Updated upper limits on the isotropic gravitational-wave background from the LIGO, Virgo, and KAGRA fourth observing run through April 2025

We report results from a search for an isotropic stochastic gravitational-wave background using data collected by the LIGO--Virgo--KAGRA Collaboration. The analysis uses data from the first observing run through April 1, 2025, during the fourth observing run. New frequency-domain cuts are implemented to address a class of non-stationary spectral noise features that were not effectively identified and mitigated by existing data-quality checks in past analyses. Consequently, previously analyzed data from the fourth observing run are re-processed with the updated cuts. We find no evidence for a stochastic background signal and place upper limits on the gravitational-wave energy density. In particular, for a background following a power law with spectral index 2/3 as predicted by inspiralling compact binaries, we find ΩGW(25\,Hz) ≤ 2.0 × 10⁻⁹, while scale-invariant backgrounds are constrained to ΩGW(25\,Hz) ≤ 2.8 × 10⁻⁹, both at the 95% credible level for a log-uniform prior on ΩGW. Relative to the constraints from previous data recomputed with the new frequency-domain cuts, these limits improve by a factor of 1.4. We also update bounds on alternative gravity scenarios predicting non-standard polarization modes, and we verify that correlated magnetic noise sources remain below the sensitivity of this search. Combining these observational constraints with population models of compact binary coalescences informed by the latest gravitational-wave transient catalog, GWTC-5.0, we predict the amplitude of the compact binary background to be ΩCBC(25\,Hz) = 6.3+5.0-2.2 × 10⁻¹⁰ at the 90% credible level.