Planck Epoch Through the Phase-Indexed Velocity Stabilization Lens of Extended Classical Mechanics (ECM)

This work presents a methodological reformulation of the Planck epoch within the framework of Extended Classical Mechanics (ECM). Rather than treating the Planck regime as a singular explosive origin, the study introduces a structured phase-indexed transformation model in which primordial dynamics are governed by regulated frequency-mass evolution. The central methodological construct is Phase-Indexed Velocity Stabilization (PIVS), a formalism in which velocity emerges from an initially superluminal manifestation regime and asymptotically stabilizes at v = c at a terminal phase index of 360°. Within this framework, light-speed invariance is not assumed but derived as a phase-locked stabilization condition. The Planck regime is modeled as a NAM-dominant (Negative Apparent Mass) gradient state, where Mᵃᵖᵖ ≡-ΔPEᴇᴄᴍ governs redistribution into manifested matter (ΔMᴍ) and kinetic manifestation (ΔKEᴇᴄᴍ). This method treats the early universe as a gradient relaxation process, providing a unified analytical structure for the emergence of time, velocity invariance, matter differentiation, and gravitational structure.