address note 01: why the UBC bound is special

Comment:

    maybe say why it's so special: the constant is supposed to not
    depend on the coefficients of the morphism!

(The following series of commits this one included will be addressing
Niccolo's comments.)
address note 02: exclude the origin in the...

projective space definition.

Comment:

    This definition is wrong, you should throw away the null (n+1)-uple!
address note 03: wording

Comment:

    "over some field K", rather than "in some space"
address note 04: wrong sign in inequality

Comment:

    The sign of the inequality goes the other way!
address note 05: wording

Comment:

    This is a strange choice of words.
address note 06: confusion around the N=4 theorem

Original code:

    Moreover, for each such $c \in \Q$, $\phi_c(z)$ has exactly four
    such periodic points (whereas for any $c \in \Q$, $\phi_c(z)$ has at
    most four periodic points of period 4 defined in some quadratic
    extension to $\Q$).

Comment:

    I don't understand. I thought the c given in the formulas were the
    only c's that give us quadratic 4-periodic points - and they give us
    four of them - while every other c has no quadratic 4-periodic
    points.

Previously, by "period 4" I'm also including exact period 1 and 2, but
obviously this should be confusing to everyone except the original
author (me) at the point of authoring (a week later I might find
it super confusing myself), so I'm trimming this out.