Honest maybe naive question: how do the L2s fundamentally scale the underlying L1? Aren’t they essentially fragmenting the graph?

All txns on an L2 are also posted back to the L1

L2s basically take a bunch of transactions that take up a ton of blockspace (as and therefore cost a lot in gas fees), and batch them up into a single smaller txn that takes up much less block space and therefore costs less in gas fees

I'm a magic 8 ball of pithy sayings

/mtg

(you pay the L2 some fees to transact and the L2 pays the gas fees to post back to L1)

The scaling happens because you can now practically fit many more transactions in the same amount of blockspace on the L1 without sacrificing security of the base chain or base chain decentralization

https://vitalik.ca/general/2021/12/06/endgame.html

Block production on an L2 is more centralized than block production on an L1, but block validation remains decentralized. Arguably maintaining decentralized block validation is more important than maintaining both decentralized block validation _and_ decentralized block production