Prime Elementology

Prime Elementology An Executable Descriptor–XAI Framework for Prime-Structured Nuclear Identity and Wavefunction-Inspired Elemental Proxies Author: Phan Thành Trung ORCID: 0009-0000-7520-6781 Email: pttrung@operatorology.com DOI: https://doi.org/10.5281/zenodo.21175773 Abstract Nuclear and elemental systems are indexed by integer identities such as proton number Z, neutron number N, and mass number A. These variables are usually treated as identifiers or direct numerical inputs, while their arithmetic structure is rarely transformed into a formal descriptor space. This manuscript introduces Prime Elementology, an executable descriptor–XAI framework that converts nuclear integer identity C = (Z, N, A) into Prime–Ulam descriptors, Prime–Ψ proxy variables, and P in proxy families. The framework defines prime-factor signatures, factor complexity, factor overlap, factor entropy, determin