Passage: During the Classic period the major branches began diversifying into separate languages. The split between Proto-Yucatecan (in the north, that is, the Yucatán Peninsula) and Proto-Chʼolan (in the south, that is, the Chiapas highlands and Petén Basin) had already occurred by the Classic period, when most extant Maya inscriptions were written. Both variants are attested in hieroglyphic inscriptions at the Maya sites of the time, and both are commonly referred to as "Classic Maya language". Although a single prestige language was by far the most frequently recorded on extant hieroglyphic texts, evidence for at least three different varieties of Mayan have been discovered within the hieroglyphic corpus—an Eastern Chʼolan variety found in texts written in the southern Maya area and the highlands, a Western Chʼolan variety diffused from the Usumacinta region from the mid-7th century on, and a Yucatecan variety found in the texts from the Yucatán Peninsula. The reason why only few linguistic varieties are found in the glyphic texts is probably that these served as prestige dialects throughout the Maya region; hieroglyphic texts would have been composed in the language of the elite.Stephen Houston, John Robertson and David Stuart have suggested that the specific variety of Chʼolan found in the majority of Southern Lowland glyphic texts was a language they dub "Classic Chʼoltiʼan", the ancestor language of the modern Chʼortiʼ and Chʼoltiʼ languages. They propose that it originated in western and south-central Petén Basin, and that it was used in the inscriptions and perhaps also spoken by elites and priests. However, Mora-Marín has argued that traits shared by Classic Lowland Maya and the Chʼoltiʼan languages are retentions rather than innovations, and that the diversification of Chʼolan in fact post-dates the classic period. The language of the classical lowland inscriptions then would have been proto-Chʼolan.

Question: What do they commonly refer the inscriptions as?
Classic Maya language