Dual-Constant Unified Geometry across Scales

The paper presents the Mass–Energy–Spacetime (MEST) framework, in which spacetime and mass–energy are regarded as dual measurable structures of a single physical system. Relativity encodes how mass–energy determines spacetime geometry, but it does not explicitly describe the reciprocal correspondence of spacetime to mass–energy structures. From observational fits we identify three structural tensor equations—MEST-2, MEST-2n, and MEST-n2—that supplement relativity by providing this complementary description. These equations successfully reproduce a wide range of astrophysical phenomena, including galaxy rotation curves (covering mass-concentrated, diffuse, high-luminosity, and low-surface-brightness systems), gravitational lensing profiles, and characteristic features of the cosmic microwave background (blackbody spectrum, cold spots and their polarization, hot spots, voids, and shoulder-like anomalies). Consistency extends to particle-physics experiments, where CMS 13 TeV Drell–Yan production, combined HERA deep inelastic scattering, and OPAL fermion-pair data all exhibit the same structural scaling. Across these diverse systems, the analysis consistently yields two invariant constants: a scaling relation α ∝ r₀ and a cross-scale duality E₀r₀ ≈ ħc. These constants emerge as necessary consequences of the MEST balance equations and are independently validated by observational data, providing a mutual cross-check across more than twenty orders of magnitude. Together they motivate a Constant-Unified Geometry principle, suggesting that apparent dark-matter-like phenomena and high-energy resonances are dual manifestations of a single structural law of spacetime.