The Kayser–Cuny Mathematical Tables in Molecular and Synthetic Biology: A Molecular Information Framework

The Kayser-Cuny Mathematical Tables present a numerical framework that reveals hidden patterns and invariant relationships within the genetic code through the lens of atomic composition, combinatorics and mathematical logic. By assigning logical values to each codon based on the numbers of protons, neutrons and electrons of its constituent nucleobases, this work uncovers deep symmetries and numerical regularities at multiple organizational levels. These invariants are explored through Boolean algebra, combinatorial analysis and a proposed Theoretical Codonic Unit (TCU), providing new perspectives for understanding codon organization and protein encoding. Serving as a comprehensive reference, this volume provides reproducible calculations and classification tables designed to support research in molecular biology, synthetic biology, bioinformatics, artificial intelligence and molecular information science. In a separate document, I describe a deterministic method for the de novo generation, simulation, and assembly of proteins from numerical invariants intrinsic to the genetic code, including a proof of concept based on human red blood cell proteins. Complete Research Corpus Kayser-Cuny, V. (2025). Meta-Genesis. Towards a Biology without Matter, based on Pure Logic. Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code (Abstract and compilation). Zenodo. https://zenodo.org/records/21002033 Kayser-Cuny, V. (2025). (Part 1) Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code: A Combinatorial and Atomic Analysis. Zenodo. https://zenodo.org/records/21002648 Kayser-Cuny, V. (2025). (Part 2) Multiscale Numerical Invariants and Fractal Properties of the Genetic Code: Internal Constraints and Multiscale Packet Distributions Revealing a Universal Grammar. Zenodo. https://doi.org/10.5281/zenodo.17272500 Kayser-Cuny, V. (2025). (Part IV-part 3) Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code: A Unified Theory of Biological Information, from Stars to Codons. Zenodo. https://doi.org/10.5281/zenodo.17370443 Kayser-Cuny, V. (2025). (Part VI-part 3) Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code: Data Availability [Data set]. Zenodo. https://doi.org/10.5281/zenodo.17306204 Kayser-Cuny, V. (2025). Data Availability Part 2 [Data set]. Zenodo. https://doi.org/10.5281/zenodo.17368936 Kayser-Cuny, V. (2025). (Part III) The Mirror-Twin Paradox: A New Approach to DNA Understanding the Implications of an Inverted Genome and Its Applications in Molecular Genetics, Neuroscience, and Medicine. Zenodo. https://doi.org/10.5281/zenodo.15390489 Kayser-Cuny, V. (2025). Meta-Genesis. Towards a Biology Without Matter. From Boolean Algebra to the Expansion of Life: Binary Arithmetic and Multi-Dimensional Projections of the Genetic Code. Zenodo. https://doi.org/10.5281/zenodo.17494922 A Deterministic Method for the Generation, Simulation, and Assembly of De Novo Proteins Based on Numerical Invariants Intrinsic to the Genetic Code: Part 1. Kayser-Cuny, V. (2026). The Kayser–Cuny Mathematical Tables in Molecular and Synthetic Biology: A Molecular Information Framework (2026th ed.). MTMVP. https://doi.org/10.5281/zenodo.21001829 ISBN: 9782489162035 Part 2. Kayser-Cuny, V. (2026). PROOF OF CONCEPT Multi-scale Numerical Invariants and Fractal Properties of the Genetic Code: A Combinatorial and Atomic Analysis using the Erythrocyte (Red Blood Cell) as an Ideal Mathematical Model for AI-Based Proteomic Analysis. Zenodo. https://doi.org/10.5281/zenodo.21003215 The author 2023: Elected Fellow of the Linnean Society of London (Biology);2023: Elected Fellow of the Royal Anthropological Institute of Great Britain and Ireland;2024: Elected Full Member of the Genetics Society;2025: Affiliate Member of the Royal Society of Chemistry. Molecular geneticist by training, with specialization in particle physics, chemistry of Life, paleogenetics/evolutionary genetics, and astro/exobiology. Post-graduated in molecular cytogenetics in French medical school. Academic and research trajectory spanning Canada, the United States, France, and Switzerland (Educational Outreach Internship at CERN, 2018).