The cosmological constant problem — the 10⁵⁵–10¹²⁰ order discrepancy between quantum field theory estimates of vacuum energy and its observed cosmological value — rests on the 1967 Zel'dovich identification of vacuum energy with the cosmological constant. This paper develops a dynamical sequestering mechanism in which vacuum energy gravitates locally within bound structures but is screened from cosmological expansion. We introduce the elastic membrane model as a physically grounded analogy and show that it is not merely pedagogical: the Einstein–Hilbert action is an elastic energy functional minimized at zero curvature, gravitational waves confirmed by LIGO are elastic oscillations of spacetime, and Sakharov's induced gravity programme (1967) derives the elastic modulus from quantum field theory. Spacetime is, in a physically precise sense, an elastic medium. The trace-free Einstein equations of Ellis, van Elst, Murugan, and Uzan provide the geometric foundation: Λ emerges as an integration constant independent of vacuum energy, within a formulation locally equivalent to general relativity. Building on this separation, we develop the complete dynamical history of cosmic expansion — from the highly curved initial state (Big Bang), through mutual relaxation of matter and spacetime geometry, to the present epoch of accelerating expansion driven by geometric elasticity. The paper yields three key results. First, the sequestering mechanism preserves the equivalence principle locally while modifying global vacuum contributions to the Friedmann equations. Second, the observed near-flatness of the universe need not be an initial condition requiring inflation but may be the natural late-time outcome of geometric relaxation, with a positive feedback loop in which decreasing curvature facilitates faster expansion. Third, the transition from deceleration to acceleration at z ≈ 0.7 is identified as the epoch at which geometric elasticity begins to dominate over matter-driven dynamics. The framework uses only established physics — general relativity, quantum field theory, and E = mc² — without invoking new matter particles or fine-tuning. The screening scalar field is introduced as a collective mode (analogous to a phonon) mediating the vacuum's elastic response. This is Paper 5 in a programme of 17 papers developing the hypothesis that quantum vacuum energy gravitates locally. The paper includes two rounds of peer review with detailed author responses. Keywords: vacuum energy, cosmological constant, cosmological constant problem, sequestering mechanism, dark energy, dark matter, elastic vacuum, trace-free Einstein equations, unimodular gravity, flatness problem, cosmic expansion, Zel'dovich identification, Sakharov induced gravity, gravitational waves, Casimir effect Related identifiers: Is part of: "What If the Vacuum Gravitates Locally? — A Comprehensive Research Programme" References: Kriger, B. (2026). Theoretical Separation of Quantum Vacuum Energy from the Cosmological Constant. DOI: 10.5281/zenodo.18987982 Notes: Recommended for submission to Foundations of Physics. Includes two rounds of peer review (Appendix A). Authors: Kriger, Boris ORCID: 0009-0001-0034-2903 Affiliations: ¹ Information Physics Institute, Gosport, Hampshire, United Kingdom ² Institute of Integrative and Interdisciplinary Research, Toronto, Canada Upload type: Publication / Preprint License: CC BY 4.0 Description: