Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful \emph{fully lifted} (fl) statistical interpolating/comparison mechanism for bilinearly indexed random processes. Here, we present a particular realization of such fl mechanism that relies on a stationarization along the interpolating path concept. A collection of very fundamental relations among the interpolating parameters is uncovered, contextualized, and presented. As a nice bonus, in particular special cases, we show that the introduced machinery allows various simplifications to forms readily usable in practice. Given how many well known random structures and optimization problems critically rely on the results of the type considered here, the range of applications is pretty much unlimited. We briefly point to some of these opportunities as well.

翻译：我们的伴随论文《Stojnicnflgscompyx23》引入了一种非常强大的针对双线性索引随机过程的完全提升（fl）统计插值/比较机制。在此，我们提出该fl机制的一种特殊实现，其核心基于沿插值路径的平稳化概念。我们揭示、情境化并呈现了插值参数之间一系列非常基本的关联关系。作为额外收获，在若干特例中，我们展示了该机制可简化至易于实际应用的形式。鉴于众多已知随机结构与优化问题关键依赖于此类研究成果，其应用范围几乎不受限。我们也简要指出了其中一些潜在应用方向。