The remarkable universality of the cuprate Tc dome suggests a very fundamental unifying principle. Moreover, the superconducting gap is known to persist above Tc in the pseudogap phase of all cuprates. So, contrary to BCS, the gap cannot be the order parameter of the transition. In this work, we show that both the Tc-dome and the pseudogap line T * (p) arise from a unique and identifiable principle : the interaction of localized 'pairons' on an antiferromagnetic square lattice. The topological constraints on such preformed pairons give rise to both the Tc dome and the pairing energy simultaneously. It also provides a natural explanation for the critical doping points of the phase diagram. The model matches perfectly both the T * and Tc experimental lines, with only one adjustable parameter.