Generative Paper 2: Vacuum as the Minimal Condition of Definability

The concept of vacuum has undergone profound changes throughout the history of physics. In classical physics, vacuum was understood as empty space. In quantum field theory, it became the lowest-energy state of quantum fields, populated by fluctuations and virtual particles. Although these descriptions differ substantially, they share a common assumption: the vacuum is defined within an already existing physical universe. Space, time, geometry, and physical laws are all presupposed before the vacuum is introduced. This paper explores a more fundamental question: What remains if every one of these assumptions is removed? Rather than treating the vacuum as a physical entity, we propose that it should be understood as the minimal condition of definability. At this level, the vacuum contains no geometry, no spacetime, no fields, no particles, no energy, and no information. It is not a physical background but the logical foundation that makes the emergence of physical structure possible. We argue that such a vacuum requires only two primitive components: a Domain, which provides the possibility for definition, and a Mapping, which realizes the act of definition. Every additional concept—including coordinates, geometry, fields, and physical laws—already represents further structure and therefore cannot belong to the vacuum itself. The objective of this paper is not to derive physical reality, but to establish the most minimal and internally consistent definition of vacuum upon which progressively richer mathematical and physical structures may later be constructed. This article is part of a broader theoretical program investigating the emergence of spacetime, geometry, and physical structure from the ψ–Θ–χ continuum. Earlier works in this program explore different layers and stages of the framework, ranging from foundational pre-structural regimes to geometric realization: Generative Paper 1: Infinite Generative Field as the Origin of Physical Reality Generative Paper 2: Vacuum as the Minimal Condition of Definability Generative Paper 3: Primitive Recursive Functions as the Architecture of Recursive Organization Generative Paper 4: From Recursive Organization to the ψ–Θ–χ Architecture Generative Paper 5: Organizational Space and Organizational Fields