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

It's nice to have a consensus layer with limited blockspace and robust L2s offering resold blockspace at a discount with specialized use cases/properties.
Then everyone can verify the root chain and any other chain they care about, but can safely ignore chains they don't care about while existing in the same ecosystem.

I have been asking this question for a while! Excited to hear what others have to say

I'm a magic 8 ball of pithy sayings

/mtg

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

(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

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

not 100% on my understanding but I thought it was mostly offloading all the compute…basically more processing power?

It’s the scaling trilema. You can have throughput, decentralization, or security. Pick two. But if you can delegate security and decentralization to the L1, then you are free to pursue throughput