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The concentric rings were a 1964 big car styling cue but this is an F85 emblem. The "bull horns" went away for 65.
You can see the concentric rings on the 1964 F85 cap, but the emblem went to "longhorn" that year.
The emblem on the OP's cap is 61-63 F85, but there's no evidence of a factory cap that looks like that.
The reason why I think it might be aftermarket is that the "bull head" logo is slightly different from the one on the factory 61-63 caps. Note that on the factory caps, the tips of the "horns" come to a point. On the Don's cap they are squared off. Also note that on the 61-63 factory caps, there is no raised lip around the emblem. This was only done in the 1964 caps (and that applies to the 61-63 full wheel covers as well).
OK, I just found this image on the web from a long-closed ebay auction. The description said 61-63 F85, but who knows?
These are 1963 Oldsmobile F-85 Poverty Caps. I have them on my "1963 Oldsmobile F-85 Deluxe", they did not come on the car but the person I purchased them from said that they were Dealer Take-Offs. Mine has the lip frame around the outsides of the bull horns. There is also a Factory Picture below of them on a 1963 Oldsmobile Club Coupe.