A Structural and Dynamic Modeling of the Collatz Conjecture: An 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 replacing the analysis of individual trajectories with the study of a deterministic hydrographic network, we highlight rigid mechanisms of transmission and absorption of the arithmetic flow. We demonstrate in particular how the modulo 8 filter, coupled with a binary parity analysis, imposes an algebraic stopping wall on the ascending phases of trajectories, thus reducing the conjecture to a well-defined problem of chaining finite blocks of information.