Is the blue-and-white porcelain general jar the official kiln?

yes. According to the query of personal library network, the Tianzi style of blue and white porcelain general jar is a kind of style of Chenghua official kiln, and Chenghua Tianzi jar is very famous. It is a small pot with short neck, straight mouth, rich shoulders, abdomen and wide bottom. The height is generally about 1 cm, and the bottom of the pot is written with the word "Tian" in blue and white, hence the name.