The Zero Null Space with Operator O-Null: An Algebraic Formalism for the Physical Zero

This paper introduces a clear mathematical framework defining a true physical zero that is distinctfrom the standard quantum vacuum. In quantum field theory, the vacuum state |Ω⟩ is not empty; itcontains fluctuating energy fields. By creating a dual system composed of a unique Physical NullVector (|∅₀ ⟩) and an O-Null Operator (Ô₀ ), we build a model where absolute nothingness actsas a passive identity element under quantum addition (superposition), while keeping a measurablesignature when acted on by the operator. We prove that this vector must have a norm of zero(⟨∅₀ |∅₀ ⟩ = 0). Finally, we show how this framework can be used to study the Cosmological Constantproblem and the Black Hole Information Loss paradox.