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We propose a mathematically consistent framework that unifies holographic entropy bounds with a novel concept of spacetime elasticity to address the cosmological constant problem. In this cyclic cosmological model, the universe undergoes repeated expansions and contractions, mediated by a quantum geometric bounce inspired by Loop Quantum Cosmology (LQC). The vacuum energy density, traditionally assumed constant, emerges dynamically from the universe’s holographic entropy content, scaling as ρ_Λ∼E_p/N^2 l_p^3, where N denotes the number of Planck-area-sized degrees of freedom on the cosmic horizon. Spacetime elasticity is modeled via an effective scalar field potential tied to the compression of the cosmic scale factor, contributing a dynamical pressure component that evolves cyclically. The holographic ratio N ensures entropy invariance across cycles and leads to a natural suppression of the vacuum energy by over 120 orders of magnitude, resolving the fine-tuning problem without exotic fields or anthropic assumptions. Observable deviations in the dark energy equation of state are predicted at redshifts z∼1-2, providing testable signatures for future surveys such as Euclid and DESI. This approach bridges quantum gravity, holography, and cosmology within a unified geometric paradigm.