The first step of the petition involved finding the "Confirmation Number" in the USPTO's PAIR system. From here I was able to find out that the filing status is "Abandoned -- Failure to Pay Issue Fee". Also of note is the fact that the status was set to "Abandoned" only after the "Notice of Allowance and Fees Due" was allowed to expire. The fact that the USPTO granted preliminary approval to this patent application is troubling.

Could you describe your research? If you've been researching this and have put out or know of any relevant publications, it can act as prior art for this application. You could also post those on askpatents.com, which patent examiners are known to look at occasionally.

I have not created any works that can be considered prior art for this patent application (which is actually now abandoned). My research primarily involves exploiting the computationally intensive aspects of the Collatz function (and its inverse) to construct cryptographic systems. Systems whose elements are computationally difficult to deconstruct, but trivial to construct and verify are of particular interest to me.