Quantum Valence Constants and Structural Stability in DNA: The 10-5-6-5 Numerical Isomorphism as a Biological Ledger

Background This research establishes a definitive numerical isomorphism between the thermodynamic stability of DNA and the quantum electronic patterns within its double helix. While previous models have suggested linguistic correlations based on atomic mass reduction, they lacked a mechanistic explanation. This study bridges that gap by analyzing DNA as a bioeconomic system of maximum efficiency governed by valence-bond constants. Methods : Utilizing the Lewis (1916) valence-bond model and quantum orbital analysis ( s,p occupancy), we quantified the electronic density of a specific four-level DNA fragment (T-A, C-G, T-A, G-C). We introduced an Electronic Exchange Matrix to map hydrogen bond donors and acceptors and calculated the structural stability based on the ratio of total bonds to Group 15 valence pillars. Results : The analysis identifies a recurring 10-5-6-5 sequence that is fundamentally required for structural integrity. The number 10 represents the "Cohesion Force" of the hydrogen-bond interface (Yod); 5 corresponds to the valence of Group 15 pillars (Nitrogen/Phosphorus) and the 5' carbon directionality (He); and 6 represents the covalent oxygen bridge in the phosphodiester backbone (Vav). Quantum mapping reveals that these values are macroscopic manifestations of the lowest energy states available in p-sublevel distribution. Conclusions : This discovery provides a verifiable framework for Quantitative Biotheology, postulating that the "Signature of God" is a mathematical constant essential for preventing molecular de-cohesion. The 10-5-6-5 sequence represents the "Thermodynamic Efficient Frontier" where biological information and physical matter converge in harmonic balance.