Topological Elasticity of the Vacuum: A Geometric Resolution of Multiple Cosmological Tensions

Topological Elasticity of the Vacuum: A Geometric Resolution of Multiple Cosmological Tensions This paper presents a parameter-free resolution of three major cosmological tensions - the Hubble (H0H_0 H0), S8S_8 S8, and ΩmΩ_m Ωm discrepancies - using a single dimensionless constant derived from spherical topology: χ=e1/4π≈1.0828χ = e1/4π ≈ 1.0828χ=e1/4π≈1.0828 Applied to CMB-inferred parameters, this constant yields predictions matching late-time observations with less than 1% deviation across all three tensions simultaneously. Independent gravitational wave measurements and a 2026 neutrino–dark matter interaction study converge on identical values from different mechanisms, strengthening the observational case. The paper further presents a formal derivation of χχ χ as a mathematical theorem within the Information Theory of the Vacuum (ITV) axiom system - establishing that χχ χ is not a fit parameter but the unique stable fixed point of recursive information dissipation in an isotropically expanding medium. The Euclid mission (2026–2030) will provide the precision measurements required to confirm or falsify the predictions made here.