The Gravitational-Wave Transient Catalog (GWTC) is a collection of candidate gravitational-wave transient signals identified and characterized by the LIGO-Virgo-KAGRA Collaboration. Producing the contents of the GWTC from detector data requires complex analysis methods. These comprise techniques to model the signal; identify the transients in the data; evaluate the quality of the data and mitigate possible instrumental issues; infer the parameters of each transient; compare the data with the waveform models for compact binary coalescences; and handle the large amount of results associated with all these different analyses. In this paper, we describe the methods employed to produce the catalog's fourth release, GWTC-4.0, focusing on the analysis of the first part of the fourth observing run of Advanced LIGO, Advanced Virgo and KAGRA.
