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.
Soumendra Nath Thakur (Mon,) studied this question.