Re: Completely independent...
This is a very good offer for one to consider ( when thinking of kaśmir śaivism ). There is an extention to this idea that sm78 offers. In kaśmiri śaivism the '3rd brahma' or tṛtīyam brahman is considered. What can this be ?
Simply because there is no other than Shiva. Universe is a result of expansion (or contraction, both view is ok) of shiva through his power of self-reflection/self-reference/vimarsha/shakti. (according to KS not SM). The novel idea of KS is that consciousness is not a transcendental sat-chit-ananda (which is compared to Light or Illumination in KS). Because a transcendental bliss is still helpless, as Shankara's nirguna brahman is helpless in front of Maya. Consciousness is ofcourse Illumination/Light but also has the power of self-reflection, to reflect on itself, to travel across itself and thus expanding (contracting) itself into any form, shape, space or time . This is shakti or vimarsha shakti. And universe is a result of this. And Shiva can do this because he is svatantra or possess absolute free will to do whatever he wants to do with himself.
It is a standard point of reference that brahman is considered as oṁ-tat-sat in vedānta. In trika ( or kaśmir śaivism ) it is called the 3rd brahma. That is , in oṁ-tat-sat it is the 3rd defining idea or sat that is considered. Yet this brahman is considered vast ( bṛhat) , all pervading (vyāpaka) and is completely in union with śakti.
In vedānta one may call out brahman as oṁ-tat-sat or as sat-cit-ānanda. In kaśmir śaivism this whole concept can be related with one word sauḥ ( sa +au + ḥ) and is considered amṛtbīja, the very heart (hṛdaya) of bhairava ( paramaśiva).
So we find this brahman in kaśmiri śaivism yet more tightly coupled with śakti. It is called the 3rd brahman as there is more alignment with śiva ( or bhairava).
_oṁ śāntiḥ śāntiḥ śāntiḥ