We develop a novel technique for resizable Hadoop cluster's lower bounds, the template matching rectangular array of inverted Index summarization expressions. Specifically, fix an arbitrary hybrid kernel function ݂ ∶ {0,1} → {0,1} and let ܣ be the rectangular array of inverted Index summarization expressions whose columns are each an application of ݂ to some subset of the variables ݔ ଵ , ݔ ଶ , … , ݔ ସ . We prove that ܣ has bounded-capacity resizable Hadoop cluster's complexity Ω(݀), where ݀ is the approximate degree of ݂. This finding remains valid in the MapReduce programming model, regardless of prior measurement. In particular, it gives a new and simple proof of lower bounds for robustness and other symmetric conjunctive predicates. We further characterize the discrepancy, approximate PageRank, and approximate trace distance norm of ܣ in terms of well-studied analytic properties of ݂, broadly generalizing several findings on small-bias resizable Hadoop cluster and agnostic inference. The method of this paper has also enabled important progress in multi-cloud resizable Hadoop cluster's complexity.