Should exploratory and incomplete work be part of a thesis? I just finished the first draft of my thesis in computational neuroscience. It contains all the published work and some other material that is relevant to the main theme of the thesis. I deliberately kept some very recent work out of it because I thought it won't add any value to the reader. 

Now I am tempted to include this exploratory work into the thesis as well since I've put quite a lot of time on it. This work is an attempt to extend the main results of the thesis. The problem statement is well defined with a good literature survey but no concrete result.

I can probably add to the appendix? Or epilogue (doesn't sound great for a technical document)? Or is it a bad idea altogether?
That may be something to add in a "further work" section as part of the conclusion.