Mapping of ECM Negative Apparent Mass and Effective Mass to Astronomical Observational Mass Components

This note formalizes the correspondence between Extended Classical Mechanics (ECM) mass terms and standard astronomical observational mass components. In ECM, ordinary matter, matter mass, dark matter, and gravitating mass retain their conventional observational interpretations. However, the observational dark-energy sector is reinterpreted not as an independent ontological entity, but as an emergent large-scale manifestation of negative apparent mass arising from the redistribution of potential energy, represented by Mᵃᵖᵖ ≡ −ΔPEᴇᴄᴍ. The effective mass formalism naturally unifies local gravitational behaviour and cosmic accelerated expansion within a single relational framework.