Scaling Chemical and Biological Model

AbstractThis paper introduces a unified, discrete geometric scaling framework that directly maps the molecular and atomic mass (expressed in Daltons, Da) of physical, chemical, and structural biological entities onto their exact empirical linear dimensions (expressed in nanometers, nm). Moving away from traditional stochastic biological folding algorithms and continuous thermodynamic volumetric estimates, we reveal a structured register-shift architecture operating across two interconnected systems: a four-tier macroscopic layout for proteins and viral mega-assemblies, and a binary doubling periodic layout for foundational chemical elements. For macromolecular systems, the model utilizes precise, direct divisors (200, 10 000, 25 000, and 3 000 000) representing quantized spatial scaling states. For primary life-building blocks (Carbon, Nitrogen, Oxygen, and Phosphorus), the model introduces a periodic doubling rule (the 160 to 320 scaling register) calibrated against the geometry of Carbon as the baseline of organic life. The mathematical projections derived from this combined model demonstrate an exceptional alignment accuracy of over 95 percent against real-world experimental data, ranging from fundamental covalent atomic radii to heavy human oncoproteins and complete macro-viral virions (HIV-1).