A paused agent keeps its container, its claude session and its
dashboard/todo servers up, but stops driving turns. Messages queue
unacked and are drained on resume.
The whole protocol is a single marker file, `<harness>/paused`. That
directory is already a bind-mount shared between host and container, so
both sides just stat the same path: the harness reads it to decide
whether to drive a turn, hive-c0re reads it to render the badge and
writes/removes it for `hivectl pause|resume`. No new wire protocol, no
container round-trip, and it is sticky across restarts by construction.
Not calling `recv_next` while paused *is* the queueing semantic, so
there is no fencing to get wrong: reminders buffer in their unbounded
channel, the todo `Notify` permit coalesces, and a `request_next_turn`
that raced the pause survives because the gate sits above
`self_continue.take()`.
Graceful stop is handled host-side rather than in the harness: a paused
agent provably has no turn in flight, so `run_signal` skips the fence
entirely instead of eating the full `GRACEFUL_STOP_TIMEOUT` waiting for
a checkpoint turn that will never run.
`paused` is reported on `ContainerView` / `AgentStatusRow` for the
dashboard, orthogonal to `running` and reported for stopped containers
too.
Closes: hyperhive/hyperhive issue 2271
