Zulfia Feasibility Theory: Constructed Feasibility and the Generated Domain of Physics

AbstractSince Newton (1687), every theory in physics and mathematics has supposed itsdomain of validity before analysis begins. Newton supposed Euclidean space. La-grange supposed a feasible constraint set. Hamilton supposed phase space. Einsteinsupposed a smooth manifold. Dirac supposed a Hilbert space. Feynman supposeda space of all paths. For four centuries, no framework asked what constructs thefeasible domain — it was always supposed, never generated.This paper introduces Zulfia Feasibility Theory — the first complete theoryin which the feasible domain is not supposed but constructed and generatedfrom within the Zulfia Decomposition Mapping Z(x, u) = η(x, u) + ∆(x, u) [1]. TheZulfia Feasible Domain FZ is generated by η and ∆ together at the moment ofdefinition — unavoidable, inseparable, and self-sustaining.Five theorems establish the complete theory: Domain Construction, Do-main Generation, Domain Unavoidability, Domain Inseparability, and theClassical Domain Recovery theorem — proving that every classical domain inphysics is a special case of FZ .