I think it is mathematically no true. And Etaler implements a modified TM alforithm. Let me try to explain.
First of all. For any given bit in a SDR, since the TM predicts weather a bit is on or not by using cells in the column, the TM has cell_per_column ways to activate it. Secondly, Etaler implements the connect-to-all synaptic growing algorithm. Causing it assuming identical input patterns with unknown context to be the same unless the context suggest otherwise or learned the relation later on.
From Etaler’s TM’s perspective, the sequence [A, A, A] is [A, A, A]. And the sequence [A, B, C, B, C, D] will initially recognized as [A, B, C, B, C, D] until it discovers it actually be [A, B, C, B’, C’, D].