Bit-Position Dynamics and a Lower Bound for Collatz Cycle Length
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We present a novel reformulation of the Collatz conjecture by leveraging the binary structure of positive integers, focusing on the sequence of odd terms. Through an analysis of leading and trailing bit-position dynamics, we derive a substantial lower bound of at least 17,026,679,261steps for any hypothetical non-trivial cycle, offering new insights into its structural constraints.
