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human
Being verbally accused of cheating. I don't know how to defend myself.

Throwaway account...Just in case.

As a background, I am majoring in physics and am on track to graduate early and being able to get into an Ivy League level grad program (PhD).  I've taken my schooling very seriously throughout my life, mainly because that was the only thing I was ever good at.  Getting good grades is my proof to myself that I am pushing myself to my personal goals.  Also, I have never cheated on an assignment, ever.

Our department is fairly small, so I have daily interaction with all of my professors.  I considered all of my professors my personal friends and mentors.  They all encourage group work, which we have been trained to do since our first semester, and most genuinely care about our education.  However, the lines have started to blur a little in one of our physics courses.

It all started a few weeks ago, when my friend and I went to the library to work on an assignment.  A couple of our classmates found us as we were working and joined us.  My friend and I had already worked out 3/4 questions by the time they arrived, and still had them on the marker board because we had not written them down yet.  We started working on our 4th problem and help our classmates where we could (the material was very confusing because we weren't explained the theory behind the method).  We finished our homework, answered any last questions and left to go turn our homework in.

Fast forward to next week, it was implied to the class that we had cheated.  Naturally curious, I asked why.  We got a round-about answer that didn't make much sense.  I wanted to get to the bottom of the issue, because I take this seriously.  I went to the professor's office and asked for an explanation.  According to him, I cheated because my classmates copied my work with my permission.  My argument against this was that his syllabus encourages us to work together.  Not only that, but my classmates invited themselves into our study area, copied our work, then submitted it verbatim as it was written on the board.  I continued saying that it isn't my concern what they submit, so I shouldn't be held responsible.  I made sure to make the point that I told my classmates not to copy our work, but to make sure they understood the general "flow" of what we were doing.

The advice he gave seems to conflict with everything we had learned up to now: he wants us to stop working as a group.  My classmates are my friends.  I've known most of them for almost 2 years.  We've had all the same classes, worked together through any troubles.  Now I'm being told to turn a cold shoulder to them.

Here's where I have my problem. I'm now labelled as a cheater by him.  Almost every chance he gets, he reminds me that I am a "suspect".  

An example of above: Today I was working on another physics class homework.  The teacher of this class (call him X) provides excellent lecture notes that we use as a guide during his lecture (he posts them online before class).  Then, when we do the homework, they act as concise notes for quick references.  Yesterday (during class) I was having some difficulty following my professor.  The class has low math requirements, so general assumptions have to be made to skip around the math.  Unfortunately, the homework required that I understand the assumption, which I didn't.  So I look the problem up after attempting to solve the problem.  I find the question posted in another professor's online exam, so I look at that.  Professor Y (the one accusing me of cheating), comes over and without understanding the situation, accuses me of copying the answer.  Had he looked, he would have noticed that the exam's solution, and my solution, were two entirely different things.

This is what annoys me.  He walked into Professor X's office and told him that I was cheating by copying the answers. I was in disbelief that he would do that right in front of me.  I ignored it, thinking he was trying to elicit a response, and continued to try to understand the material.  5 minutes later, he comes back (while I was still trying to understand everything).  He sees that I am still trying to figure everything out, then walks back into Professor X's office and says: "You know [thegrieved] is out there copying the answers, and you aren't going to do anything about it?".  Professor X: "No, it's fine." Professor Y: "Well, if I were you, I would give him a 0 (zero) for cheating. That's what I would do."  Professor Y walks back into his office, and that's the last I saw of him that day.

Maybe I'm overthinking things, but it's like he has it out for me.  Professor X has taken time to understand my learning style.  I attempt the problem, then go looking for more information before attempting again.  I genuinely try to learn the material, but try to correct myself before I get it stuck in my head.  I've never copied someone else's answer.  I always make sure I understand it.

This is more of a rant than anything.  Feels nice to blow off some steam.  Any suggestions on the situation would be appreciated.

TL;DR: Professor accused me of cheating by allowing classmates to copy my work with my permission (I didn't).  Get labeled as a cheater (I am not).  Now he won't drop the issue.
gpt
Go directly to the department head (chair.) Do not pass go. Do not collect $200. Explain yourself completely and quickly. Don't let it become a bigger issue than it is already. Accusation of academic dishonesty (no matter how trivial) must be dealt with quickly, or they WILL bite you in the ass.

If that gets you nowhere, look for an ombudsman or similar. Don't be shy.