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There are at present ${\cal O}(100)$ gravitational-wave candidates from compact binary mergers reported in the astronomical literature. As detector sensitivities are improved, the catalog will swell in size: first to ${\cal O}(1000)$ events in the A+ era and then to ${\cal O}(10^6)$ events in the era of third-generation observatories like Cosmic Explorer and the Einstein Telescope. Each event is analyzed using Bayesian inference to determine properties of the source including component masses, spins, tidal parameters, and the distance to the source. These inference products are the fodder for some of the most exciting gravitational-wave science, enabling us to measure the expansion of the Universe with standard sirens, to characterise the neutron star equation of state, and to unveil how and where gravitational-wave sources are assembled. In order to maximize the science from the coming deluge of detections, we introduce GWCloud, a searchable repository for the creation and curation of gravitational-wave inference products. It is designed with five pillars in mind: uniformity of results, reproducibility of results, stability of results, access to the astronomical community, and efficient use of computing resources. We describe how to use GWCloud with examples, which readers can replicate using the companion code to this paper. We describe our long-term vision for GWCloud.