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The "Cutter" crease seen on cowboy hats is a modified "Cattleman" crease. In the 1970's the "Cutter" crease had bumps put of the side crease of the crown of the cowboy hat.
The bumps on the crown gave cutters more head room in their cowboy hat when performing on a cutting horse in the cutting arena.
You would have seen a "Cutter" crease on one of the most famous cutter - Matlock Rose. Rose born in 1925 died in 2008 earned the NCHA World Championship in 1964.