finish final.tex
add N = 5 model to final.tex
address Chris's concerns

Quoting Chris:

This is an excellent writeup.  I have just a few comments on it, which
I've outlined below.  By the way, I loved the title of the section
"Desperately seeking quadratic periodic points."  It make me chuckle.

* "Our entire research project" -> "This work"
* There are some instances of weird paragraphing like in the middle of
  page 2.  In general, try to not to have one or two line paragraphs.
  Here, I think you could combine all the paragraphs after Definition
  1.2 into one paragraph.  This sort of thing happens throughout the
  report.
* Write a little more before Conjecture 1.7 - say, briefly, what the
  empirical evidence is.
* All sentences should end with a period (even those leading up to a
  definition/theorem/conjecture/etc.).  If you feel you absolutely
  cannot transition into the theorem/definition/etc. with a period, you
  may use a colon.  Using colons is common practice among some
  mathematicians, but I personally am not a huge fan.  This happens
  throughout the paper.
* There are some typos in the beginning of Section 3.1.
* Top of page 7 - Never begin sentences with mathematical symbols.
* Go easy on the footnotes.  I think a lot of what you put in the
  footnotes belongs in the body of the text.
* Proposition 4.4: is the end (t = z_1+z_3) unnecessary?  This follows
  from the formula so if anything, you can make it a remark
  afterwards...
* Bottom of page 11: missing period.
* Page 13: "actual" and "actually" aren't the best words.  Maybe "to
  find the precise number of rational points c \in \mathbb{Q} such
  that..." and just remove the "actually."
* I think the (2002) and (2011) are unnecessary.
* Above 5.1.1, there is a sentence which is a little goofy.
* Second to last paragraph: "to see if it always happens" - there should
  be a more sophisticated way to rephrase this sentence.
* In general, the paper can be a tough read because there are many
  things that you assume the reader knows (e.g. birationally equivalent,
  the modular curve X_1(16), etc.).  It would be nice if there were a
  way to make it easier for non-experts given the context of this
  program.  Many research papers define basic terms in order to solidify
  notation and make it a bit easier for other mathematicians to jump in.