Gamma Theory v200-EX_4: Mathematical Framework for Cosmic Timeline Calculation via Γ_eff Parameter Identification

This work, Gamma Theory v200-EX_4, establishes the first mathematical framework that enables numerical calculation of the cosmic contraction onset time and the Big Crunch time based on the extended Friedmann equation of Gamma Theory. The four parameters αΛ, γΛ, ηU, and νU are identified from DESI and Euclid observations, allowing the full time evolution of the effective cosmological constant Λ_eff(t) to be derived. The results include: a bridge equation linking DESI observables w0 and wa to Gamma Theory parameters; a contraction onset time of approximately 11 Gyr; a Big Crunch time of approximately 20 Gyr; the triple coincidence Λ_eff = 0, νU = ||ξU||² / (4ηU), and the collapse of the Ebihara Boundary; structural and numerical agreement with Tye’s DESI-based model; and a mathematical description of the post–Big Crunch state κ_null ∈ iℝ³. Gamma Theory is presented as the only framework that provides a mathematical description of the universe beyond the Big Crunch.