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Here I present a new model for the itinerancy of the strings of holes in theCuprates HTSC. The model assumes various scenarios with respect to the order ofthe holes hopping and evaluates the weighting parameters for the differentscenarios. The new model still results in the aggregation of holes intostrings, but yields a spectral distribution for the itinerancy rates of thestrings. From this distribution I infer a spectral distribution for themagnetic interaction between the strings, which suggests also a spectraldistribution for the pseudogap parameter, and some relevant experimentalfunctions. Apart from these distributions, the basic assumptions of formerrelevant theories remain intact. Such assumptions are the existence of theanti-ferromagnetic phases A and B, the basic structure of the pseudogap groundstate, the excitation operators, and the field. The ground state and the fieldare basically divided into two bands, the gapless low energy band, and the highenergy band. Due to the wide distributions, the bands may be partiallyoverlapped.

The Itinerancy and Interactions of the Linear Strings of Holes in Copper Oxide Superconductors