Can I mine on the Arweave network with a dynamic IP?

[JamesPiechota]

Yes - but there are some caveats:

Miners benefit by getting the latest set of blocks and transactions as fast as possible to
limit the time wasted mining against a stale chain tip. Miners can get blocks 2 ways:

1. By polling their peers for new blocks and transactions
2. By being notified of new blocks and transactions by other miners

If you have a dynamic IP you may not get notified by your peers as quickly as a miner with
a static IP. However your miner will continue to poll, so the lag will be minimal.

A slightly bigger issue is your "peer reputation". All peers in the network maintain a rating
for all other peers based on past activity. It basically boils down to the amount of valid
data exchanged. As your node sends valid data to peers, your reputation increases. Reputation
is currently tracked by IP:PORT, so whenever your IP changes, your reputation will be reset.

Reputation primarily comes into play when you mine a solution, Peers will process the solutions
of higher reputation peers first. So if you have a low reputation and mine a block at about
the same time as a miner with a higher reputation, there's a greater chance that your block
will be processed later and potentially orphaned.

See How Mining Works for more information