Beyond the animal it carries, a branch enters three fixed sets of relations that the almanac and the fate-calculation tradition use constantly. Shen belongs to the trio Shen, Zi and Chen, one of the four groups of three branches spaced four apart which are read as combining into Water. It clashes with Yin, the branch six places away, and it forms one of the six harmonies with Si. These relations are properties of position in the twelve, not of the animal.
The branches also do more work than the year cycle they are best known for. They divide the day into twelve double hours, so Shen names a period of two hours as well as a year and a month; they mark the twelve directions of the compass, Shen standing at west-southwest; and they carry the twelve stations against which the movement of Jupiter was tracked, which is one proposed origin for the twelve-year cycle itself.
The stem-and-branch day count is the longest continuously running day count known. Numbering days by ganzhi begins in the Shang inscriptions and has run without acknowledged interruption since, through every dynastic change and every calendar reform, because the cycle of sixty is independent of any astronomical quantity and therefore needs no correction. Chinese historical dates from the classical period onward can be checked against it.
Shen opens the autumn in the month assignment. Its clash with Yin is one of the six, and because Yin opens the year the Shen and Yin axis divides the year in half, which is a structural fact rather than an interpretive one: the twelve branches applied to twelve months put any pair six apart six months apart.
Sources Chinese Mathematical Astrology: Reaching Out to the StarsHo Peng Yoke with The Chinese Sexagenary Cycle and the Ritual Origins of the CalendarAdam Smith