Qudits-36: A Ternary Vector Space Formalization of DNA Hydrogen Bond States for Biomolecular Information Encoding
Record type:
The conventional representation of DNA information as a
quaternary alphabet {A, T, G, C} abstracts away the physical
substrate that stabilizes the double helix: hydrogen bonds
between complementary bases. We propose Qudits-36, the
foundational formalism of the TQIM-Davoh (Théorie Quantique
de l'Information Moléculaire de Davoh), which models the
discrete states of hydrogen bonds using balanced ternary
logic T₃ = {-1, 0, +1}.
Three original constructions are introduced under the
MICA framework (Matrice d'Intrication Coordonnée par les
Amplitudes — Matrix of Intrication Coordinated by Amplitudes):
the KyriosMICA Vector Space (EVK), the KyriosMICA Resonance
Energy (ERK), and the KyriosMICA Resonance Matrix (MRK).
The framework demonstrates that the CG+CG+CG codon space
yields up to 19,683 states — a factor of ×307 over the
classical model. On four high-resolution crystal structures
(PDB: 4EWZ, 3I40, 1MSI, 1D65), MRK signatures successfully
distinguish A-form from B-form DNA and insulins at different
pH values, differences invisible to the quaternary model.
This formalization constitutes the native mathematical kernel
of Science 4.0, aligning physical biological substrates with
bio-inspired logical architectures.
Institution: kyriosMICA Research Institute · Benin,
West Africa · Decoding Life. Encoding the Future.
Implementation (MICA-Kernel v1.0):
API (live):
Pre-registered prediction (April 2026):
MRK rank ≤ 3 predicts mutation hotspots in SARS-CoV-2.
Mann-Whitney p = 0.0002. Point-biserial r = -0.482.