I am generally suspicious of any attempt to make the manifestation process into a grand formula, because it has a habit of coming to bits. However, in the spirit of putting everything into equations, I couldn't resist taking another stab at it. Please realise that the universe is far too complex to be put into a specific formula - the equation is more to be a reminder of success components.
Success, S = S (Creation, Attraction) = S(C, A)
Success is a function of the Law of Creation and the Law of Attraction. The Law of Creation allows us to flexibly maneuver our awareness within the sea of awareness, or pure potential, to anchor an awareness in an energetic pattern that supports us. Once rooted into that pattern, we can employ the energies of attraction to magnetise that which we purely desire. We re-Create ourselves in a form that can Attract what we desire.
The facilitator of this simple scheme is the ability of conscious awareness to move flexibly beyond the normal range of thought. Your equation for freeing conscious awareness:
Freedom of conscious awareness, F = F(Intention, Conscious of the content of awareness, Surrender)
Intention is that which mobilises the movement in awareness. It is a very light, very gentle thing. Anything heavier or more forceful tends to create friction, because it is driven by (or at least cultivates a fertile environment for) desperation born of fear. It is pure intention, and it won't be of any surprise now to any reader of this series when I say
Pure Intention = Intention - desperation/fear.
The effect of being conscious of the content of awareness is tricky. You are employing multiple views. Ultimately as awareness fades into the sea of awareness, it becomes pure. However, on the trip there, having a view of what is going on helps. The key is to notice. If I had to give a sub-formula:
Conscious of awareness' content = Noticing content of experience + Insight
Noticing is a third person perspective. It is conscious awareness monitoring itself. Notice when discomfort arises. Notice when pleasure arises. Notice when desperation or fear arises. And based on your observation, explore this further. You will gain the insight necessary to release the chains by which you are bound. The things that hold you back: wanting approval, wanting survival, wanting control (ala Lester Levenson and Sedona Method) or, if you prefer the Hendricks approach: feeling flawed, feeling disloyal or not wanting to abandon, believing success is a bigger burden, the crime of outshining. Notice the stories of justification that arise. Question them with The Work of Byron Katie. You will find the stories to be false. With this insight you will gain the courage to use the third part of the Freedom formula - surrender.
When you have discovered that which holds you back, and you realise it is false, then it is easier to surrender the stories. Surrender is an interesting one to put a formula to. It's a theme I've harped about for quite some time, but never been more specific about. Let's try an equation on that:
Surrender or complete vulnerability = Releasing all inner protective barriers + Willingness to experience whatever comes especially emotionally
This shows a maturity, for in creating complete vulnerability, we no longer feel the urge to lie to ourselves. It cuts through our tendencies to fudge and keep secrets from ourselves. Releasing all the inner barriers is daring to look at yourself in ways that are different from the usual. It may be flattering or not, but if you do not look you can never invoke the perspective. When you no longer hide from your feelings, then no inner gremlin can budge you from your path, because it will have no bargaining chip. All emotional blackmail fails, both from within and without, because you have commited to experience whatever comes completely. The instinct to survive, or wanting to survive, is usually strong. It feels out of control, with no assurance of approval, and all the factors of wanting come into being.
The dying flaring of the ego tries to snatch at bits and crumbs of stories to make the pain more bearable. However, determined willingness to experience, and experience fully, the brunt of what comes, will drive back these illusions. It is like a dam has broken and water has poured forth. It is not your part to save a dam that is broken. It is your part to experience and survive the flow of energies released, and live to rebuild something even more glorious. Attempting to build yourself too early results in suppression, and ultimately even more heartache in the long run.
That's a lot of equations. I want to put out just one more, without too much elaboration, on the nature of conscious awareness' aspects itself. This equation is less about doing, but more a statement about how conscious awareness automatically moves and functions.
Conscious awareness, C = C(Masculine principle, Feminine principle)
The masculine principle is that energy which arises dynamically. It is taking action. It is belief. It is the building of thought structures. It has to do with strategising, implementing, sustaining, growing. As conscious awareness grows in passion, the masculine principle often takes its form. But underneath all this activity is the yin side, the feminine principle. The feminine principle has to do with what awareness is rooted in, what identity has been created. Both complement each other. The masculine principle initiates, the feminine principle supports, but the masculine cannot exist without the feminine, and thus the feminine comes first.
And as we come to the end, we have to ask what creates the whole impulse for the manifestation process to begin. What is the initial spark of attraction?
Impulse of manifestation = Self-arising Volition (not Will, which is a masculine principle force) + Awareness + Harmonic resonance
I'll leave you to ponder that. It has great implications for the issue of free will.