There is a proposition that Alperton to Mornington Crescent can be achieved in four moves. However proof has not been accepted for the existance of this number.
*peers closely at this for some days* I have only one comment; it's just a passing comment, I don't think it affects anything, but perhaps our learned friend could clarify: Playing a Zone 1-6 Travelcard explicitly revokes everything northwest of Moor Park, which is fine, but I'm interested in the position of the Chesham spur at peak times. How does this affect the freem around Aldgate East? Just asking.