Immutable quantized transport in Floquet chains

We show how quantized transport can be realized in Floquet chains through encapsulation of a chiral or helical shift. The resulting is immutable rather than topological the sense that it neither requires band gap nor affected by arbitrarily strong perturbations. Transport still characterized quantities but shift prevents phase transitions. To explore we introduce concept shiftbox, explain relevant both for momentum-space dispersions and real-space transport, study model systems with strictly transport. Natural platforms experimental investigation these scenarios are photonic constructed waveguide arrays, as well topolectrical mechanical systems.