Geometric Theory of Atomic Structure and the Periodic Table of Elements in Discrete Geometric Physics: Derivation of the Mendeleev Table from the 26-Vertex Cubic Lattice
Year: 2026
Type: article
Abstract: This work presents a complete derivation of the periodic table of elements and all atomic properties — ionisation energies, atomic radii, electronegativities, and spectral lines — from the geometry of the 26‑connected cubic lattice with topological invariant Σw = 14. It is shown that atoms are hierarchical solitons of the lattice: the nucleus is a bound state of nucleons at level N=66, and electrons are light solitons (quasiparticles) at level Nₑ=71.035. Electron shell filling numbers (2, 8, 18, 32) follow directly from the topological constraints of the lattice. The variational principle on the lattice yields closed‑form expressions for all atomic parameters without empirical fitting coefficients. A complete table for all 118 elements is provided, with theoretical values compared to NIST, CRC Handbook, and Pauling scale data, showing excellent agreement (mean deviation <1% for Z≤80). Hydrogen, which previously showed a 4.4% deviation in the analytical approximation, is refined by numerical solution of the discrete Schrödinger equation on the lattice, giving exact agreement with experiment. Relativistic corrections for superheavy elements (Z>80) are included. The theory predicts an island of stability at Z≈120–126 and N≈180–190. All numerical parameters used are derived from the lattice invariants and variational minimisation, not from empirical fitting. This version is fully updated to be consistent with the corrected Volume 1 of DGP (2026). The work includes full derivations, tables, Python code for reproduction, and comparisons with experimental data.
Author: Ivan Davidenko
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166311131