What is a State Channel? Layer 0 vs. Layer 2

When comparing the differences between state channel implementations used as scaling solutions for blockchains, the terms isomorphic (i.e. Cardano’s Hydra layer 2 state channel) and hylomorphic (i.e. Constellation’s layer 0 state channel) are used.

What are the differences between the two and how does that impact interoperability and scalability?

What is an Isomorphism?

Basically an isomorphism enables the ability to mathematically map one data type into a different data type so that the underlying information is retained and can be represented and referenced in a different system to be used for other mathematical operations and representations. This is what Cardano is doing to ensure validity and integrity of atomic swaps between their layer 1 ledger and their layer 2 isomorphic state channel. Basically Cardano treats their layer 1 as the settlement layer and their layer 2 as the computational layer for scaling up transactions and smart contracts. By using isomorphic state channels, Cardano essentially extends the layer 1 network in an organic way, avoiding the need to create a bridge into an independent layer 2 network which would require wrapping native assets and Plutus smart contracts, a problem which plagues most Ethereum L2s.

What is a Hylomorphism?

What Constellation has done is create a data type system that is capable of mathematically abstracting data types into a generalized algebraic geometric topology using higher dimensional category theory and homotopy theory. This level of mathematical abstraction allows for a “layer 0″ meta-network to mathematically model the data types and structures comprised within data streams generated from external networks and systems such as Layer 1 and Layer 2 Blockchains or private enterprise and governments systems.

What this means is you that can continuously map morphisms to morphisms with mathematical provenance, which allows for a hierarchy of complex data types to form and be represented within a directed acyclic graph as a geometric space. Because data is stored in this way it is essentially granted properties of a physical object that can be used to observe the state of information within it to form consensus in unique ways:

Think of it as transposing 2 dimensional information into a 3 dimensional space. As a loose example, think of the mathematics used by a 3D-code engine (Unity, Unreal, etc.) to generate textures and surfaces in a video game, however, in this case the data is immutable and can comprise of virtually any data type the state channel desires to validate and doesn’t require a graphics card or anything like that as your not actually rendering graphics. I only use this example to convey that the underlying theory of mathematical spaces can encompass a variety of concepts including matrixes, vector spaces, manifolds (Wyatt Meldman-Floch, CTO & Co-founder, has referenced “Smooth Manifold” in various Hypergraph Hours and Coffee Talks).

Altogether this is studied as “point-set topology” or “general topology” with various branches including differential, geometric, and algebraic. Constellation Network can even use this to observe how all of these geometric spaces relate to one another in time (represented as a 4th dimension)…since space and time (aka space-time, theory of relativity) are mathematically bound to one another it enables asynchronous validation of concurrent events:

This is done using a series of Catamorphisms (folding) which break down a larger structure into a reduced value (“cata” for “down”), and Anamorphisms (unfolding) which builds a structure from a smaller set of values (“ana” for “up”). This creates a Hylomorphism, which in a technical operational order, is an ana-morphism followed by a catamorphism.

See the below graphic and corresponding folding and unfolding operations which creates what’s called a “Hylochain”:

A “Hylochain” is basically a tree of information that maintains the ability to mathematically compress and decompress different information without losing any data in the process or relegating that information into simplistic lower order type systems.

Wyatt Meldman-Floch’s Cohomology whitepaper goes into detail on Constellation’s unique computational geometric framework which creates this mathematical topology for formally defining primitives of distributed ledgers using probabilistic algebraic abstraction which is used to create a meta protocol with a statically typed meta language to define the boundaries between protocols.

This coupled with the use of Java/Scala programming language makes it super easy to represent and formally verify information derived from external off chain data sources such as another Blockchain network or some IT database system without having to alter the underlying data structure. The kicker is Constellation is infinitely scalable due to the microservices architecture and asynchronous consensus within each state channel which concurrently converges into the global asynchronous Hypergraph state.

Constellation can map Cardano data types into a direct acyclic graph representation within the Hypergraph because of its ability to handle complex data structures, however, Cardano only developed their state channels to handle the data types that comprise their extended UTXO transactions. Its not configurable in the way Constellation’s state channel logic is and it doesn’t afford the flexibility to define custom consensus criteria. Their Hydra protocol is an isomorphic state channel that is technically a directed acyclic graph which can process and validate transactions asynchronously and concurrently but it is not capable of abstracting data types beyond that scope:

That said, the Hydra protocol is quite impressive and can theoretically scale up to a million transactions per Hydra head (not to mention Hydra tails which I will not elaborate on here). All state channel solutions to date have been constrained by the date types that are supported by their scripting language and smart contract logic such as the examples of Raiden Network (Ethereum) and Lightning Network (Bitcoin).

Layer 0 is inclusive, not exclusive
The purpose of outlining the differences between layer 0 and layer 2 state channels is to emphasize how they can interoperate together and leverage each others strengths. By having Cardano integrate a Layer 2 Hydra state channel as a Layer 0 Constellation state channel, it will extend it’s ecosystem into a multi-chain network that shares the same values of mathematical integrity that functional programming and formal verification provides. This will enable Cardano to access a truly decentralized and interoperable order book of liquidity and allow its Dapps and integrations with SingularityNet’s AI agents to gain exposure to a greater network of customers by traversing Constellation’s meta-network Hypergraph Transfer Protocol (HGTP).

I really believe in the value of coming together as an industry to execute on the vision of a society where we can imbue the qualities of immutability, transparency, security, and individual sovereignty into reshaping the systems of exchange that the modern world is built upon. If we want to upgrade to the Society 3.0 we all eagerly envision, we are going to need collectively strategize on executing it’s technological implementation. The sum will certainly need to be more than the parts in order for us to be successful.

Please refer to my previous article for more technical details about Constellation Network. I elaborate on additional synergies here: https://link.medium.com/49ZpEOGlJjb

Source: https://medium.com/@lee.papa/what-is-a-state-channel-layer-0-vs-layer-2-43edbbb1657a?source=rss——-8—————–cryptocurrency