I've finished masters and I've worked on my independent research for few years but never published anything nor I haven't posted any of my research work in public. The reason I did not publish is that I was working on the project and now I am about to finish it.
Now, I want to apply for a PhD position related to the field I worked in. My question is, should I make my work public first (post it on arXiv and on my personal website and github) or apply to PhD group and send them a paper of my work? I've pondered over both options.
With the first option I think the advantage is that I can secure my idea and no one can steal it. I worked really hard on the idea but is there any good way to secure it, though? The disadvantage might be that no one gave me feedback on my work and a mentor will help me polish my work/paper. Also, when it comes to disseminating and publishing my work I think people will take me more seriously if my work is within a PhD group? I am also wondering what will happen if I send them my paper and then they reject my PhD application.
What's your opinion on this matter and how I can make my work more accessible to other researchers? I do not care much about publishing it if there are other ways researchers can see my work and give me feedback whether my idea is worthy.