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This work aims to uncover arithmetic regularities within the standard genetic code using nucleon counts.

July 21, 2026Open Access

Arithmetic structure of the standard genetic code

Key Points

This work aims to uncover arithmetic regularities within the standard genetic code using nucleon counts.
Analyzed proton sums, neutron sums, total nucleon counts, and their differences across codon groups.
Explored relationships defined by Rumer partition and third-position chemical axes.
Conducted Monte Carlo analysis under a random-code null model and verified findings with independent scripts.
Documented systematic divisibility by 37 across codon groups.
Identified cross-group equalities and modular symmetries within nucleon counts.
Supported findings with reproducibility scripts and visualizations archived at Zenodo.

Abstract

This preprint reports arithmetic regularities in the standard genetic code. The analysis examines nucleon-count quantities — proton sums (P), neutron sums (N), total nucleon counts (T), and their difference (Δ = P − N) — across codon groups defined by the Rumer partition and by third-position chemical axes (Keto/Amino, Strong/Weak, Purine/Pyrimidine). It documents systematic divisibility relations, in particular by 37, together with cross-group equalities and modular symmetries. The complete data and code supporting this work — input and computed datasets, a reproducibility script, supplementary control scripts, a Monte Carlo analysis under a random-code null model, an independent verification script, and an interactive visualizer — are archived as a separate Zenodo record (DOI: 10.5281/zenodo.20360037) and developed at github.com/RuslanKhafizov/genetic-code-arithmetic. Version v4 revises the Monte Carlo analysis under a unified random-code null model, adds independent verification, and updates the corresponding statistical interpretation.

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