Keeping the map

First Trans Person to Obtain Legal 'Non-Binary' Sex Status Changes Back to Birth Sex in Blow to LGBT Movement

In a multi-gendered world with complete transformations there can be no map.  Any backward path would be unknown, or more precisely, should be neutral to the party.

The more interesting case is the gender traveler that retains the map. They can hop between gender nodes, close the loop in the map and always point back to the start. However, at no point has the traveler been completely regendered. So does the traveler become, ultimately, genderless by traveling among the options?