Geometric Genomics & Aging Framework

METADATA Title: Geometric Genomics and Aging Framework: From 600-Cell Polytope to Therapeutic Peptide Design Author: Morató de Dalmases, Lluís (ORCID: https://orcid.org/0009-0009-2658-1433 Description: This comprehensive package presents a unified geometric framework for understanding genome architecture, protein conformation, and aging through the lens of the 600-cell polytope {3,3,5} and Conway knot topology K₁₁ₙ₃₄. The work spans from genomic spectral analysis to therapeutic peptide design for Alzheimer's disease. Key Results Spectral Genomics: HOXA intergenic distances exhibit 9 bp quantization (p = 2.1×10⁻⁴) Harmonic ratios 1:3:2/3 conserved across human, mouse, and zebrafish Bicoherence analysis reveals non-linear phase coupling (BF₁₀ = 18.3) TAD boundaries align with harmonic transitions (p = 0.037) Geometric Protein Analysis: Amyloid-β KLVFFAE quaternion norm ‖q‖ = 0.484 (3.2% from Z0 point) Tau PHF6 VQIVYK quaternion norm ‖q‖ = 0.510 (2.0% from Z0 point) Z0 point condition ‖q‖ = 1/2 corresponds to Riemann zeta zeros Therapeutic Design: CYGDWCY cyclic peptide with inverse torsion T = -0.28 rad/Å Geometric Efficacy Index GEI = 1.00 (perfect topological cancellation) Binding energy E_bind = 23.3 kcal/mol Deep Learning Framework: TorsionNet: time-lagged autoencoder for conformational analysis Classification accuracy: 85-92% for pathogenic variants Restores conformational reversibility in pathological states Repository Structure text geometric_genomics_aging_framework/ │ ├── README.txt # This overview │ ├── papers/ │ ├── 01_spectral_signature_human_genome.pdf │ ├── 02_geometric_descriptors_protein_conformation.pdf │ ├── 03_geometric_therapy_alzheimer.pdf │ ├── 04_geometric_design_CYGDWCY.pdf │ ├── 05_quaternion_unification_matter.pdf │ └── 06_unified_geometric_deep_learning.pdf │ ├── code/ │ ├── 1_generate_figures.py # Spectral genomics figures │ ├── 2_quaternion_protein_analysis.py # Protein conformation analysis │ ├── 3_quaternion_alzheimer_analysis.py # Therapeutic peptide analysis │ └── 4_torsionnet_model.py # Deep learning framework │ └── supplementary/ ├── mathematical_constants.pdf # Constants from 600-cell geometry └── quaternion_tables.pdf # Amino acid quaternion tables Mathematical Foundations The framework is built on these fundamental constants from the 600-cell polytope {3,3,5}: Constant Symbol Value Angular defect δ₀ 0.118682 rad Golden ratio φ 1.618034 Photonic viscosity η_γ 0.208 Möbius projections N 37 Conway knot torsion T 0.34 rad/Å Z0 point norm ‖q‖_Z0 0.5 Geometric Efficacy Index GEI = 1 - ‖T_path + T_Tap‖ / (‖T_path‖ + ‖T_Tap‖) Perfect cancellation: GEI = 1.00 Jones Polynomial (Conway Knot K₁₁ₙ₃₄) V(t) = t⁻² - t⁻¹ + 1 - t + t² Quaternion Representation Each amino acid is represented as a unit quaternion:q = a + b i + c j + d k Genetic code as quaternion multiplication:A → 1, C → i, G → j, U → kCodon = q_b₁ · q_b₂ · q_b₃ Software Requirements All Python code requires: Python ≥ 3.8 NumPy, SciPy, Matplotlib PyTorch (for TorsionNet) Biopython (for PDB processing) Running the Code Generate all figures: bash python code/1_generate_figures.py Analyze protein sequences: bash python code/2_quaternion_protein_analysis.py python code/3_quaternion_alzheimer_analysis.py Train TorsionNet: bash python code/4_torsionnet_model.py License This work is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).Code is licensed under MIT License. Version History Version 1.0 (March 2026): Initial release Complete spectral genomics analysis Quaternion-based protein conformation framework CYGDWCY therapeutic peptide design TorsionNet deep learning implementation Related Publications This package accompanies the following publications: Spectral Signature of the Human Genome: A 3-6-9 Harmonic Framework for Topological Closure in R⁴ Geometric Descriptors of Protein Conformation: A Quaternion-Based Framework for Amyloid-β Aggregation Geometric Therapy for Alzheimer's Disease: Design of a CYGDWCY Nanopor-Tap Geometric Design of CYGDWCY Nanopor-Tap for Alzheimer's Disease The Quaternion Unification of Matter, Genetics, and Aging Loss of Conformational Reversibility Defines Pathogenic Protein States Funding This research received no external funding. Contact For questions or collaboration inquiries, please contact the corresponding author through the Zenodo platform. DOI: https://doi.org/10.5281/zenodo.19301742 Date of Deposit: March 29, 2026 FILES LIST (for upload) README.txt (this file) papers/01_spectral_signature_human_genome.pdf papers/02_geometric_descriptors_protein_conformation.pdf papers/03_geometric_therapy_alzheimer.pdf papers/04_geometric_design_CYGDWCY.pdf papers/05_quaternion_unification_matter.pdf papers/06_unified_geometric_deep_learning.pdf code/1_generate_figures.py code/2_quaternion_protein_analysis.py code/3_quaternion_alzheimer_analysis.py code/4_torsionnet_model.py supplementary/mathematical_constants.pdf supplementary/quaternion_tables.pdf KEYWORDS geometry, genomics, quaternions, 600-cell, Conway knot, Alzheimer's disease, protein folding, spectral analysis, deep learning, torsion, Riemann hypothesis, aging, therapeutic peptide, HOXA, amyloid-beta, Tau, topological closure