How to reply to reviewers on a unintentional wrong proof in my research paper?

How can I convince a professor or graduate student to be the co-author of a paper I have written (by just giving me their comments) when they don't know me?

• Since  my supervisor is not active at all, I am looking for a way to receive  feedback (about my research plans, ideas, results, and papers) in an  active researcher in my research field. I am wondering if it is possible  to get help from some researchers among the authors of your "previous  works". They usually answer questions about their papers, but when the  discussion goes beyond their paper, they show no more interest and do  not reply the emails.  I used to take this simple strategy: 1) Write a manuscript 2) submit it to a top-ranked conference 3)  If the paper is rejected, use the reviews by the referees of the  conference (including their suggestions, typos, ...) to improve the  work. 4) go to step (2)  (i.e. submit it to another conference) until it get accepted. However,  each review cycle takes too much time. I want to skip this ridiculous  cycle and ask a professional in my research field to directly help me  improve my work, rather than reviewing my work as an unknown referee.  This has a benefit for them: they will be the co-author of one more  paper.  Also, unlike the blind-review process in conferences, we know  each other and can collaborate if both of us are interested. Of course, researchers from the top-ranked US universities are busy doing their own projects, but I think no one hates to be listed on papers that other people have worked on by just giving them a feedback. While they do such a work for free for conferences and journals (as reviewers), why they resist being benefited by directly helping me? It Is there a smart way to ask them to collaborate with you and convince them that they will be profited by helping me?

• Answer:

  Generally you don't.  Being a co-author means that you are putting your professional reputation to vouch for the quality of the paper.  If there is a problem with a paper on which you are a co-author, it could destroy your career.  Helping you has no risk to them, but being listed as a co-author has extremely high professional risk.  So researchers will not allow their names to be used as co-author if it is not a paper they have either written or supervised.  They usually won't mind being listed in the acknowledgements section.