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[References.: 75 tit.]

We study the spin-exotic JPC=1−+ amplitude in single-diffractive dissociation of 190  GeV/c pions into π−π−π+ using a hydrogen target and confirm the π1(1600)→ρ(770)π amplitude, which interferes with a nonresonant 1−+ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile these experimental findings. We study the nonresonant contributions to the π−π−π+ final state using pseudodata generated on the basis of a Deck model. Subjecting pseudodata and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the JPC=1−+ amplitude and also for amplitudes with other JPC quantum numbers. We investigate for the first time the amplitude of the π−π+ subsystem with JPC=1−− in the 3π amplitude with JPC=1−+ employing the novel freed-isobar analysis scheme. We reveal this π−π+ amplitude to be dominated by the ρ(770) for both the π1(1600) and the nonresonant contribution. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the JPC=1−+ amplitude.