Stable motivic trivial fibre decomposition over integers and framed motives

Using the trivial fiber topology we describe motivic $\mathrm{\infty }$-loop spaces and fibrant replacements in the motivic stable homotopy category ${\mathbf{S}\mathbf{H}}_{{\mathbb{A}}^1,\mathrm{N}\mathrm{i}\mathrm{s}}(B)$ defined over one-dimensional base schemes $B$.