Pseudo-Proof of Constrained Sudoku is co-np
No, it's not a persuasive proof.

Before you can have a valid proof, you must first precisely state whatever it is you are trying to prove.  You haven't done that.

A language (a decision problem) is in co-NP if it satisfies certain requirements.  You have not defined a language; you have not defined a decision problem.  You use the phrase "Constrained Sudoku" but you have not given a precise definition of what formal language that is intended to refer to.

What you list as a "definition" of co-NP is actually an English-language summary of the definition; it's not a substitute for knowing the precise mathematical definition.

The reasoning in your "proof" is faulty.  You write:


  I use an algorithm that in essence says "no" when [...]. Therefore, Constrained Sudoku is co-np.


That doesn't follow.  Just because you have an algorithm that sometimes says no, doesn't mean that the corresponding problem is in co-NP.  There are additional requirements, which you haven't checked.

I'd like to give some general advice.  Before trying to tackle this problem, I suggest you spend a bunch of time studying the fundamentals.  Set aside Sudoku and your ideas for a few weeks, and find an online course where you can learn complexity theory.  That will give you a mathematical framework that, once you've learned it, you can come back and apply to Sudoku.  Until you've done that, it is pointless to continue trying to frame questions like this.