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The experimental results at LHC have steered the theory community towards the most general description given the particle content (a.k.a. Effective Field Theory). Aligned with the very essence of science, this program aims at approaching the electroweak-sector with the least possible assumptions. In this drive for expanding theory horizons, geometry has proven a valuable tool to treat field redefinitions, optimize amplitude computation, and formulate fundamental questions about the Higgs nature.