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Polar ring galaxies are rare systems with two planes of stars and gas at nearly right angles, making them natural experiments for testing the shape of the gravitational field. When published models fit the dark matter in these systems, the results keep coming out in geometrically extreme shapes, squished flat or stretched long, rather than the roughly ball-shaped halos that standard theory expects. The modeling is also demonstrably degenerate: two teams modeled the same galaxy within the same paradigm, both found extreme flattening, and they pointed it in perpendicular directions depending on which visible component was treated as dominant. Three competing frameworks can all explain these extreme shapes in massive systems where there is enough visible mass to provide everyone an escape route. This paper proposes a way to break that tie: find a polar ring light enough that it cannot reshape the host galaxy's gravitational field and use it as a probe, crossing through the host's gravity at a right angle. A smooth crossing would suggest a three-dimensional cloud. A steep gradient at the midplane would suggest something more concentrated and lower-dimensional. The EP/Hermes framework further predicts that the steepness should depend on the host galaxy's age, a pattern that neither standard dark matter theory nor MOND would naturally predict. The claim level is proof of concept: the published data already contains the right experiment, the results are not trivial, and a specific observation would settle what the current literature cannot.