Dimension Part 1 - An Axiomatic Framework in Extended Classical Mechanics for the Emergence of Perceived and Abstract (Hyper)Dimensions from Origin, Existence, Existential Events, and Chronology

This work (Dimension Part I) develops an axiomatic ontological framework within Extended Classical Mechanics (ECM) to explain the emergence of dimensional structure from a pre-geometric origin state. The study begins by re-examining the conceptual foundations of “origin,” “point,” and “dimension” in conventional physics and identifies their dependence on an already-established spacetime background. To address this limitation, ECM introduces a non-spatiotemporal pre-manifest phase state characterized by a fundamental frequency condition ( f₀ > fᴘ ), interpreted as the ontological origin of physical manifestation. Within this framework, the universe is modeled not as an instantaneous singular event, but as a continuous phase transition from uneventful existence to eventful existence. The transition is governed by sub-Planck energetic oscillations, expressed through a quadratic phase-displacement structure and frequency–energy equivalence, which define the earliest non-spatial state of existence. The model establishes that physical chronology arises only after the completion of the first full phase-cycle (x° = 360°), which generates the first distinguishable event and corresponds to the emergence of the Planck time interval (tᴘ). The ontological sequence—Origin → Existence → Existential Events → Chronology—is formalized as the foundational mechanism through which measurable temporal ordering arises. In this view, dimensions are not primitive geometric entities but emergent constructs derived from discrete phase-cycle completions. Consequently, time is not assumed as a background parameter but is derived from structured phase evolution, while spatial and higher-dimensional structures are deferred as emergent consequences of chronology. This formulation provides a consistent pre-geometric basis for dimensional emergence, linking frequency, phase, and energy transformation to the origin of measurable physical structure.