  We have successfully integrated $\Lambda_{\rm s}$CDM, a promising model for
alleviating cosmological tensions, into a theoretical framework by endowing it
with a specific Lagrangian from the VCDM model, a type-II minimally modified
gravity. In this theory, we demonstrate that an auxiliary scalar field with a
linear potential induces an effective cosmological constant, enabling the
realization of an abrupt mirror AdS-dS transition in the late universe through
a piecewise linear potential. To eliminate the sudden singularity in this setup
and ensure stable transitions, we smooth out this potential. Realized within
the VCDM theory, the $\Lambda_{\rm s}$CDM model facilitates two types of rapid
smooth mirror AdS-dS transitions: (i) the agitated transition, associated with
a smooth jump in the potential, where $\Lambda_{\rm s}$, and consequently $H$,
exhibits a bump around the transition's midpoint; and (ii) the quiescent
transition, associated with a smooth change in the slope of the potential,
where $\Lambda_{\rm s}$ transitions gracefully. These transitions are likely to
leave distinct imprints on the background and perturbation dynamics,
potentially allowing the observational data to distinguish between them. This
novel theoretical framework propels $\Lambda_{\rm s}$CDM into a fully
predictive model capable of exploring the evolution of the Universe including
the late-time AdS-dS transition epoch, and extends the applicability of the
model. We believe further research is crucial in establishing $\Lambda_{\rm
s}$CDM as a leading candidate or guide for a new concordance cosmological
model.
