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This work aims to formalize the global dynamics of the Collatz sequence through structural modeling.

June 14, 2026Open Access

A STRUCTURAL AND DYNAMIC MODELING OF THE COLLATZ CONJECTURE Approach via the Marker Method and Binary Escalation

Key Points

This work aims to formalize the global dynamics of the Collatz sequence through structural modeling.
Introduced a four-level structural taxonomy for analysis.
Used a modulo 8 filter and binary parity analysis to impact trajectory phases.
Developed a formalization of inverse junctions across absorption wells.
Demonstrated rigid mechanisms controlling arithmetic flow transmission and absorption.
Identified algebraic stopping walls affecting ascending trajectory phases.
Enhanced model with structural frameworks to analyze 'sawtooth' trajectories.

Abstract

This article introduces a formalization of the global dynamics of the Collatz sequence through the lens of a four-level structural taxonomy. By substituting individual trajectory analysis with the study of a deterministic hydrographic network, we highlight rigid mechanisms governing the transmission and absorption of the arithmetic flow. We demonstrate how a modulo 8 filter, coupled with binary parity analysis, imposes an algebraic stopping wall on the ascending phases of trajectories. This second version enriches the model by introducing a formalization of the inverse junction across all absorption wells, providing a rigorous structural framework for analyzing "sawtooth" trajectories.

A STRUCTURAL AND DYNAMIC MODELING OF THE COLLATZ CONJECTURE Approach via the Marker Method and Binary Escalation

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Abstract

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