The Nakamoto consensus
The innovation that Craig Wright brought to the world was how to distribute authority widely, the Nakamoto consensus. That was a radical, world-changing idea, since it competed head-on with the "listener" part of the bicameral mind, what authority people follow as external mediation.
Smart Contracts
In 1997, Nick Szabo wrote about smart contracts in Formalizing and Securing Relationships on Public Networks, and Vitalik Buterin combined the idea of smart contracts with the Nakamoto consensus, for a turing complete blockchain, the Ethereum "world computer".
Lattices and sharding
With BitLattice, Hibryda's innovation is that lattices have intrinsic properties that make sharding possible, the integrity of the individual shards, and the lattice in its entirety, can be proven with mathematical proofs, using wave-functions.
Vitalik Buterin was talking about the vision of sharding as early as 2014, and similar to how smart contracts could only be developed once the blockchain had been invented, it seems like sharding will become possible with lattices as a new medium, where transactions are stored in the subtle structure of a lattice instead of in a chain (line) of blocks.
Timeline of the evolution of the network-state
Bitcoin in 2009, Ethereum in 2014, and BitLattice in 2018, are points on a graph where each new innovation is made possible by the previous innovation, first the Nakamoto consensus, then smart contracts, and then lattices. Another idea that may fit in is Ohad Asor's Tau language, that began to be talked about in 2015, Nakamoto consensus + smart contracts + tau language + lattice state.
References
Smart Contracts Described by Nick Szabo 20 Years Ago Now Becoming Reality - Bitcoin Magazine
The first instance of Tau MetaLanguage (TML) has appeared on Github!