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Calculation of Total Geometric Twist in a Specific EH Circuit

A specific EH circuit has several different kinds of twist. These EH circuits are geometrically simple and precise and therefore each kind of twist can be exactly calculated. The previously developed total twist for AH and NH ignores unit twist plus strucural twist =utt. However any attempt to relate twist to energy in a specific circuit will need to sum these constant twists with the total circuit twist in a given circuit. Thus the total twist when including utt would be an addition to the polynomials already given.

The topological twist has both a global and a local metric. A short segment of EH links has a local twist. The entire closed circuit has a local twist confined to its own ribbon twist and a global twist depending on how many entwinned circuits are occupied that link with it. An unoccupied circuit leaves holes and does not add linking twist. The entwinning and up down meandering add linking and writhing twist respectively. This complicates the calculations but by breaking them down to specific types of twist the exact twist can be determined. A computer program is the best way to do this but this discussion here showing how to write the program is needed.

List of twists in an EH circuit:

unit linking twist= ult= +1 per link (see page 11)
unit structural twist= ust = -1/4 per link (see page 11). It could also be seen as -1/2 twist per link since an adjacent link is in the same orientation when it is in a straight line such as xx. Thus as the new link moves forward along itself it must rotate 180 degrees to put it back in the same orientation, but moved forward one link.
unit total twist = utt = ult+ ust = 0.75 per link=+0.75L where L is the total circuit length. If the twist of ust is -1/2 then utt = 1/2.

The below twists are negative for AHn and positive for interior NHn circuits.

circuit twist = ct = 1/2 times no. of changes of xy or traverse direction in the circuit.
Circuit twist is linear when seeking total twist in AHn or NHn, see polynomial for it in calcs.

linking twist = lt = Sum((xt>=3)-1)/2 (see page 6)
Where each linear x traverse of links is 3 or longer subtract 1 and add them all up then divide by 2 to get the total linking number. Each unit of linking number is equivalent to 1 twist(from knot theory).
Linking twist is linear when seeking total twist in AHn or NHn, see polynomial for it in calcs.

writhe twist = wt = (Sums(MinMax(abs)Sum of z-4))/4 (see page 6)
Writhe twist is not linear and therefore it must be
calculated separtely per n if seeking AHn or NHn total twist. A polynomial for its average estimate is possible.

circuit total twist = ctt = ct+lt+wt+utt.
the above should be enough info on twists to begin progrmming
Each of these twists is affected if some circuits are missing in an entangled group.