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Rules:
Some spots are fine, others have seams. There are marked seams on the mesh, but the UV map is seamless, and removing the marked seams seems to have no impact.
Edit: No seam visible when looking at normals or tangent via a geometry node, nor when looking at the UV map applied to the model as color. I'm pretty sure it has to be something to do with the UV mapping node.
Edit 2: I've uploaded the file here.
People can help figuring out quicker if you share blend file. Remove anything that is unrelated or not sharable, purge unused data blocks, pack resources, upload somewhere.
This is not my area of expertise so I can't be of much help.
Because they're tangent space normals, and where there are seams, tangent space changes sharply. It is not that the normals (world space or object space) are discontinuous; it is that the tangent space is discontinuous, and so the tangent space normals are discontinuous, even though the world space normals are not. (Tangent space is a space where the +Z vector points in the direction of the sampled normal and the +X vector points in the direction of increasing U, from your UV map. The normal map color is a remapped vector intended to be interpreted in this tangent space. The direction of increasing U changes sharply across seams. Which is okay.)
Seems different on this case where normal map is continuous but tangent normal is not. I guess you can unwrap the ring in one piece to have only one seam and hide it somehow.
Almost always related to Texture Coordinate
The usual method is to plug a texture coordinate into a mapping node and then the mapping node into the vector input of the texture. The texture coordinate node controls how a texture's position maps to a mesh's surface. The mapping node let's you make adjustments to that mapping. Example below:
Unfortunately, has no effect. I think the default for image texture nodes is to use the UV coordinates.
Maybe it's from the mesh? In edit mode select all vertices and merge them by distance. It's probably not this but this has magically repaired my meshes too many times
No changes. :(
Hmm, does it have any colour when in edit mode? Maybe it's a crease?
The edge is highlighted in red, since I have a texture seam marked there, but the texture is seamless so it shouldn't be creating a seam from my understanding. I've uploaded a copy of the file here.
If you use a smooth by angle modifier and set it to 60° the line will dissapear, although it seems to mess with the reflection too, I'm new to this too so I'm not of much help.
You may need to enable smooth shading for the respective objects?
Already enabled, and while there are some sharp edges, this one is left round. Even clearing all sharp edges makes no difference.