Dear Copy Editor,

Thank you for your work on our paper "Finite-type invariants of w-knotted
objects, I". You are amazing! We agree with of most of what you have
done, and we are impressed with some of the changes (in particular,
nobody yet was able to figure out our figures and edit them!).

Anyway, we do have some comments:

Following the referee's comments on part II of this sequence of papers,
we have decided it would be better to refrain from using the phrase
"projectivization", which appear in our papers a small number of times.
Is it possible to make this change in part I as well? If so, the changes
required are rather small:
  1. On page 119 line 22 change "... functor from the category of groups ..."
     to "... functor $\gr$ from the category of groups ...".
  2. Same page, lines 22-23: remove the clause "called {\em
     projectivization} $\proj\colon  Grp \to GrAlg$".
  3. Same page, remove footnote 17.
  4. Same page, line 24: change "\proj" to "\gr".
  5. On page 123, line 35: change "After projectivization we" to "After
     applying $\gr$ we".
  6. Same page, footnote 19: change \proj to \gr, twice.
  7. Page 128 line 15, "projectivization" -> "$\gr$".
  8. Page 161 line 18: "projectivizations" -> "associated graded spaces".

We much prefer our citations as they originally were: like [AET] rather
than like [1]. As readers we are more comfortable reading acronyms than
reading numbers: if a citation appears repeatedly, say [AET], we quickly
learn that it means "that famous paper by Alekseev Enriquez and Torossian",
while making this association with a number takes much longer. As authors
we would like to be helpful to our readers!

Page 101 line 23: We prefer it as it was, with "Much as" rather than
"Like".

Page 104 line 27: "The u-, v-, and w-knotted" -> "The stories of u-, v-,
and w-knotted" (our mistake!).

Page 109 line 5: Un-insert the "in" - the reference there really is to
"above (1)".

Page 109, figure in middle: We prefer our figures on the right, as they had
been in our submission, if only because it saves printed pages. Yet this of
course is a journal decision. This applies to many other figures throughout
the paper.

Page 118 line 25: Change "For v-braids, we still don't know if an
expansion exists" to "For v-braids, an expansion exists by a difficult
result of P.~Lee,~\cite{Lee:VirtualIsQuadratic}".  Then in page 170 line
11: In between the two P. Lee bibitems, add:

\bibitem[Lee2]{Lee:VirtualIsQuadratic} P.~Lee,
  {\em The Pure Virtual Braid Group is Quadratic,}
  Selecta Mathematica {\bf 19-2} (2013) 461--508, \arXiv{1110.2356}.

(This result of Lee was not yet available when we first wrote that
paragraph. It was already available when we submitted the paper, but we
failed to remember to make the change).

Page 124, top: If that figure cannot move back to be an inset on the right,
perhaps it should be "flattened" so as to fit in two rows? A flattened
version of that figure is in the following 3 files:

http://drorbn.net/AcademicPensieve/Projects/WKO1/figs/StrandDoublingF.fig
http://drorbn.net/AcademicPensieve/Projects/WKO1/figs/StrandDoublingF.pstex
http://drorbn.net/AcademicPensieve/Projects/WKO1/figs/StrandDoublingF.pstex_t

Page 125 lines 21-21: Too much space between the "Q" and the "wBn" (3
places).

Page 138 line 4: We believe the sentence was better as it was, yet we will
accept your judgment.

Page 166 line 12: It is sad that our glossary was omitted. (We're not
arguing, though).