:кухня на неделю"
+    fresh = await stack.world.conversations.find_bound(
+        frontend="telegram", external_id=f"{USER}/12"
+    )
+    assert fresh.id != branch.id
+    assert fresh.status == "open"
+    assert fresh.title == "кухня на неделю"
+
+
+async def test_a_named_topic_keeps_its_name(stack: Stack) -> None:
+    stack.bot.topic_created("план", 13)
+    stack.bot.message("hello", thread=13)
+    await stack.until(lambda: stack.sent_with("hello"), what="reply")
+    assert not any(t.startswith("edit:13:") for t in stack.bot.topics)