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)

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Key words: Quantum Biology, Synthetic Biology, Biomathematics, Bioinformatics, Information Theory, Genetic Code, Combinatorics, Invariants, Codons, DNA, Atoms, Numerical Scales, Mathematical Constants, Discrete Mathematics, Astrobiology, Exobiology.

Abstract: After several years of research, I am completing the Meta-Genesis cycle — Toward a Biology Without Matter, Based on Pure Logic — a work in which I identified a sequence of numerical invariants linking the chemistry of the stars to molecular biology, thanks to a mathematical lens (one equation), a change of dimensional perspective similar to that of the Square in Flatland discovering the existence of cubes, or to the conceptual transition from the circle to the Bloch sphere in quantum physics.

This sequence spans every scale:
→ the stars (where the CHON elements — carbon, hydrogen, oxygen, and nitrogen — are born),
→ the nucleic acids (adenine, guanine, thymine, and cytosine),
→ the theoretical duplets proposed by Francis Crick,
→ the triplet codons,
→ up to a hypothetical quaternary code,
→ but also the amino acids, and even viruses and alternative systems considered in exobiology
(silicon, phosphorus, sulfur).

The same constants reappear at every level — as if life were written in the same mathematical grammar as the matter from which it arose.

That’s what I call: A Unified Theory of Biological Information — From Stars to Codons.

Building on the work of Turing, von Neumann, and Shannon, I have mathematically demonstrated that the genetic code behaves as a universal logical automaton — a system that self-organizes from its own syntax. Just as electronic engineers apply the first law of Boolean algebra to optimize an on/off circuit, one can view the codon table as a logical schema: each triplet acts as a binary input pattern, and the corresponding amino acid is the deterministic “output” of this logical operation. From stars to codons, life computes its own coherence — and life is, above all, information before it is chemistry. Even better, they made it possible to establish predictions regarding a hypothetical quaternary genetic code, later confirmed experimentally, as well as predictions involving amino acid and protein combinations. Remarkably, the same invariant patterns also emerge in silicon–phosphorus–sulfur combinations, with a difference of only about 2%, suggesting a broader chemical universality. These findings open the way to new applications in synthetic biology, but also in exobiology, where they may serve as a powerful tool for modeling and detecting alternative forms of life.

EDIT (October 31, 2025): Version 3 is released. 

This last part of Meta-Genesis, entitled “From Boolean Algebra to the Expansion of Life: Binary Arithmetic and Multi-Dimensional Projections of the Genetic Code,” demonstrates that the genetic code can be interpreted as a universal logical structure organized according to the principles of Boolean algebra and binary arithmetic. The four bases of DNA (T, C, A, G), arranged in triplets, form a six-dimensional Boolean hypercube (2⁶ = 64 states) whose spherical projection reveals three fundamental numerical invariants (1, 96–97, 128) that ensure systemic coherence across all biological scales.

The cubing of the code appears as the mathematical condition for its completeness, linking binary logic to the three-dimensional geometry of life and defining the genetic code as a biological analogue of the Bloch sphere, a quantized information space.

This framework reframes life not as organized matter, but as the geometric manifestation of a self-coherent logical field, where biological diversity corresponds to an informational expansion analogous to the cosmic expansion of the universe.
Each living form is thus a local and temporarily stabilized projection of a global combinatorial system. Thus, the genetic code can be interpreted as a discrete Hilbert space, in which codons behave as quantified states of biological information.

The conceptual originality lies in a paradigm shift:

• from descriptive to generative,

• from chemical to logical,

• from biological to cosmological.

The genetic code emerges as the mathematical signature of life — a universal language whose multiple projections generate the apparent diversity of living systems while preserving the continuity of a single logical invariant underlying all biological existence. 

Complete Primary Data, Computational Materials and Bibliography

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/17525084

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/17068843

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

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. Accepted for 2026 in a post-graduate program in molecular cytogenetics at a medical school. Academic and research trajectory spanning Canada, the United States, France, and Switzerland (Educational Outreach Internship at CERN, 2018).