Topological and Combinatorial Observables of a Prime-Induced Complex

This dataset contains numerical observables derived from a simplicial complexconstructed from prime numbers under multiplicative constraints. For increasing prime bounds x and a fixed global cutoff M, the dataset recordscombinatorial and topological quantities associated with the resultingprime-induced complex. These include counts of vertices, edges, and triangularfaces, as well as the Euler characteristic of the complex. In addition, the dataset documents the proportion of integers up to M whosesmallest prime factor does not exceed x (“explained” space) and the complementaryremainder. The data are purely descriptive and were generated for transparency andreproducibility. They do not encode theoretical interpretations or claims.Structural interpretations are provided exclusively in the associatedtheoretical publication.