I've heard the claim that the current Chinese calendar was introduced some times around 2637 BCE by Emperor Huang Di. Apparently, written records date back to about 4,000 years ago and before that the Chinese didn't put dates on their documents. Does anybody know how well supported is this claim? Is it possible that the historical evidence is not accurate, and that the calendar and Chinese writing could have happened a few centuries later than the above-mentioned dates? Thanks.
The Yellow Emperor (Huang Di) is a mythical character to which many inventions are attributed. However, like King Arthur or Robin Hood, there is no evidence that he ever really existed.
The legend actually does not credit the Yellow Emperor with creating Chinese script, but rather to his historiographer and magician named Chang Jie.
The earliest forms of Chinese writing that can directly trace to modern Chinese writing are called Jiaguwen script (甲骨文). Over 150,000 fragments of Jiaguwen were found at Anyang in Henan Province.
The Jiaguwen writings were carved on tortoise shells which were then cracked by burning in a fire. The pattern of cracking allowed divination and fortune telling. The Jiaguwen script dates to the late Shang Dynasty and a few continued to be used into the early Zhou dynasty. The dates being spread between 1400 BC and 1050 BC.
Jiaguwen was already a well defined writing system by at that time leading some to speculate the the first script was several hundred years earlier than this.
Since these writings were made on tortoise shells, an organic matter, they can be accurately dated using modern methods such as carbon dating or similar. We don't only depend on historical documentation. We can thus be reasonably certain of the dates involved.
Re-reading your question, I think you have miss understood what the Chinese calendar is. The Chinese used a calendar to measure time and place events but not in the way that we use a calendar today. They don't write dates on documents using the Chinese calender like we might write 7-16-2013. There isn't a single start point from which everyone begins. There is not Chinese calendar equivalent of 1AD.
The Chinese used reigns of emperors to measure years e.g., the year 825 BC was marked as the 3rd Year of the Xuan King Jing of Zhou (周宣王三年). From the Han dynasty on, the reigns were given names by the emperor. These regnal names might be changed several times during the rule of one emperor. The Ming and Qing usually used one regnal name per emperor. However, no reigns were used prior to 841 BC during the Zhou dynasty.
So the Jiaguwen script doesn't say what year and date it was writen. It may mention times, days, months but not a year that can be translated into our modern calendar system. So there is no document to say how old it is.