Before starting discussing about your question, there is one thing you have wrong in your question. in every day greeting, Japanese either bow with their arm along their leg when they are man or they put their their hands in front of their belly together and then bow whenever they are woman. In Japan's case, palm together is reserved exclusively when it comes to prayer, when greeting are performed in place of worship. Especially buddhist temple. Shintoism temple' greeting is the same as everyday greeting.

Now we can discuss further about your question. As you can probably guess from the precedents sentences, how people bow in the Asian countries are highly influenced by the religion they adopted (nation wise).

There are 2 major religions in case of Eastern and southern Asia (which I simplified a lot): Buddhism and Confucianism (to which we can, in case of this thread, reattached with Taoism and Shintoism (they are different and it will be interesting to explain their differences history wise)).

I wrote a lot but I felt really short here, it's basically Buddhist=palm together and Confucianism fist in palm because of their religious signification it's really really hard to explain in English, i'm French and fluent in Chinese but that's really difficult for me to translate in appropriate wording in English of all these religious texts without the need to explain every subtilities and all the reference within the text, as if not by the nature of Chinese language a single sinogram can have multiple signification, as if not my sources are by nature already translated from Hindu, as if not the religious texts are often annotated by multiple school of thinking, and as if not there is multiple tendencies withing ONE school. The base of why Buddhist greet with plam together start with 1 sentence : 三界无有别，唯是一心作 in the "10 stages sutra" a Buddhist religious text. There is helas fuxking (sorry for that) not 27 lines, not 27 paragraphs, not 27 pages but fucking 27 volumes that explain this one line of sentence in 1 school of thinking knowing there is 3 major schools of thinking in China alone. From what I briefly read from Chinese theologist palm together is more or less the Occidental "peace sign" with link to the cosmos, how the holy light educate the faulted, purity and other 22 significations on why bow with palm together that I'm incapable of translating to you with the appropriate wording. The Confucianism side of thing is more simple. The bow fist in palm in the Zhou era is a lot more spectacular than today's. It's "heart in hand, bow to sky, bow to earth, bow to everything in-between, and bow to your dearest visitor that everything went well" a roughly 3 minutes ritual in today's reconstruction. Confucianism appropriate this as it's focus in politeness/courtesy/civility then with time it's simplified to today first in palm salute.

So to answer your question, yes it's historically accurate, the only difference is that Chineses koreans and Japanese are highly influenced by Confucianism, where other south east Asian countries are influenced by Buddhism.

Edit : I forgot source

Xinzhong Yao An introduction to Confucianism, Cambridge University Press

Han Emperors" in Cambridge History of China: Volume I xxxix-xli Cambridge University Press

Stephen F. Teiser. Introduction - The Spirits of Chinese Religion. Donald S. Lopez, Jr. Religions of China in Practice Princeton University Press.

杜维明. 《儒教》. 陈静 译. 上海: 上海古籍出版社. 2008. ISBN 9787532569397 （中文（简体））.

渡边义浩. 〈日本有關「儒教國教化」的研究回顧 https://web.archive.org/web/20141030193654/http://www.chinarujiao.net/p_info.asp?PID=145

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