CAS II: Symmetric Partitions as Kolmogorov Models

תקציר מקורי באנגליתarXiv:2609.40290v1 Announce Type: cross Abstract: In algorithmic statistics a string x is explained by a finite set containing it, and Kolmogorov's structure function records the smallest such model at each level of complexity. Vereshchagin's strong models, those computable from the data by a total algorithm, are essentially the cells of simple partitions. We read a partition of binary strings as a hypothesis, with the cell containing x as its model, and develop algorithmic statistics over symmetric partitions: the orbit partitions of groups acting on strings. The Galois connection between subgroups and partitions gives each ambient group a lattice of symmetric partitions, with canonical certificates, canonical costs, and an algebra of hypotheses. The resulting structure function and symme