Rivkin

This one is Meiji so the purpose might be unclear (decorative), but I've seen quality netsuke which were miniature and semi-functional swords. Sometimes dolls also have neat swords.

Nah, does not look like a shoshin granite. Imitation.

It is out of polish, with a very crudely moved hamachi, married with modern repro tsuba. However, I personally don't see glaring mistakes which Chinese typically make. The signature is chiseled faintly, in Japanese rather than Continental calligraphy, the nakago has decent patina. Sugata is a bit strange, being completely straight it is not a good match for the nakago, but such things do happen and most elements are executed ok-ish. Also I suspect its not a particular expensive smartphone placed closer to the nakago, it tries to auto-correct for distortions in optics (the cheaper the optics the more it distorts) and therefore it might be straightening the blade. The work itself is periodic gunome with even togari-choji appearing in some "gunome" elements. This is something one sees on showato now and then, on Chinese fakes, but it also appears on Bizen and Bizen like swords from the end of Muromachi. Overall I would be inclined to think its Bizen Yasumitsu from 1560s. Its a lower grade sword in poor condition, but I don't think its a crime.

Without full clear image of the nakago its difficult. It can still be from around 1570 in poor polish, but we need to see the full nakago without angles etc.

.... I got to learn writing seller's description like this one.

In my limited experience, recent NBTHK papers to "Wake" have a decent chance of being challenged. Basically its a small Kamakura period group that sometimes forged with stand out mokume hada not unlike some of Aoe works, sometimes did very ko Ichimonji looking quiet style with indistinct itame jigane, you have suguha-notare, you have saki choji, and at times you have both on the same blade. Their hamon tends to be a bit on a weak side with limited expression. So if its Bizen but clearly a weird one there is a recent tendency to say Wake. When its shown to someone else they might say instead Aoe or some mainline Bizen smith. Ofcourse if you send it to a drastically different shinsa high chance they'll say Muromachi Kaga. Its not a very distinctive style and therefore "Bungo-Kaga" is a real risk when looking for alternative opinion.

The writing style is consistent with Muromachi.

Its something quite weird. Nakago is more or less clearly 20th century or at least no later than the very end of Edo. Sugata which is as straight as they come, uncommon kissaki proportions. Silver inlaid signature which makes little sense. But at the same time everything is done with diligence, it does not have the aura of some crappy thing churned out in search for a random buyer. This is the kind of case where I would look at activity and if its good, it can still be a decent blade, with a puzzle.

Honami Nishu loved writing sayagaki to big names...If it was ko Bizen it was at least Tomonari, if Naminohira it was Yukiyasu, if Sairen - Bungo Yukihiro. More optimistic than green papers. Otherwise... there is unfortunately not much to be seen in photos. Suppposedly it has great jigane, which maybe true, but the photographs do not present any evidence.

I have seen maybe three or four truly important swords with a history of being in the US. Out of hundreds. It matches statistics on kokuho quite well. 99% of the top tier swords did not leave Japan and were never in the hands of the occupation troops. Accordingly, I am not certain what kind of intentions did the occupying powers have vis-a-vis swords. Often the laws banning "all weapons" are issued not with the purpose of actively confiscating those but to simplify court-martials: establishing any connection with a "weapon" becomes a sufficient cause for punishment.

Its most likely naginata, but its not clear how much it lost, so it can be late Nanbokucho, early Muromachi, if severely reshaped it can be late Muromachi. Most likely (very little which is seen and taking into account someone who knows words Nagato Sa thought it is one) the hamon will be midare-gunome-sort-of-ish... which can be Mino, can be sue Sa, can be even atypical Bizen - taking in mind its in a very poor polish. There is a slight chance with better pictures there will be something warranting something more specific.

Nagamitsu tends to have very well defined choji, with a few exceptions. This one is notare-midare. Other things are weird as well.

There are surprisingly many Masamune TH. Some are TH because they have a lot of damage; I personally believe there were two "Masamune" - real one, early smith with a very calm work, and someone from 1330-1360, very close to Go with a crazy over the top style, but at least one fukure per blade. If you don't see fukure, it has been suriaged (yes, he could do fukure in nakago). If there are 4 fukure each 1-2cm in size (there are such blades) it does not get above TH. The second case is Masamune which becomes Shizu at Juyo (too much masame to ignore).

With me looking at the package raises questions. To be short and practical if the blade has no modern papers I would disregard the origami. If it has papers to Nagamitsu I would disregard internet opinions. In deep theory its possible its Nagamitsu and origami is original, but there are significant things I don't like about either one.

95% of "serious" nihonto crowd 70 and older believe "you should not photograph a blade". Its a waste time and a sign of being unprofessional. One is supposed instead to hold it and "read" it by reciting out loud what you see. Accordingly you kantei by "reading" the blade and then comparing the description to texts. This allows one to study potentially without ever seeing a real nihonto, you just go through oshigata and textbook descriptions. First problem, you visit different societies and people in Japan with the same blade and you realize the terminology changes considerably. Its like martial art, you have a dojo, a sensei, and he knows how to do things. Second, a single word "itame" covers about 30-40 very different hada. Third, oshigata and textbooks cover only the "classics", i.e. how Kunitoshi is supposed to look like, not how it can look like in real life. Often studying sayagaki and "papers" from 1900+ generation it feels many back then studied a lot of oshigata and very few actual blades.