arXiv:2611.14008v1 Announce Type: new Abstract: We consider exact and interval-valued interpolation of multivariate copulas at arbitrary finite configurations in the unit cube. We first characterize when the prescribed data are compatible with a quasi-copula and derive explicit extremal quasi-copula envelopes. The copula interpolation problem is thereby reduced to a copula sandwich problem between these envelopes. Restricting them to the canonical rectangular grid generated by the data coordinates yields a finite linear feasibility system whose elementary-volume constraints are encoded by a cell--vertex incidence matrix. Farkas' lemma then identifies the criterion of Omladi\v{c} and Stopar with an explicit certificate of infeasibility. Although this criterion is indexed by infinitely many formal cell combinations, we show that it suffices to test finitely many vertices of a sign-polytopal subdivision. We also extend the construction to $k$-increasing discrete quasi-copulas for $2\leq k\leq d$.