Energy–Frequency–Mass Mapping as an Equivalence Principle in Extended Classical Mechanics (ECM)

This work formalizes the Energy–Frequency–Mass (EFM) Mapping as an equivalence principle within Extended Classical Mechanics (ECM), establishing an explicit unified conservation chain: E ↔ f ↔ M Although the underlying logic has always been present throughout ECM, it has previously remained distributed across separate formulations involving manifestation, frequency-governed emergence, apparent mass formation, effective mass behaviour , and gravitation. The present work unifies these components into a single coherent conservation framework. In ECM, total energy is conserved through: Eₜₒₜₐₗ = PEᴇᴄᴍ + KEᴇᴄᴍ where potential energy (PEᴇᴄᴍ) is fundamentally frequency-governed. Manifestation begins when stored primordial frequency approaches the Planck threshold frequency (fᴘ), initiating energy displacement and observable emergence. PEᴇᴄᴍ → f → M This establishes the ECM interpretation: stored primordial frequency → threshold crossing → released manifested energy. Once the hidden frequency reservoir crosses the Planck boundary, observable physical manifestation begins. This formalism further clarifies that manifestation begins when Negative Apparent Mass (NAM) crosses the Planck threshold, converting hidden frequency content into observable existence. Under this framework, redshift, gravitational phase delay, and time distortion become direct consequences of frequency redistribution rather than independent phenomena. The result is a unified conservation ladder: PEᴇᴄᴍ → f → M demonstrating that energy, frequency, and mass are not separate entities, but conserved representations of the same underlying existential content. This removes the previous appearance of ECM containing separate frameworks for energy, frequency, mass, gravitation, and manifestation. Instead, all become projections of one conserved existential process. Frequency governs manifestation; manifestation produces apparent mass; apparent mass modifies effective gravitational behaviour ; observed energy shifts correspond to frequency redistribution; and gravitation emerges directly from frequency-governed mass redistribution. Consequently, in ECM, the Energy sector connects directly to the Frequency sector, the Frequency sector connects directly to the Mass sector, and the Mass sector connects directly to the Gravitation sector without conceptual discontinuity. Gravitation is therefore no longer treated as an isolated force law, but as a manifestation-state consequence of conserved energy–frequency redistribution.