5 Point Energy Minimization Suite


This webpage has links to my work that relates my (claimed) solution of the N=5 case of the 1977 Melnyk-Knop-Smith Conjecture. This conjecture predicts the power-law phase transition in 5-point energy minimization. A special case of my main result is a solution to Thomson's 1904 problem about 5 electrons. I had already solved this some years ago. Here is a reference: Here is my monograph, which (I claim) solves the N=5 case of the MKS conjecture: My various failed attempts to get some version of this monograph published have left me doubtful that I will ever publish it. In spite of my efforts to make the latest version of the monograph modular and checkable, the monster still gives the impression of being too difficult to referee. I wrote the latest version with the idea that it could be checked in a distributed way, with a team of people each verifying small parts. I even included a complete logic tree for the proof. (See Figure 0 in the monograph.) However, I did not quite make the details of the distributed checking process clear. While the proof divides neatly into independent parts, these parts rely on some common background material in a way I did not make explicit. So, it is not obvious what each member of a team of verifiers would need to read. To make the distributed checking process clear, I have broken the monograph into 7 papers which are all independent from one another. This adds some length, because now some background material appears in several different places. On the other hand, each paper can be checked separately from the others. Paper 0 gives the overall argument, simply assembling the results from Papers 1 - 6. Here is a discussion of the dependence of these papers on the computer. Papers 3 - 6 rely on relatively straightforward computer programs, written either in Mathematica or Java. These programs perform their calculations with exact integer arithmetic. The programs are relatively short and a competent programmer (in each case) could probably reproduce the programs in a day. The software you can download for Paper 5 is quite extensive, but most of it is present for the purposes of experimentation. The proof part is quite short. Paper 2 relies on a big Java program that runs its calculations using interval arithmetic. The calculations take about a day to run. The program comes with an extensive graphical user interface and its own documentation. Given the detail with which I have described the calculation in Paper 2, I think that a good programmer could reproduce the code for Paper 2 in a few weeks.