Nonexistence of a universal rectangular center for general quadrilaterals

Let $ABCD$ be a general quadrilateral, and form the central quadrilateral by selecting one triangle center, specified by a single center function, in each of the four half triangles determined by the diagonals. Universal rectangularity nonexistence conjecture. There is no center function such that the central quadrilateral is a rectangle for all quadrilaterals $ABCD$. This predicts that no universal triangle-center construction yields rectangular central quadrilaterals for every general reference quadrilateral; the claim is presented as an open conjecture from the paper's computational investigation.