Automorphisms of the Young-Fibonacci tableau tree

We classify the automorphisms of the unfolded upward-path tree of the Young-Fibonacci lattice.  Nontrivial local permutations occur exactly at path vertices of shape \(2^k1\), where the branches ending in \(2^k11\) and \(2^{k+1}\) may be exchanged.  Every compatible portrait is realized, and we compute the orders of all extendable finite-level quotients.

This manuscript addresses the intended mathematical problem identified in the source.

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Mathematics subject: math.CO; source problem: OP-0230.