Inner product in the join

The inne producgt. One can see the two graphs crawled a cross of the two. The null nodes passes through, it is a valid node. At any time the combined logic can declare a match and halt the process. I will enable the distributed poropery easily, letting both cursors descend in the same loop. Or, the attachments can guide the push pop sequence with return status.
  This join loop will follow a diagonal of matching Dots, the shortest path to completion when any Dot element can terminate the match function..

 "a.b.c"   join   "d.e.f"
 "a ." : "d ."
   "a ." : "e ."
     "a ." : "f ."
       "a ." : " @"
         "b ." : "d ."
           "b ." : "e ."
             "b ." : "f ."
               "b ." : " @"
                 "c ." : "d ."
                   "c ." : "e ."
                     "c ." : "f ."
                       "c ." : " @"
                         " @" : "d ."
                       " @" : "d ."
                       " @" : " "
                     " @" : " "
                     " @" : " š"
                   " @" : " š"
                   " @" : " µ"
                 " @" : " µ"
               " @" : " µ"
               " @" : " Ð"
             " @" : " Ð"
             " @" : " ë"
           " @" : " ë"
           " @" : "  "
         " @" : "  "
       " @" : "  "
       " @" : " !"
     " @" : " !"
     " @" : " <"
   " @" : " <"
   " @" : "W ."
 " @" : "W ."