Linear Superposition as a Core Theorem of Quantum Empiricism

Clarifying the nature of quantum state |Ψ⟩ is at root problems with insight into counter-intuitive postulates. We provide a direct—and math-axiom free—empirical derivation this object as an element vector space. Establishing linearity structure—quantum superposition—is based on set-theoretic creation ensemble formations and invokes following three principia: (I) statics, (II) doctrine number in physical theory, (III) mathematization matching two observations each other (quantum covariance). All constructs rest upon formalization minimal experimental entity—the registered micro-event, detector click. This sufficient for producing ℂ-numbers, axioms linear space (superposition principle), statistical mixtures states, eigenstates their spectra, non-commutativity observables. No use required spatio-temporal concepts. As result, foundations theory are liberated to significant extent from issues associated interpretations, philosophical exegeses, mathematical reconstruction entire edifice.