Across diverse physical systems, from nuclear matter to cosmic plasmas, stable structures exhibit recurring patterns of bipolar organization, layered morphology, and counter-rotating flow, despite operating under vastly different force laws and energy scales.
This work proposes that such recurrence reflects a universal interaction topology rather than a universal force.
Building on a vortex-based description of interacting flows, we identify the tri-vortex monopole as the minimal stable interaction unit in a continuous medium.
Each vortex is shown to possess an intrinsic four-arm spiral architecture imposed by symmetry and circulation conservation in a bipolar environment.
When three vortices, two of like polarity and one of opposite polarity, interact, their spiral arms cannot connect arbitrarily.
Topological closure, phase coherence, and energy minimization force the system to organize into a double-loop structure: an internal coupling circuit formed by three direct arm connections and an external return circuit formed by four additional arm pathways that link the top and bottom vortices with the lateral vortices.
The redistribution of the six resulting degrees of freedom of binary polarity yields exactly seven distinct global configurations, corresponding to a hierarchy of seven stable interaction layers.
This layer count follows combinatorially from the six binary variables, independent of any specific force or material substrate.
The tri-vortex monopole and its seven-layer hierarchy thus constitute a geometric attractor for interacting flows, providing a unified topological foundation for layered structure formation across scales and disciplines.
Subsequent papers will demonstrate how this universal topology is realized in specific physical contexts, including nuclear binding, biological growth fields, and astrophysical plasma structures.
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