A private key is a 64-character hexadecimal string (made up of digits 0–9 and letters a–f). Each address on each chain has its own private key. For example, an EVM private key controls assets on ETH, BSC, Polygon, and all other EVM-compatible chains — but it doesn't cover BTC or Solana, which have their own private keys.

The recursive circuit takes 64 different proofs (π0, ..., π63), hashes (h0, ..., h63), equities (e0, ..., e63), and debts (d0, ..., d63) from the lower-layer circuits as inputs. It combines these inputs and produces 3 outputs: a new hash (hrecursive), total equity (erecursive), and total debt (drecursive).