Websocket fan-out gateway

Design a websocket fan-out gateway for a live-events product that holds 10M concurrent persistent connections and must deliver a published message to all subscribers of a channel (some channels have 2M subscribers) with p99 delivery under 500ms. Connections are long-lived, clients reconnect constantly on flaky mobile networks, and the system must survive a gateway node dying without dropping the whole channel. Walk through the connection tier, the fan-out path, subscription/routing state, and the central trade-off.