How many possible hypotheses
I'm not seeing where the relationship between hypotheses and research paper is. I know what the relationship is in reality, but your question is a bit unorganized. Perhaps we could think about it in a different way... 

I would first create a definition of possible hypotheses (i.e., $H_{0}$ and $H_{1}$ are my two possible hypotheses, and every hypothesis will have both a null and an alternative), and then associate a $H_{0}$ with a $H_{1}$ such that a combination of both null and alternative hypotheses equate to one hypothesis. 

With this, it's a matter of iteratively counting.


With $p \in P$, where $p$ is a paper in the set of papers $P$,
With $w \in W$, where $w$ is a word in a set of words $W$ that indicate whether $p$ is a research paper or not,
With $i$ as the number of times a $w$ occurred in a $p$, 
count the number of times a $w$ occurs in each $p$ and iterate $i$ accordingly.