Your concept of burden of proof is so twisted I am not sure what the point is.
I'm going to say this one more time. The burden of proof is yours. So prove it.
Burden of Proof
A fallacy is when someone makes an argument based on unsound reasoning. Burden of proof is one type of fallacy in which someone makes a claim, but puts the burden of proof onto the other side. For example, a person makes a claim. Another person refutes the claim, and the first person asks them to prove that the claim is not true. In a logical argument, if someone states a claim, it is up to that person to prove the truth of his or her claim.
A negative claim is a colloquialism for an affirmative claim that asserts the non-existence or exclusion of something. The difference with a positive claim is that it takes only a single example to demonstrate such a positive assertion ("there is a chair in this room," requires pointing to a single chair), while the inability to give examples demonstrates that the speaker has not yet found or noticed examples rather than demonstrates that no examples exist (the negative claim that a species is extinct may be disproved by a single surviving example or proven with omniscience). The argument from ignorance is a logical fallacy. There can be multiple claims within a debate. Nevertheless, it has been said whoever makes a claim carries the burden of proof regardless of positive or negative content in the claim.
All your dancing around is nothing more than that. The burden of proof is yours as you can provide it but refuse to.
