Master document; proof of "no backfill" for exactly 1

Here is the LaTeX and PDF for the "master document" (i.e., the document containing all of the sections). I included section titles for 14 and 174 (M) and 13 and 134 (H) as placeholders.

The proof of "no backfill" for Exactly 1 is at the top of page 4. The other new thing is that I introduce the claim of "no backfill" in the third paragraph of Section 2: Exactly 1 (page 2).

A couple of things to consider for the "no backfill" proof for Exactly 1:

• I showed it for the rotated version; should we bother to show afterward that it also holds for the unrotated version?
• In the second paragraph of the proof (the "assume holds for n and show holds for n+1" part), I may need to say a bit more. For example, I may need to show that the sites outside B_N_(n+1) cannot affect sites in B_N_(n+1) because of Lemma 2 (analogous to the statement in the previous paragraph in which I show that sites outside B_3 do not affect sites in B_3 because of the boundary of empty cells formed by Lemma 2). Or is what I have written enough?