The Omega Mapping: A Unified Analytical Framework for Fundamental Constants via the Self-Power Field

We present a novel analytical framework that unifies distinct fundamental constants-specifically π, e, ϕ, and i-through a single generating function F (s) predicated on the self-power term s -s .By analyzing the function F (s) = 2(1-s -s ) -1 -1, we demonstrate that it is isomorphic to a hyperbolic cotangent acting on a complex potential field, defined here as the "Omega Coordinate" (Ω = s ln s).Through the application of the Lambert W function, we derive exact closed-form inverses for these constants, revealing that they exist as specific resonant points on a continuous complex manifold.This paper establishes the formalism of Ω-Space, bridging the gap between geometric, growth, and algebraic constants.