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

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.