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We present the Living Swift-XRT Point Source catalogue (LSXPS) and real-time transient detector. This system allows us for the first time to carry out low-latency searches for new transient X-ray events fainter than those available to the current generation of wide-field imagers, and report their detection in near real-time. Previously, such events could only be found in delayed searches, e.g. of archival data; our low-latency analysis now enables rapid and ongoing follow up of these events, enabling the probing of timescales previously inaccessible. The LSXPS is, uniquely among X-ray catalogues, updated in near real-time, making this the first up-to-date record of the point sources detected by a sensitive X-ray telescope: the Swift-X-ray Telescope (XRT). The associated upper limit calculator likewise makes use of all available data allowing contemporary upper limits to be rapidly produced on-demand. These facilities, which enable the low-latency transient system are also fully available to the community, providing a powerful resource for time-domain and multi-messenger astrophysics.