
This work introduces a symbolic, parity‑based address system for the Collatz iteration. Odd integers are assigned finite roles, and transitions between these roles generate integer‑coded address sequences derived from a generative principle called the Big Bang Formula (BBF). The framework provides a uniform encoding for all intermediate states, clarifies how parity information propagates through the accelerated map, and reveals structural constraints that exclude certain periodic configurations. The resulting address system establishes a foundation for further combinatorial and structural investigations of Collatz‑related integer sequences.
3n+1, Reset of Number-System, Big Bang Formula, self-expanding number-system, Pattern of Links, Collatz-Conjecture, Numeric Topology, 2-dimensional number system
3n+1, Reset of Number-System, Big Bang Formula, self-expanding number-system, Pattern of Links, Collatz-Conjecture, Numeric Topology, 2-dimensional number system
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