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The thread on this forum entitled "Non Trivial Identities" has had the most responses of any thread to date (39 responses so far).  The thread contains a great deal of useful information, including a detailed analysis of non-trivial identities of length 12q.  The thread may be found at http://cubezzz.homelinux.org/drupal/?q=node/view/114 (you have to login to see all the responses).

I tend to view the problem of analyzing identities more in terms of duplicate positions than in terms of identities, but you can of course easily transition from one view of the problem to the other.  In any case, the problem of finding a formula for the number of moves at each distance from Start is closely tied to the problem of finding duplicate positions and/or non-trivial identities.