Blockchain Cohomology

Abstract

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.