Hidari-mitsudomoe Mon and Association With the Numazu-Mizuno Clan

[ckaiserca]

I have a koshirae for a sword that Lord Mizuno Tadanori, the last hereditary leader of the Numazu-Mizuno Clan, supposedly carried. The menuki and fuchi-kashira both feature Hidari-mitsudomoe (three commas) mon. When I searched online for an association with the Numazu-Mizuno Clan for this Mon, I couldn't find any evidence. Still, when I asked ChatGPT, it says that they were fudai daimyō (hereditary vassals of the Tokugawa) and that the Mizuno clan, including its Numazu branch, historically used the Hidari-mitsudomoe mon as their family crest. Can anyone provide a source for confirmation of this information? 
 

Also, the mimi of this sword's tsuba bears a repeating pattern of what I believe to be another mon, a gold leaf pattern. Is there an association there?

 

I have attached photos of the rim of the tusba, fuchi, and menuki. 
 

Thanks for any help that you can provide!

[PNSSHOGUN]

Daimyo owned items would likely exhibit a primary family Mon, along with their specific branch Mon. I would place zero trust in anything AI comes out with regarding such matters.