1. CVM State: It's an internal 32-byte register, not pre-shared. For each operation, it's initialized from a unique nonce (e.g., enc_nonce). This nonce is transmitted publicly with the ciphertext as part of a structured payload. The CVM's subsequent state evolution is secret, as it depends on the master key and operational history. It's an input to the round key derivation, not the round key itself.
2. Path Determination: The path is determined by the ciphertext chunk. During decryption, the ciphertext is used with the key and current state to find the path before it's decrypted.
3. Path Collision: This is critical because it implies a state collision. Since round keys are derived from the state, a state collision at the same Labyrinth node would cause catastrophic key reuse. The state ratchet is designed to make this negligible.