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In the Standard Model, the mass of the Higgs boson is greatly destabilised by quantum corrections, and free parameters of the model need to be extremely fine-tuned in order to arrive at the measured Higgs mass. A fundamental aim of this program is to quantify the extent to which current measurements and searches can constrain models which attempt to restore naturalness by extending the SM. The expected sensitivity from future high precision running at the LHC and of planned non-collider experiments will also be studied. This program deviates from related work in this field by maintaining a sharp focus on the naturalness question and how well a top quark partner can resolve it in different theoretical scenarios using a range of measured observables.