Equal contribution noted in paper draft without prior discussion My thesis has been accepted as a paper. Now, with the camera-ready submission deadline close, a new footnote appeared in the final version of the paper stating that the first (me) and second author have equal contribution. This has not been discussed with me.

In the paper, I have used the second author's algorithm (implemented as part of different project) as a component in the presented pipeline. His algorithm is an implementation of a complex paper with small modifications. It does not hold contributions in the paper by itself but it is an important component. The novelty of the paper is using this component in the context of a different task by combining it with other methods in a certain way. All the parts of the pipeline apart from this component, also all the experiments and evaluations have been done by me as part of my thesis. Can equal authorship still be reasonable in this case? What are the conditions for  equal contribution authorship? He still spent a lot of time on this component, but it was as part of his own project.

The second author is a PhD student and maybe he can benefit from equal contribution authorship (although not sure exactly how it works). However: What is the impact of such equal authorship on me as a first author? I plan to use this paper in my CV, potentially for a PhD candidate position - can equal authorship make a noticeable influence when looking at the paper?

Thanks in advance.

TL;DR: 
Primary Question:


How to handle an equal authorship appearing in the final paper draft which was not agreed upon in advance?


Subquestions:


What are the conditions fo equal contribution of authors?
What are the implications for the first author, if any?
How to handle an equal authorship appearing in the final paper draft which was not agreed upon in advance?


This can be tricky. I strongly suggest that you bring up your concerns with your advisor and figure this out together. The key point here is that you should be collegial, but if you believe the attribution is undeserving you should definitely be assertive and explain why. Your advisor should have consulted with you before making any changes to author contribution (this is something they should know how to handle), but given that they didn't, it's reasonable to bring up the topic. 

I would not change things myself, I would not confront anyone aggressively. If you have other strong publications that showcase your independence then it may be better to let this go as the marginal effect on you is minimal. My experience is that these things rarely get turned back, but I may be mistaken. 


  What are the conditions to equal contribution of authors?


Well, if the two authors have made roughly equal contributions. This is often hard to quantify. Here’s another perspective: the other person in your example, call her Alice, could say: “I implemented a complex algorithm that took effort and skill to do. All that ResearchNewbie did was run a few experiments using this algorithm. I could’ve gotten an undergraduate programmer to run them! Why should they be first authors?”


  What are the implications for the first author, if any?


It’s very important. You should show some degree of independence before you graduate. Graduates who have no lead authorships can be perceived as unready to be an independent scholar.