The Origin Axiom: A Unified Field Theory Rooted in the Impossibility of Nothingness

This paper presents a unified field theory built on a single irreducible principle—the Origin Axiom—which posits that absolute nothingness is not just physically implausible, but logically and topologically forbidden. From this premise, we derive a fundamental “no-solution” equation: Λ := eiφ^δ + 1 = 0 Here, φ is the golden ratio and δ is an irrational exponent. Because this expression can never equal −1 (as φ^δ cannot be an odd multiple of π), it represents a permanent obstruction to perfect cancellation, implying that existence must persist as the unavoidable remainder of this impossibility. From this axiom, we construct a single complex scalar field: Φ(xμ) = ε · eiS(xμ)/ħ This field encapsulates the oscillatory logic of existence itself. The associated Lagrangian features a non-linear potential shaped by the golden ratio, resulting in spontaneous symmetry breaking, vacuum degeneracy, domain walls, and localized energy structures (oscillons). These phenomena give rise to emergent gauge interactions, effective spacetime geometry, and quantum behavior—all within a common scalar framework. The theory has shown promise in unifying gravitational and quantum effects and offers fresh approaches to vacuum energy, cosmological evolution, and particle mass generation. It also opens paths for testable predictions involving residual vacuum tension and field-based structure formation. This work is shared with the aim of initiating critical discussion and welcomes scientific feedback. It is offered as a contribution toward deeper unification in physics, rooted in a fundamental impossibility rather than an assumed symmetry.