Extended Classical Mechanics: Core Operational Framework and Dynamical Mass–Energy Relations

This foundational exposition presents the core operational framework of Extended Classical Mechanics (ECM), establishing a unified theoretical hierarchy that interconnects phase displacement, temporal evolution, frequency states, and dynamical mass–energy equivalence. The work develops a comprehensive mass–energy taxonomy in which ordinary matter, dark matter, and dark energy emerge as distinct manifestation sectors within a common phase–frequency–dynamical-mass framework, rather than as ontologically independent substances. Particular attention is devoted to the photon propagation state and the negative apparent-mass formalism, yielding a continuous energy-conservation chain from potential-energy displacement to manifest kinetic energy and frequency, alongside rigorous notational conventions ensuring precise epistemological boundaries within the extended classical formalism.