Sexagesimal Harmonic Mathematics (MAS) – Thermodynamic Transformations, Modified Gibbs Function (Δ G_MAS), and Stochastic Wave Dynamics: Parts I–III

Abstract This multi-part technical monograph introduces Sexagesimal Harmonic Mathematics (MAS), a novel theoretical framework utilizing modular symmetry () and topological discretization of the phase space to address longstanding challenges in theoretical physics, combustion thermodynamics, and kinetic chemistry. Part I establishes the foundational group theory, defining the modular ring and the Śūnya ground state () as a topological pivot for entropy reduction and symmetry invariance. Part II introduces the Harmonic Phase Impedance () and the Modified Gibbs Free Energy function (), presenting the mathematical derivation of the Resonant Activation Collapse theorem and stochastic wave dynamics for monodisperse fuel atomization. Part III formulates the Stoichiometric Residue Tensor () and the zero-residue theorem for hydrocarbon oxidation (), demonstrating the mathematical mechanism for suppressing the Zeldovich pathway ( elimination) and achieving complete, clean combustion without toxic byproducts (). Included datasets and LaTeX source files provide full algebraic proofs, differential operator equations, and protocols for physicochemical validation via thermal analysis (DSC/TGA) and interfacial tensiometry. This body of theoretical research and mathematical formalization is submitted to the National Nanotechnology Laboratory (LANOTEC) as a proposal for a joint research project, aimed at the physicochemical, thermal, and nanometric characterization of the additive at the laboratory scale. This framework of scientific cooperation seeks to validate the harmonic coupling metrics through differential scanning calorimetry (DSC) and interfacial tensiometry assays, with the fundamental purpose of establishing the essential prior phase for the subsequent execution of dynamic testing, homologated exhaust gas measurement (, , ), and thermal-mechanical performance evaluation in engine test benches, which will be carried out in direct coordination with the School of Mechanical Engineering at the University of Costa Rica (UCR).