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It is shown how to endow a hierarchy of sets of binary patterns with thestructure of an abstract,normed C*-algebra. In the course we also recover anintermediate connection with the words of a Dyck language and Tempereley-Liebalgebras for which we also find that an effective arithmetic code is possiblealbeit of greater complexity. We also discuss possible applications associatedwith signal theory and waveform engineering on possible ways to embed discretecomputational structures in an analog continuum substrate.

Encoding discrete quantum algebras in a hierarchy of binary words