  In this article, we give a proof for a geometric presentation theorem for any
irreducible scheme $X$ smooth projective over a discrete valuation ring $R$. As
a consequence, for any reductive $R$-group scheme $\mathbf{G}$, we prove that
any generically trivial principal $\mathbf{G}$-bundle over $X$ glued to a
principal $\mathbf{G}_U$-bundle over the affine line $\mathbb{A}^1_U$ for a
semilocal affine scheme $U$.
