I am a master student trying to approach potential PhD advisors in Canada. Unfortunately or not, I believe I have solved an important problem in my field. I have submitted my work to a journal, awaiting a response. If this does not look cranky enough, I also had bad grade in my thesis, and my undergraduate major is not in that field.
The real question is, should I attach my manuscript in my email to the professors to show that I am not a crank (or the opposite)? Because I can't put it on arxiv (a signal that I am a crank), so the only way for professors to verify that I have potential is to show I have research experiences.