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After reading this useful link and following some of the repair suggestions, I still cannot fix the manifold edges.

What is non-manifold geometry?

Its not clear to me where the issue lies? I do not want to add a thickness to the area yet until I resolve the non-manifold. Any suggestions are appreciated. Thanks!

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Anything with 0 thickness is non-manifold. Manifold is a shape with volume of which all faces are facing "inward". Your model has no volume and therefore no "inward", so it is non-manifold

You "not wanting to add thickness to the area yet until resolving the non-manifold" is exactly what is causing it to be non-manifold. If a shape has no thickness, it CANNOT be manifold.

Think of it as trying to fill the volume of a 3D shape up with water and then shaking it around. If water leaks out, or you simply cannot fit any water in it because it has no thickness: then your shape is non-manifold.

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