Dimensions Part III: Frequency-Phase Ontology of the Pre-Planck Regime in Extended Classical Mechanics (ECM)

This work develops a unified ontological description of the pre-Planck regime within the framework of Extended Classical Mechanics (ECM), where physical reality is not initially expressed through spacetime, matter, or classical dynamics, but through a continuous frequency–phase evolution. The primordial state of existence is modeled as an ontological frequency field characterized by a fundamental decomposition f₀ = fᴘ + Δf₀, representing a continuous transformation between a pre-manifest frequency domain and the Planck-regime boundary. The theory introduces phase evolution x° ∈ (0°, 360°) as the primary ordering parameter from which chronology, energy transformation, and dimensional emergence are subsequently derived. A key result is the invariance of the ontological frequency separation Δf₀, interpreted as a complete phase-cycle constraint governing the transition from pre-manifest to emergent physical structure. Within this framework, energy conservation is reformulated in ontological terms through ΔPEᴇᴄᴍ = ΔKEᴇᴄᴍ, representing internal phase-energy redistribution rather than spatial motion. This leads naturally to the emergence of apparent mass as a derivative ontological quantity Mᵃᵖᵖ = −ΔPEᴇᴄᴍ, which remains unmanifest until phase-closure conditions are satisfied. The framework further introduces a phase-state proportionality parameter k₍ₓ∘₎, which governs energy–frequency scaling in the pre-manifest regime and continuously converges toward the Planck constant h at the manifestation threshold. The emergence of dimensions is shown to arise hierarchically after chronology, which itself emerges from ordered phase-closure transitions. Observational physics is recovered through successive mappings from ontological frequency, through Planck-regime correspondence, to manifested source–observer relations. Overall, ECM presents a structured ontological pathway from frequency-only existence to classical physical reality, offering a unified interpretation of pre-spacetime evolution, energy emergence, and dimensional formation.