Dimensions Part I & Part II: An Axiomatic Framework in Extended Classical Mechanics (ECM)

This two-part work presents an axiomatic ontological framework within Extended Classical Mechanics (ECM) for the emergence of perceived spatial dimensions and abstract (hyper-)dimensions from a pre-geometric phase state. Rather than assuming space, time, and dimensions as fundamental constituents of reality, the framework derives them through the ontological progression: Origin → Existence → Existential Events → Chronology → Dimensions. Part I establishes the ontological foundation by introducing an original pre-Planckian phase state characterized by a fundamental frequency that exceeds the conventional Planck frequency. In this earliest regime, the universe is described as an energetic phase configuration in which physical manifestation has not yet occurred. Although the system possesses a well-defined energetic structure, its phase wavelength remains below the Planck-length threshold, preventing the emergence of observable matter, space, and gravitation. The first distinguishable frequency transformation, together with the progressive accumulation of phase, culminates in the completion of the first 360° phase cycle. This event establishes the first measurable temporal interval, demonstrating that chronology emerges from an ordered succession of completed phase cycles rather than from a pre-existing temporal background. Part II extends this ontological sequence beyond the first phase-cycle closure and develops the emergence of dimensions. Continued phase evolution releases the system from sub-Planck confinement, allowing measurable spatial extension to arise. Within the ECM framework, the observable dimensions of length, width, and depth are interpreted as emergent manifestations of accumulated phase evolution rather than as fundamental geometric containers. Time is likewise interpreted not as a fourth spatial coordinate but as an independent hyper-dimensional ordering parameter that records the sequential evolution of physical states. The framework further distinguishes ontological frequency transformations from observational frequency mappings, thereby separating the pre-manifest energetic domain from experimentally accessible physical descriptions. Throughout both parts, the analysis remains consistent with the ECM manifestation principle linking phase potential energy, phase kinetic energy, and matter manifestation, while recognizing that apparent mass, effective mass, gravitation, and other dynamical quantities emerge only after chronology and dimensional structure have been established. Consequently, dimensions are interpreted not as primitive properties of the universe but as emergent consequences of structured phase evolution. This work provides a unified ontological foundation connecting the pre-Planck phase domain with the subsequent emergence of measurable spacetime and offers a coherent conceptual framework for further development of Extended Classical Mechanics.