It is my first post in 'ACADEMIA'. I am a PhD student working in nuclear medicine. In my first two years of PhD, I had approached my thesis problem in a certain way which is isolated from the existing literature due to lack of experience and also due to the fact that my PhD guide is new in this field. I had tried to communicate the work in a good journal ('Physics in Medicine and Biology - IOP'). We submitted the paper in May 2018. There was a conflict between two referees. One referee praising the work and other referee has lots of issue with the feasibility study of the work. Initially, it has gone through a major revision, and after resubmission, it was rejected-to-resubmit. Unfortunately, my guide can't find the time, and after a long one year break, she had submitted the paper in the same journal in October 2019. But this time editor of the journal get changed and finally they have decided to reject the paper. So we finally submitted the paper in 'Medical Physics' on December 2019. And now it is under review.
Coming to my questions, now that I am in my 5th year in PhD, I have to finish the thesis within one year. So in 2019, I have approached the thesis problem using a different approach and produce some amount of work, and I hope this will be publishable. And now I have started working one another method. Provided that my PhD guide can find time to check the manuscripts, I am concerned about my first work in terms of its publishability and how can I defend the work in my thesis review phase. The reason is, at this moment, I think that my first approach is not a convincing solution to the problem. Instead, the approach raises a conjecture. That is what I was told in the final review by the referee, which I feel is the only referee comment I am happy with. The referee pointed out that "either you show thorough experimental evidence of your hypothesis or you prove your conjecture in a proper mathematical way". I have two backup plans for it.
Option-1: If that paper gets accepted in this new journal, then I will not extend the first approach (due to time constraint) and will try to complete my thesis with other two methods that I have worked later (with possibly two more publications).
Option -2: If that paper does not get accepted, then I have to work more on that and see whether the hypothesis that I have proposed is really can be true in reality or not.
My questions are -
(1) If I am unable to publish that paper and can't find enough time to work further one that then how should I present the work in my thesis?
(2) If I found that my conjecture is wrong, then how should I present the work in my thesis? I know a wrong solution is sometimes more interesting. But remember it is not a physical theory. Instead, it is a statistical technique that I have tried to develop and "failed (may be)". Although one of my PhD examiners had said that "even it fails still it is a good trail to solve the problem".