Here is a lead for sandbox researchers

We define the relevant information in a signal x ∈ X as being the information that this signal provides about another signal y ∈ Y . Examples include the information that face images provide about the names of the people portrayed, or the information that speech sounds provide about the words spoken. Understanding the signal x requires more than just predicting y, it also requires specifying which features of X play a role in the prediction. We formalize this problem as that of finding a short code for X that preserves the maximum information about Y . That is, we squeeze the information that X provides about Y through a ‘bottleneck’ formed by a limited set of codewords X˜. This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure d(x, x˜) emerges from the joint statistics of X and Y . This approach yields an exact set of self consistent equations for the coding rules X → X˜ and X˜ → Y . Solutions to these equations can be found by a convergent re–estimation method that generalizes the Blahut–Arimoto algorithm. Our variational principle provides a surprisingly rich framework for discussing a variety of problems in signal processing and learning, as will be described in detail elsewhere.

Brad DeLong spotted this because he watches the sandbox tech.   This is another version of what is exciting us all, formal methods for matching algorithms between two sequences.  This one is worth a read if you are a mathematician at Coinbase, for example.  Or, for example, if you were a mathematician at Microsoft and wanted your company to make zillions in Fintech, then you might check this article. 

This choice quote:

A fundamental problem in formalizing our intuitive ideas about information is to provide a quantitative notion of “meaningful” or “relevant” information.

What I call 'significant' , trade books ordered as compact generators of the typical sequence. Take the significance measure as how much innovation does this transaction add to the stable statistics of the process; a good definition.

These folks, in 1999, went ahead in time and stole my ideas.

In multi color, we have two or more sequences Xi, each simply something about the typical sequence Y.  The incoherence between the sequence X, against Y is the bit error. We have invented a method of mutual coherence in maximum entropy systems, completing the analogy to Euler systems.

Three color leads to surfaces that are isomorphism of the some object having 'holes' surrounded by smooth surfaces. Our concept of loan and deposit is two matching surfaces operating as a sphere packer.   Add the third color, say he ledger fee, small.  You split the sphere packers into mostly independent groups, and add a 'hole' in doing so, or something like that.  (I am still learning the stuff).
An easier think is that the third color manages skew in the system transaction distribution.  This was kind of the point, mapping a statistical algebra of mean, sigma and skew against a surface geometry by noting the hole dimensionality, a kind of degrees of freedom match between systems.

Follow this line if you are into the provisioning of auto traded pits.