Thank you for clarifying.  I will continue the investigation! The main difference between your approach and what I am doing and discovering now, is the perspective on personality and sense of identity. Here you have personified kundalini and the intellect:

Stated otherwise, if the intellect feels that it should serve the purpose of the core-self, it will find that the senses will betray it because their master is the kundalini not the core-self.

From the perspective of my current meditation, the sense of identity provides the display of personality based on it's identification with sensual contact and also with memories and thoughts which arise in the container of the intellect (buddhi analytical organ).   When thoughts diminish, there is an accompanying stillness in that organ.  This stillness seems to be based on the sense of identity's interest being either withdrawn or placed elsewhere, i.e on the breath or into naad sound.  

Regarding this statement:

 My opinion is that the sense-of-identity cannot diminish.

If this is taken to be true, would it then be correct to say that kaivalyam is when the core and the sense of identity are separated from all the other adjuncts?  In this case, the sense of identity is always with the core, even in the state of kaivalyam.

Michael Beloved’s Response:

I have personified the adjuncts because the convention is that we personify many things. For instance, my father, a seaman use to call the ship which he worked on as a she. It is a fact that sometimes when one is in a certain position in reference to even an inanimate object that the gadget behaves in a way which justified it being called as if it were a person.

Certainly the kundalini displays qualities and actions which might cause a yogi to consider it as such, In fact in Vedic tantra in some books, kundalini is regarded as the great mother of the creation.

But all the same some yogis deny this. For instance, Yogeshwarananda my primary teacher for meditation, denied that the earth was personified even though in the Vedic literature, like the Puranas, it is personified as a celestial woman named Bhumi.

I would verify that your statement below is valid:

correct to say that kaivalyam is when the core and the sense of identity are separated from all the other adjuncts?  In this case, the sense of identity is always with the core, even in the state of kaivalyam.

In addition there will come a time, when the core-self splits off from the sense-of-identity which it is tagged with in this subtle and gross creation. It uses that sense-of-identity until the point of total break-away. Then it no longer has it and the core-self or atma finds itself to be looking in another direction where that adjunct has no application and does not register in any way.