Build the Online Indicator — the green dot next to every contact's name in your chat app, plus the "last seen 12 min ago" line that follows it. Used by Slack, Discord, WhatsApp, Messenger, Teams, Instagram, LinkedIn — every product with a contact list. Sounds simple. It is not.

Three things make this problem hard at production scale:

1. N² watch problem. Every user is both a presence publisher and a presence subscriber. At 1B DAU each with ~500 contacts, the naive eager-broadcast design produces 500B subscription edges and ~250M frames/s of fanout. Physically impossible.
2. Ephemeral state at billion-user RAM scale. ~500M concurrent online users × ~100 B/record = ~50 GB per region — hot, in RAM, all the time, fully replicated.
3. Approximate by design. The product line "last seen 12 min ago" is a privacy + capacity invariant, not a UX choice. Quoting last_seen precisely (±1 s) leaks PII and forces hot-path persistence; quantizing to ±60 s solves both.

The architecture is the canonical Discord/Slack/WhatsApp shape: a long-lived WebSocket to a stateful gateway, a sharded actor tier holding hot presence in RAM, a separate fanout relay tier as the N² solver, an ephemeral cache for cross-shard reads, a durable spine for the audit trail, and a quantized last-seen store for the offline case.