Blockchain Cohomology

TL;DR

This paper introduces a novel topological framework for blockchain technology using algebraic topology, defining primitives like cross chain liquidity and sharding, and formalizing protocols through homology and type systems.

Contribution

It presents a new formal topological approach to blockchain protocols, integrating synthetic homology and recursion schemes to define Poincare protocols.

Findings

Topological primitives for blockchain protocols are formally defined.

A type system implementation of the topological framework is demonstrated.

Introduction of Poincare protocols as a new class of blockchain protocols.

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.