This record originally contained two papers uploaded together. They have now been separated into independent records: Aboualy, A. (2026). The Dynamic Equilibrium Principle... DOI: 10.5281/zenodo.18903975 & boualy, A. (2026). The Geometry of Water... DOI: 10.5281/zenodo.18904521

Abstract (English)

Two companion papers present a semiclassical unification of molecular structure. Paper 1 — The Dynamic Equilibrium Principle: a structural scaling law proposing that stable physical systems persist through bounded dynamical motion, with equilibrium scales forming a discrete logarithmic hierarchy anchored to a fundamental confinement radius. Demonstrated on water, H₂, and planetary orbits. Includes falsifiability statement and working template for new systems. Introduces Tuma'ninah — a named condition of sufficiency within bounds. Paper 2 — The Geometry of Water: a semiclassical unification of its structural scales, demonstrating that Slater screening, the H₂⁺ Bohr–Sommerfeld treatment, and a Coulomb–Pauli balance model converge on the same logarithmic ladder of distances anchored to the Bohr radius and Z=8. O–H bond (1.810 a₀, 0.06% error) and H···O hydrogen bond (3.820 a₀, 2.57% error) recovered without water-specific adjustable parameters.