Kashmir Shaivism produced several distinguishable strands built on shared foundations, and the Spanda school is the one that took its name and its organising concept directly from this text rather than from a place, a lineage or a broader doctrinal label. Where the Krama school organised itself around a sequence of ritual and visionary stages and the Kaula current around transgressive embodied practice, the Spanda school treated the single insight that consciousness is intrinsically vibratory activity as sufficient ground for an entire soteriology: since spanda is already the nature of everything experienced, the practitioner's task is to recognise the vibration underlying a thought or sensation rather than to still it or escape it.
The text generated a commentarial tradition of its own within a generation or two of its composition, most notably Kshemaraja's Spandanirnaya, which reads the karikas alongside the Shiva Sutras as a single coherent system and supplied much of the vocabulary later students of Kashmir Shaivism use to describe the relationship between the two texts. Later Kashmiri authors continued to treat the Spanda Karikas as a text worth commenting on in its own right for centuries afterward, evidence that it was received as scripture rather than as a secondary gloss on something more authoritative.
Abhinavagupta's own synthesis in the Tantraloka absorbed the Spanda school's vocabulary thoroughly enough that spanda functions as one of the core technical terms of his entire system, which is one reason the question of whether he regarded the Karikas as scripture on the same footing as the Shiva Sutras, or as an important but secondary elaboration, matters to how the whole architecture of his synthesis is read.