Quadratic Networks is a novel approach for fully on-chain community membership where new members can only mint the NFT to join the network if they have on-chain nominations from existing members equal to the square root of the size of the existing network.

It has a couple of key benefits, including:

Fully on-chain data, no off-chain point of failure or admin control
Maintain the vibes of the group as it scales
Decentralize membership curation decision-making by making it legible and open to all existing members with equal votes
Slow the growth of the network over time

Using these memberships, we can also directly integrate with emerging verified credential systems like Zupass that allow us to use ZK proofs to verify on-chain NFT membership without doxxing wallet addresses.