  We follow existing distributed systems frameworks employing methods from
algebraic topology to formally define primitives of blockchain technology. We
define the notion of cross chain liquidity, sharding and probability spaces
between and within blockchain protocols. We incorporate recent advancements in
synthetic homology to show that this topological framework can be implemented
within a type system. We use recursion schemes to define kernels admitting
smooth manifolds across protocol complexes, leading to the formal definition of
a Poincare protocol.
