[r-t] Helixoid pipeline completes

[Mark Davies]

Philip has prompted me to send this on to the list. My full Helixoid 
pipeline has completed, with a crop of methods that may rival "H and J". 
I sent this to Philip:

========================================================

I have some new results for you. The previous searches only fully
exhausted the smaller lists of Double methods - in particular those with 
only x, 14, 36, 58 and 18 place notations (although the TV expansion 
allowed a wider range).

Processing the bigger space, with all PNs involving at most one
consecutive place, opens up some extra paths for the (123) triplet, so
gives us new possibilities during the TV expansion. For many days
nothing popped out, but now the full pipeline has completed, it turns
out there is at least one other set of "splice-sister" methods that is
worth a look. Here they are:

Base method:
-16-58-14-14-18-38-16.34.16-14-58-58-38-1458-36-1458-16-14-14-58-38.56.38-16-18-58-58-14-38-16, 

14 = 31257486

Double splice-sisters:
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-58.14-58-58-18-16-38.56.38-58-14-14-16-14.38-56, 

14 = 31278564
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-58.14-58-58-18-16-38.56.38-58-14-14-16-14.38-16, 

14 = 31257486

You will note that we have two possible half-leads for the sister splice 
this time, which means a choice of leadends. So you could still ring 
two-spliced, but have different leadhead orders for the two Helixoids, 
which might be nice, if you don't think it makes it too hard.

There are also a number of non-Double Helixoid variations of this set 
(all with 14 leadend):

-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-58.14-1258-1258-18-16-38.56.38-58-14-14-16-14.38-56
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-58.14-1258-1258-18-16-38.56.38-58-14-14-16-14.38-16
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-1458-16-14-14-58-38.56.38-16-18-1258-1258-14-38-56
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-1458-16-14-14-58-38.56.38-16-18-1258-1258-14-38-16
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-1458-16-14-14-58-38.56.38-16-18-12-1258-1458-38-56
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-1458-16-14-14-58-38.56.38-16-18-12-1258-1458-38-16
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-1458-16-14-14-58-38.56.38-16-18-58-58-14-38-56
-16.58-38-58-58-14-16.34.16-38-18-14-14-58.14-36-1458-16-14-14-58-38.56.38-16-18-58-58-14-38-16
-16-58-14-14-18-38-16.34.16-14-58-58-38-1458-36-58.14-1258-1258-18-16-38.56.38-58-14-14-16-14.38-56
-16-58-14-14-18-38-16.34.16-14-58-58-38-1458-36-58.14-1258-1258-18-16-38.56.38-58-14-14-16-14.38-16
-16-58-14-14-18-38-16.34.16-14-58-58-38-1458-36-58.14-58-58-18-16-38.56.38-58-14-14-16-14.38-56
-16-58-14-14-18-38-16.34.16-14-58-58-38-1458-36-58.14-58-58-18-16-38.56.38-58-14-14-16-14.38-16

The next best possibility from the full pipeline is this pair:

-16-58-14-38.14-14-14-14.38.56.18-16-18-14-1458-36-1458-58-18-38-18.34.16.58-58-58-58.16-58-14-38-16
-16.58-58-18-38-18.34.16.58-58-58-58.16-58-14.58-36-14.58-14-38.14-14-14-14.38.56.18-16-18-14-14.38-16

Which can also be had with a 56 half-lead. Here both sisters are
wrong-place, though. And that appears to be it really - lots more
examples like this second set, but generally all wrong-place, and more
and more similarity between the methods in the set.
========================================================

However, as Philip pointed out, the new methods are not true Double 
methods in that their halflead and leadend changes do not match. So 
perhaps that still leaves H and J as the shining stars of the splice 
sister search.

MBD