Prime–Ulam Nuclear Integer Grid

Prime–Ulam Nuclear Integer Grid This dataset provides a computational descriptor scaffold over nuclear integer configurations defined by proton number Z, neutron number N, and mass number A = Z + N. The grid contains 51,772 nuclear integer configurations generated over the bounded domain: Z = 1–172N = 0–300A = Z + N Each configuration is represented as a nuclear integer identity: C = (Z, N, A) The dataset introduces Prime–Ulam descriptors derived from the arithmetic and prime-factor structure of the nuclear integers Z, N, and A. These descriptors are intended for computational feature engineering, exploratory nuclear-data analysis, benchmark construction, explainable artificial intelligence (XAI), residual analysis, and hypothesis generation. The accompanying files include a nuclear integer configuration grid, Prime–Ulam descriptor fields, selected illustrative nuclide tables, metadata, documentation, and reference materials. The dataset is designed to support reproducible computational experiments and should be interpreted as a descriptor framework rather than a replacement for established nuclear physics. Prime–Ulam descriptors are arithmetic feature transformations derived from nuclear integer identifiers. They are not physical constituents of nuclei and should not be interpreted as causal explanations of nuclear stability, nuclear reactions, or nuclear structure. The dataset may include computationally generated nuclear integer configurations beyond currently evaluated or experimentally observed nuclides. Such configurations are provided as descriptor candidates for computational analysis and hypothesis generation only. Associated concept paper / preprint This dataset supports the conceptual and computational framework introduced in the associated preprint: Data-Driven Arithmetical Physics: Prime–Ulam Nuclear Topology over 51,772 Nuclear Integer ConfigurationsDOI: https://doi.org/10.5281/zenodo.21078593 The preprint defines the theoretical motivation, descriptor interpretation boundaries, computational pipeline, and benchmark-oriented positioning of Prime–Ulam Nuclear Topology within the broader direction of Data-Driven Arithmetical Physics. Interactive repository and web app An interactive repository and browser-based web app are available for exploring the Prime–Ulam Nuclear Integer Grid: Repository:https://github.com/Artifactsmaker/prime-ulam-nuclear-integer-atlas Live app:https://artifactsmaker.github.io/prime-ulam-nuclear-integer-atlas/ The web app provides an interactive interface for navigating the nuclear integer grid, inspecting selected configurations, and visualizing the Prime–Ulam atlas structure. Suggested citation Phan, T. T. (2026). Prime–Ulam Nuclear Integer Grid (Version 1.0) [Dataset]. Zenodo. https://doi.org/10.5281/zenodo.21073857 Keywords Prime–Ulam Nuclear Integer Grid; Prime–Ulam Nuclear Topology; nuclear integer configurations; nuclear descriptor space; arithmetic descriptor fields; nuclear data modeling; explainable artificial intelligence; computational physics; superheavy elements; scientific dataset.