Second thoughts on the dual of the extended beta move

Continues “Dual of the extended beta move. Termination as implosion or blow-out“.

After the night I found another way to look at the dual of the extended beta move. Recall that in the previous post was proved that the dual of the extended beta move is equivalent with this mystery move.

fundam_epsilon_dual2

The graph from the left hand side can be expressed by using the (emergent algebra) crossing macros:

fundam_epsilon_dual5

This form of the graph makes obvious where to apply the extended beta move. Let’s see what we get.

fundam_epsilon_dual6

Therefore it looks like the mystery move is a combination of the extended beta move and elimination of loops. There is no need to replace the termination gate by a trivalent graph, as suggested  in the previous post, although that is an idea worthy of further exploration.

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