Are the Cantonese word 係 and the Japanese word はい related? The Cantonese word meaning "to be", written as 係 (Jyutping: hai6) sounds similar to the Japanese word はい ("hai" in various Romanizations). Both words are used to answer "yes" or "it is correct" to yes-no questions.

The Japanese Wikipedia article on Cantonese contains a sentence I find interesting:


  「係」は肯定の返事にも用いられ、日本語の「はい」の語源という説もある。


I think the second part of that says that there is a theory that 係 in Cantonese is the source of the はい in Japanese. However, the article does not provide any sources for this statement.

My questions are:


Is this theory documented anywhere? And what are the details of this theory?
Is this theory plausible?
What is the source of the Cantonese word 係 (meaning "to be", ignoring the other meanings of that character) in Middle Chinese?
What is the source of the Japanese word はい?
Is it possible that they share a common source?


related: https://www.quora.com/Are-the-Hais-in-Japanese-and-Cantonese-related
The Japanese wiki page mentions that the claim is a "folk theory" that is "denied by academics". 

An alternative etymology for Cantonese hai6 comes from 系/繫. I don't have this book, but apparently Jerry Norman suggests this in Chinese (1988). This word had a very early meaning of 'to be connected', was used as a copula in later texts, and the phonological evidence is certainly not lacking. 

To summarize the wiki article, はい is thought to come from either 拝, a courteously used Sino-Japanese word, or a corruption of similar words such as "ai" and "ei". It is only attested from the Edo period onwards, which is very recent. 

Considering the relative isolation of Japan in the past few centuries, the word would have had to travel from Japan into rural Chinese villages in the past 100 years or so. Even if this did happen, it would likely have been heavily documented by various sources. The Chinese-internal etymology is much simpler and I personally see no reason to believe the Japanese etymology without further evidence.