Mathematical and Scientific Bases of the SMETA Axiom (Base–I to Base–IV): A Structural Framework

SMETA Axiom: A Structural Framework SMETA is an axiomatic framework proposed to organize a set of independent mathematical and scientific bases describing emergence, persistence, interaction, and dissolution of existence in a unified yet non-reductive manner. The acronym SMETA denotes five operational components: S — Space: the domain in which configurations are defined M — Mass: density or occupancy representing localized existence E — Energy: intrinsic state or interaction functional governing transitions T — Time: emergent ordering parameter arising from process evolution A — Atman: intrinsic ordering or regulating principle, defined operationally rather than metaphysically The SMETA Axiom does not introduce additional assumptions beyond those explicitly stated in its constituent bases. Instead, it functions as a structural index linking the following independently formulated foundations: Base–I: A process-based Δ-model describing cyclic emergence and dissolution from an undifferentiated state Base–II: The Freedom–Unity principle, formalizing attraction and repulsion as complementary components of a single intrinsic functional Base–III: The Rajatsubhra Infinity Series (R-Series), modeling bounded cyclic existence via pulse-driven and hyperfinite constructions Base–IV: RSFD (R-Series Field Dynamics), providing field equations, force laws, and particle dynamics derived from the Freedom–Unity functional Each base is mathematically self-contained and may be read independently. The term SMETA is introduced solely to denote their conceptual alignment and mutual consistency, not to impose an overarching theory or claim empirical completeness. A dedicated formal exposition of the SMETA Axiom will be presented separately. Give step by step data for Zenodo uploading of SMETA. ZIP Start from title