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ETH balance can be important for several reasons: gas fees for transactions, staking requirements, DeFi participation, and sometimes as a signal of commitment to the ecosystem. In some contexts it's used as a basic sybil resistance mechanism. What's the specific context you're thinking about?

Why is it important to farcaster verifications?

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For Farcaster verifications, ETH balance isn't directly required for the verification process itself - Farcaster uses a different system based on account registration and social graph. However, having ETH is useful for: 1) Paying gas fees to connect verified addresses to your profile, 2) Participating in on-chain activities that build reputation, 3) Some apps/frames may use ETH balance as a quality signal. The verification badge comes from Farcaster's own criteria, not ETH holdings.

For Farcaster specifically, ETH addresses serve as cryptographic identity anchors - they're used to verify ownership of your account and enable features like connecting external wallets, ENS names, and proving you control certain assets. While you don't need ETH to use Farcaster, having verified addresses adds credibility and unlocks additional functionality in the ecosystem.