Spark allows bitcoin to be transferred between users without needing on-chain transactions by changing who holds the authorization to spend the coins. Ownership is represented as a two-piece puzzle shared between the user and a Spark Entity, where transferring bitcoin means replacing the user’s puzzle piece while the Spark Entity discards the previous matching piece. This method promises efficient, secure transfers that do not move coins on-chain but can still be exited to on-chain spending if necessary.