The knot above resembles the path taken by the donut particle to form one link of a chain segment. For the donut particle path p = 74445 and q = 4 with an equivalent toroidal "distance" of 76172 (or, 4 * 137 * 139).

The chain segment length of space is 138 links, including one of the end links. The chain segment length for an electron is 137 links. The numbers 137 and 138 result from solving a relationship.

Two key assumptions dramatically affect the solution that produces 137 and 138. First, the electron has one less link than a space chain segment. Second, the toroidal "distance" must be an integer multiple of the inverse of (n+1) * (n-1), where n is the number of links in a chain segment of space.

The stable electron has one less link and not one extra link. A missing link cannot be replaced thus increasing stability. Losing an extra link reduces stability. As a connecting chain moves one link in space it increases one chain length and decreases another. This leads to the inverse of the lengths.