Vitalik Buterin has described a blockchain, or, a "consensus technology", a global state, permissionless ledger, as being "politically decentralized, architecturally spread out, and logically centralized. " Recently there have been attempts at so called "inter-operability" with Plasma and Polkadot, platforms that use "child chains" or "para chains". Neither of those live up to the ideal of being "logically centralized". To just hash child chains into a blockchain is not a compression mechanism, it pretends to compress logic while it is actually based on trusting the validators of each separate chain with no centralized logic at all. BitLattice does logic consensus between "shards", so it is logically centralized.

What does logically centralized "sharding" look like?

BitLattice does hash-linking even when "sharded" because all "shards" rely, mathematically, on the state of all other shards, a continuous lattice even when sharded. What has been called "inter-operability" is not possible, or, not in the way it has been conceived. The equivalent of "inter-operability" becomes possible on BitLattice since the lattice structure makes it possible to have a homogenic reference field, basically a compression mechanism, based on mathematical wave functions.