New Game: Torus

First I have to thank Torben Mogensen for both posing the torus
problem and for identifying the error in my first attempt at a
solution.  Bill Taylor also deserves mention here.  We've spent a lot
of time in the same neighborhood lately with him always arriving at
the intersections a step ahead of me - not necessarily with the ideal
solution in hand, but first nonetheless.

Torus rule sheet:
  http://www.marksteeregames.com/Torus_rules.pdf

In Torus a filled board produces exactly one winner.