diff --git a/mult_distinct_p.tex b/mult_distinct_p.tex
index 5019704..489de91 100644
--- a/mult_distinct_p.tex
+++ b/mult_distinct_p.tex
@@ -19,6 +19,8 @@ To prove our hardness result, consider a graph $G(V, E)$, where $|E| = \numedge$
 
 Consider the query $\poly_{G}(\vct{X}) = q_E(X_1,\ldots, X_\numvar) = \sum\limits_{(i, j) \in E} X_i \cdot X_j$.
 
+\AR{need discussion on the `tightness' of various params. First, this is for degree 6 poly-- while things are easy for say deg 2. Second this is for any fixed p.  Finally, we only need porject-join queries to get the hardness results. Also need to compare this with the generality of the approx upper bound results.}
+
 
 For the following discussion, set $\poly_{G}^\kElem(\vct{X}) = \left(q_E(X_1,\ldots, X_\numvar)\right)^\kElem$.
 \begin{Lemma}\label{lem:qEk-multi-p}