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You might want to take care of the heel/stabilizer fix before correcting the frown. Chances are without doing that you will honing into the stabilizer or by trying to avoid the stabilizer you could...

Yes, straight strokes on a hone will put a frown in a razor especially if the spine has a curve in it, even a slight one. The blade edge should follow the curve of the spine.

Bob

You likely will have to reshape the heel/stabilizer so you do nor hone into the stabilizer. The should be a few threads on the forum on removing frowns and reshaping the hell/stabilizer. Good luck.
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