Spectral triples with multitwisted real structure

We generalize the notion of spectral triple with reality structure to triples multitwisted real structure, class which is closed under tensor product composition. In particular, we introduce a first-order condition (characterizing Dirac operators as an analogue differential operator). This provides unified description known examples, include rescaled conformal factor from commutant algebra and (on algebraic level) on quantum disc cone, that satisfy twisted Brzeziński et al. (2016, 2019), well asymmetric tori, non-scalar rescaling noncommutative circle bundles. order deal them, allow twists do not implement automorphisms triple.