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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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A Symbolic Reconstruction of Parity-Based Adress-Systems

Authors: Huber, Karl;

A Symbolic Reconstruction of Parity-Based Adress-Systems

Abstract

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green