  Since the inception of blockchain and Bitcoin (Nakamoto (2008)), a
decentralized-distributed ledger system and its associated cryptocurrency,
respectively, the world has witnessed a slew of newer adaptations and
applications. Although the original distributed ledger technology (DLT) of
blockchain is deemed secure and decentralized, the confirmation of transactions
is inefficient by design. Recently adopted, directed acyclic graph (DAG)-based
distributed ledgers validate transactions efficiently without the physically
and environmentally costly building process of blocks (Lerner (2015)). However,
centrally-controlled confirmation against the odds of multiple validation
disqualifies the DAG as a decentralized-distributed ledger. In this regard, we
introduce an innovative DLT by reconstructing a chain of antichains based on a
given DAG-pool of transactions. Each antichain (box) contains distinct nodes
whose approved transactions are recursively validated by subsequently
augmenting nodes. The boxer node closes the box and keeps the hash of all
transactions confirmed by the box-genesis node. Designation of boxers and
box-geneses is conditionally randomized for decentralization. The boxes are
serially concatenated with recursive confirmation (boxchain) without incurring
the cost of box generation. Rewards (boxcoin) are paid to the contributing
nodes of the ecosystem whose trust is built on the doubly-secure protocol of
confirmation. A value-preserving medium of payment (boxdollar) is among
numerous practical applications discussed herein.
