Generative Paper 1: Infinite Generative Field as the Origin of Physical Reality

Modern physics successfully explains a vast range of natural phenomena, yet every existing framework begins from structures that are already assumed to exist. Space, time, particles, fields, and geometry serve as the primitives upon which physical laws are formulated. While this approach has been remarkably successful, it leaves a more fundamental question unanswered: What is the simplest possible starting point before any physical structure is assumed? This paper proposes a function-first foundation for addressing this question. Instead of treating geometry or physical entities as primitive, it begins with a single recursively self-generating function. At this most fundamental level, no space, no time, and no external source of variation are assumed to exist. Consequently, every new state of the system must arise entirely from the function itself. This requirement leads naturally to the recursive relation: Fₙ₊₁ = Fₙ + F′ₙ where the derivative is interpreted not as a rate of change with respect to an external coordinate, but as the function's intrinsic generative variation. Within this perspective, recursive transitions provide the first and most primitive interpretation of time: at the foundational layer, temporal progression is identified with the ordered sequence of generative transitions rather than with an independently existing dimension. The purpose of this paper is not to derive physical laws directly, but to establish the minimal mathematical foundation upon which progressively richer structures—including geometry, spacetime, and physical interactions—may later emerge. In doing so, it shifts the starting point of fundamental physics from geometry-first to function-first. 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