Major comments:

In general, the paper is written well, and I was able to follow the discussion easily. Section 3.2 was particularly valuable for motivating the g-rules. I do think it could have been made clearer that the “car rules” on page 10 are exactly the g-rules in Lemma 3. (Well, they are not exactly the same, but I think the point is that the g-rules are a necessary consequence of assigning Laurent polynomials to the segments of the diagram following the car rules.) This is stated in the text, but only later: it might help to repeat it, perhaps as part of the statement of Lemma 3 or at the beginning of Section 3.2.

The use of computer verification in Section 3.3 is unusual but is a good choice. Typically in the literature authors would simply claim that the computation holds, with no evidence that it does; a computer implementation is a better solution.

In Section 4, it is claimed that sl2_ε^+ is isomorphic to sl2 \oplus ⟨ε⟩ when ε is invertible. I believe this claim, but I would be interested in seeing the isomorphism explicitly on generators, unless it is too complicated to write out.

Minor comments:
The “future talk” [BN10] is no longer in the future.

When I read “For our three examples D_1 ...” on page 3 I was confused where D_1 and D_2 came from because they are embedded in the text. It might be good to also show all three together in a figure.

There is a typo on page 4: “We also load minor conversion. . . ” should be “We also load a minor...”