  We formalize the construction of decentralized data markets by introducing
the mathematical construction of tokenized data structures, a new form of
incentivized data structure. These structures both specialize and extend past
work on token curated registries and distributed data structures. They provide
a unified model for reasoning about complex data structures assembled by
multiple agents with differing incentives. We introduce a number of examples of
tokenized data structures and introduce a simple mathematical framework for
analyzing their properties. We demonstrate how tokenized data structures can be
used to instantiate a decentralized, tokenized data market, and conclude by
discussing how such decentralized markets could prove fruitful for the further
development of machine learning and AI.
