Setting the Celebrity Threshold

Your fan-out worker fleet sustains 80,000 feed-cache writes per second in steady state, and you want any single post to be at least 95% fanned out within 2 seconds even during a burst where the fleet is also processing normal traffic at 60,000 writes/s (leaving 20,000 writes/s of spare capacity for a single large post).

1. Compute the maximum follower count a post can fan out to and still hit the 2-second target under that spare capacity.
2. Explain what happens to feed freshness for followers of an account just above that threshold if you don't treat it specially, and what the hybrid design does instead.
3. Is the threshold a one-time constant, or should it be dynamic? Give a concrete signal you would use to adjust it in production.