Rivkin

Nakago was cleaned recently, i.e. the rust inside characters is actually quite old. I am 80% for the signature being authentic. Probably 1670-1730, might be a lesser known generation in 1700s, it is often the case as sword market collapsed completely 1705-1710. Not a typical style for the school, but one of Edo period's attempts at something Rai-ish.

There are many old genealogies connecting the lineage to Rai or Bizen, but in reality its provincial Yamato offshoot.

Nothing clearly stating water, but often boshi area is more instructive.

Writing style, yasurime: Edo period Work: kind of Muromachi looking.

Looks like a nice Muromachi nakago with likely non-shoshin writing.

Its a bit tired, its not as impressive as the best Ryumon works, its his more Yamato than Bizen style, i.e. very Senjuin in style. The suriage is surprisingly recent and for some reason was accomponied by yasurime which was done without much dedication to the job. However without all these things we would be talking about what, TJ blade? So its all these arguments versus the price.

Boshi would reveal much. As is better picture of nioiguchi. Can be Mihara, but much more likely its Echizen Rai or someone related to it - from Rai Kunizane to Rai Kuniyasu.

Not the top but average Hizen or imitation. Yokoyama Bizen actually made good Hizen looking swords.

Possible, though with Uda of this type I would prefer to see a long kaeri.

Yamato style activities, Muromachi. The mei is ambitious but might paper with a note (Muromachi).

Yes its interesting and unusual. The hamon profile reminds one of late Muromachi. Strong nie activity like this in combination with nie hamon was seen in shinshinto and in late Muromachi, Momoyama included - some Bizen smiths at the time experimented with hard nie which forms ara nie, kinsuji, sunagashi etc..

Yamato=high shinogi. The school is known for thick kasane relative to others in Nambokucho period, mostly around 0.7cm but much larger thickness at shinogi, which if I remember correctly exceeds 1cm.

10mm at shinogi.

I would think not. Low shinogi the difference can be close to zero. In sue Bizen and a few others. Yamato is a definition of high shinogi. Typically has 0.6 (usually 0.7) -0.75cm kasane so 0.55 is very thin for it. It has shinogi kasane I think often in excess of 10mm but I don't have the books in front of me. So, no this blade does not sound like Yamato or high shinogi, but then its a very secondary information.

Its Edo period most likely, but having full nakago picture would help. Boshi contour is sort of visible but again could help.