Because Amoghasiddhi is defined almost entirely by his position within the mandala of Five Tathagatas rather than by any independent narrative or cult of his own, understanding him means understanding the system itself, which crystallized in a specific body of tantric literature, chiefly the eighth century Sarvatathagatatattvasangraha, the Compendium of the Truth of All the Tathagatas, one of the foundational texts of what later Buddhist tradition would classify as Yoga Tantra, in which the five buddhas are arranged in a mandala with Vairochana at the centre and the other four, including Amoghasiddhi in the north, occupying the cardinal directions, each systematically correlated with a colour, an element, a mental affliction to be transformed, and a corresponding wisdom. This scheme was carried from India into East Asia by pilgrim monks and translators, most consequentially by the Japanese monk Kukai, who studied esoteric Buddhism in Tang China in the early ninth century and, upon returning to Japan, founded the Shingon school around the ritual and doctrinal use of this five-buddha mandala, embedding Amoghasiddhi permanently into Japanese esoteric practice as one of its fixed cardinal points.
A parallel transmission carried the same basic framework into Tibet, where it was integrated into the highest tantra systems and continues to structure Vajrayana visualization practice today. Amoghasiddhi's entire religious identity, in other words, is inseparable from this historical mandala system's spread across two very different Buddhist civilizations, so that to ask what Amoghasiddhi does independently of the mandala is, in an important sense, to ask a question the tradition was never much interested in answering.