A Symbolic Reconstruction of Parity-Based Adress-Systems

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.