A METHOD FOR SYNTHESIZING TOPOS OF HASHES IN THE CATEGORICAL cN-SCHEME OF THE MARKOV ALGORITHM. Part 2

In the second part of the study, the synthesis of the cN-scheme of the Markov algorithm with the hash topos included in it is continued. The hash topos is included in this Markov algorithm scheme to determine whether a word belongs to its chain of occurrences by a fast algorithm without the need to iterate through the data in memory. The definition of such affiliation is necessary for the analysis of economic interactions in organizational systems in countering the laundering of proceeds from crime and the financing of terrorism. Interactions in organizational systems are considered both as occurrences of words in each other in the Markov alphabet, and as morphisms of objects in categories. The categorical cN-scheme of the Markov algorithm is also distinguished by the conclusion, which cannot be considered normal according to Markov. The topos of hashes, which consists of a composition of a five hash trees, is investigated without taking into account the structure of this five. The hash topos is used to detect and classify cycles, referred to in the study as λ-voids, and to quickly overcome the looping of algorithms when processing large amounts of data. The morphisms involved in the processing of words in the ordered and extended Markov alphabet A2M using the topos of hashes in the cN-scheme of the Markov algorithm are consistently refined and theoretically substantiated. In the course of the study, it was found that between the hashed data and the quad, consisting of a dictionary, source number, morphism number, morphism type number, it is possible to detect an isomorphic interaction, which allows, when receiving a word from the input data sample, to check whether it belongs to its chain of Markov occurrences, detecting cycles (λ-voids) in the input data samples. It is shown that the introduction of the categorical cN-scheme of the Markov algorithm into scientific circulation is the first step towards the synthesis of a variant of intuitionistic logic for the homology of the Markov algorithm. It is concluded that it is expedient to synthesize a Markov network algorithm from this scheme to search for new mathematical properties of the algorithm, with different compositions of data sources.