Data for “Witnessing genuine multipartite entanglement in phase space with controlled Gaussian unitaries” [https://arxiv.org/abs/2510.26762]. All data is provided in CSV format, where the first row (excluding the first element) is the horizontal axis and the first column (excluding the first element) is the vertical axis for 2D plots, or labels of the different traces for line plots. The data for the section “With Numerical Integration of Wigner Function Over Finite Regions” are all named discretization_{type of error}.csv, where {type of error} is actualError for the actual discrepancy between the numerical and actual integrals, approxError for the error approximated by taking the difference between two numerical integrals, and rigorousIntegral for the numerical integral computed with rigorous error bounds. All other data are given as wit{witness type}_{state}_{etc.}.csv. Here {witness type} are the controlled operations required for the witness: D = "displacement", DBS = "displacement + beamsplitter", P = "parity". {state} are the example states, either the W or cat states. {etc.} contains additional specification of the data, primarily the size of the matrix N used in the characteristic function witnesses, with the prefix Ξ for the measured phase space points.