I have added all the information I have figured out so far about splitting roots and ceiling discrepancy, as well as the colorful chart I shared here earlier, to the report on Telescoping the Integers. (link) So far, it contains nothing suggestive of new advances in integer factorization, but time and further study will tell. Some of that, I believe, will depend on whether I pop awake early with the urge to work out some more good ideas. We shall see if that happens. I could use the sleep, but if some aggravating unanswered question in my brain turns out to have a very interesting answer indeed, these efforts and reports will have been additionally rewarding.
Math Study Progress