Extended Classical Mechanics Reinterpretation of the Chernin et al. Dark-Energy Equilibrium Condition Through Apparent-Mass Dynamics A Classical Effective-Mass Reconstruction of the Cosmological-Constant Gravitational Balance Relation

This work presents an Extended Classical Mechanics (ECM) reinterpretation of the dark-energy equilibrium condition discussed in the Chernin et al. analysis of the Coma cluster. The study proposes that the observationally inferred gravitational balancing effect commonly represented through the relativistic cosmological-constant formalism may instead admit a fully classical reinterpretation through apparent-mass manifestation dynamics. Within ECM, the dark-energy contribution is represented through the relation Mᴅᴇ(R) = −Mᵃᵖᵖ(R) where the apparent mass satisfies Mᵃᵖᵖ ≡ −ΔPEᴇᴄᴍ thereby linking the observed equilibrium condition directly to the ECM manifestation structure ΔPEᴇᴄᴍ ↔ ΔKEᴇᴄᴍ ↔ ΔMᴍ rather than to relativistic vacuum-energy ontology or spacetime-curvature formalism. The work further demonstrates that the Chernin et al. cosmological-constant contribution Mᴅᴇ(R) = −(8𝜋/3)ρΛR³ can be consistently reinterpreted within ECM as an apparent-mass manifestation relation while preserving the identical observational zero-gravity equilibrium condition at the Chernin radius Rᴢɢ ≈ 20 Mpc without invoking relativistic spacetime curvature ontology. Version 1.1: Figure 1. Section Inclusion.