The OEM IRC GP-5 tires are size
80/90-17 which is already 3.0-ish. The 80 stands for 80mm or ~3.15".
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Tire sizes are a bit arbitrary and knobs add to the external dimensions of a tire beyond the width of the carcass. The same tire's width will also vary based on the width of the rim it is mounted on. If you are looking to run a wider 80/20 dual-sport tire you may want to consider running wider rims than stock. Even then, you'll find that there aren't many options that are 17", wide enough for what you desire while being skinny enough to fit the CT, and reasonably available for purchase to the USA. The IRC GP-5 in 80/90-17 is an OEM tire for the CT125 and CC110 (
Cross Cub, which even has them on tubeless wheels) and was likely designed specifically for those Honda Cubs due to a lack of dual-sport tires on the market sized to fit them. Common dual-sport tires like the Michelin Anakee Adventure, Pirelli MT60R, and Shinko 705 all run significantly wider even in their 17" front tire offerings.
A few CT125 owners in Japan are running wider rims paired with
Timsun TS823 tires in 100/80-17.
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AFAIK that brand isn't sold in the USA and because they are probably not DOT approved it would be a gamble whether or not they would make it through customs if you were to find a company willing to ship them. You
might be able to get a shop that sells Dunlop tires to order the Dunlop D604 in 80/90-17 for you which
looks slightly wider than the IRC GP-5.
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