Resonant structures in $B^0topsipi^-K^+$ decays are analyzed by performing a four-dimensional fit of the decay amplitude, using $pp$ collision data corresponding to $rm 3 fb^{-1}$ collected with the LHCb detector. The data cannot be described with $K^+pi^-$ resonances alone, which is confirmed with a model-independent approach. A highly significant $Z(4430)^-topsipi^-$ component is required, thus confirming the existence of this state. The observed evolution of the $Z(4430)^-$ amplitude with the $psipi^-$ mass establishes the resonant nature of this particle. The mass and width measurements are substantially improved. The spin-parity is determined unambiguously to be $1^+$.
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