Fant\^omas Unconfined: global QCD fits with B\'ezier parameterizations

Fant\^omas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fant\^omas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs B\'ezier curves as universal approximators for a variety of PDF shapes. Integrated into the xFitter framework for the global QCD analysis, Fant\^omas provides a foundation for general models of PDFs, while reducing the computational time compared to the approaches utilizing traditional polynomial parametrizations as well as providing an interpretable alternative to neural-network-based models. This paper outlines the structure and practical usage of the Fant\^omas toolkit, including its inputs, outputs, and implementation within xFitter. It also provides a practical example of using Fant\^omas for uncertainty quantification as well as the combination of PDF fits into a single ensemble.