Unpredictable Strings

The paper’s Theorem 4.1 claims an uncountable set of unpredictable realizations but the given proof only cites the existence of one unpredictable point for the Bernoulli shift and argues via (claimed) orbit density; it does not actually establish uncountably many unpredictable sequences or provide a direct cardinality argument (see the statement/proof block for Theorem 4.1 and surrounding discussion) . By contrast, the model’s construction explicitly builds a continuum-sized family of sequences with disjoint enforced blocks guaranteeing arbitrarily long unpredictable strings, and then notes that the canonical product space uses all sequences as realizations. Definitions of “unpredictable string” and “unpredictable sequence” match those in the paper .