The Hexalogy documents the structural foundation of the Coherosance framework — from the triangular root of the genetic code to the full modular symmetry architecture of figurate number sequences. All papers are available on Zenodo.
The origin of the genetic code's error-detecting properties remains a central question in molecular biology. We report the discovery of an Infinite Geometric Ladder generated by the digital roots of polygonal number sequences that reveals the mathematical substrate underlying the genetic code's structure.
Read on Zenodo →Following the discovery of the Infinite Geometric Ladder and the 216-24-9 Lock within the genetic code's mathematical substrate, we report a fundamental connection between this geometric framework and the Fibonacci sequence — revealing a 24-cycle temporal engine embedded in the structure of life itself.
Read on Zenodo →The structural organisation of the genetic code and the growth algorithms of biological systems have historically been treated as distinct phenomena. Building upon our previous discoveries of the Infinite Geometric Ladder, we demonstrate a unified Mod-9 substrate underlying both.
Read on Zenodo →Building on the Infinite Geometric Ladder (Paper 1), the Fibonacci-Polygonal Coherosance Bridge (Paper 2), and the Mod-9 Universal Substrate (Paper 3), we extend the paradigm into three dimensions. Tetrahedral numbers reveal a volumetric computing architecture within the substrate of reality.
Read on Zenodo →Building on the Tetrahedral Volume Engine (Paper 4), we extend the paradigm into dodecahedral geometry. The dodecahedron (12 faces) is the natural geometric expression of the substrate of eternal life, bridging 3D volumetric computing to higher-dimensional structure.
Read on Zenodo →The Hexalogy culminates here. This paper synthesises the Triplet-Window Lattice, the 13-month natural calendar, and the full modular symmetry architecture across figurate number sequences — demonstrating structural resonance with the genetic code and the complete Coherosance framework.
Read on Zenodo →[1] Tony Beede. (2026). The Triangular Root of the Genetic Code's Mathematical Substrate. Zenodo. https://zenodo.org/records/19456494
[2] Tony Beede. (2026). The Fibonacci-Polygonal Coherosance Bridge: The 24-Cycle Temporal Engine of the Genetic Code. Zenodo. https://zenodo.org/records/19476825
[3] Tony Beede. (2026). The Mod-9 Universal Substrate: Unifying Polygonal Geometry, Fibonacci Growth, and the Genetic Code. Zenodo. https://zenodo.org/records/19476765
[4] Tony Beede. (2026). The Tetrahedral Volume Engine: 3D Figurate Numbers and Tetra-Computing in the Mod-9 Universal Substrate. Zenodo. https://zenodo.org/records/19476890
[5] Tony Beede. (2026). The Dodecahedral Life Engine: Base-12 Geometry, the 12-Strand Diamond Sun Template, and the Mathematical Substrate of Eternal Life. Zenodo. https://zenodo.org/records/19487325
[6] Tony Beede. (2026). The Coherosance Framework: Modular Symmetries in Figurate Number Sequences and Their Structural Resonance with the Genetic Code. Zenodo. https://zenodo.org/records/19672848
The Hexalogy maps the mathematical substrate. The Living Sequences are the applied layer — the Foundational Axioms and the four practice sequences that translate the framework into daily operation.
View Living Sequences →The numerical foundations behind the Hexalogy: the Triangular Digital Root Sequence, Fibonacci 24-cycle, figurate numbers, and their connection to the 13-month natural calendar and Triplet-Window Lattice.
View Mathematical Sequences →The mathematics points to the pattern. The IPP maps yours specifically.