Ok here we go… I’ll just throw this out and have it done [with reservation that its of course an interpretation].

As you said Saidevo, the Mahavakyas give us different layers of meaning. Interpreted they give one meaning, non-interpreted they keep all their meanings.

However… If we look at the Ayam Atma Brahma, Tat Tvam Asi and Aham Brahma Asmi they each have 3 words. It can be interpreted as the 3 levels, body, mind, Atma (which is a common team in Upanishads etc, like Vak, Manas, Prana …). So if we put them in the scheme (mind here is the subtle body):

Body...........Mind.........Atma
Ayam..........Atma........Brahma
Tvam..........Asi...........Tat
Aham..........Asmi.........Brahma

One of the words in each Mahavakya is the connection of heaven and earth (Purusha/Prakriti). This connection is always the mind (or subtle body /Antahkarana etc).
• In Ayam Atma Brahma [3rd person], Atma (self) is Mind/heart which connects since inside mind/heart is the indweller of the heart, Hridaya-Vasi).
• In Tat Tvam Asi [2nd person], Asi (are) is Mind which connects as a clear image of Ishvara.
• In Aham Brahma Asmi [1st person], Asmi (am) is Mind which connects. It would indicate the barriers of mind broken down. Aham is “I” but also the witness (saksi) or Atma.

Prajnanam Brahma [3rd person impersonal] is not 3-fold… It’s non-personal (the other 3 are personal). It’s about Spirit/Matter or Purusha/Prakriti. It simply says: Matter is consciousness or consciousness is matter. What is here is there, what is inside is outside etc… It’s also interesting to add a vers from Katha Upanishad (1, 3, 10-11):
“Beyond the senses (Indriyas) are the objects [artha] “
The objects are more subtle than the senses themselves indicating that there is no external separated from consciousness itself. The objects exist in the mind as consciousness itself... And consciousness is Brahman so objects/physical is Brahman.

Body..........Mind..........Atma
Prajnanam..................Brahma

---

Devotee: (hope I don’t answer something you intended to do later)… anyway, you said:
“But how can we be sure that it is really so?”
When I began meditation 21 years ago, I thought I was going a bit mad after a few weeks time. What happened was the consciousness expanded and the barriers between my own mind and the physical world broke down. This and that exists, but at the same time its one substance and that’s consciousness. Alternating between those two aspects was quite fun I remember. But my ability to Alternate has long been lost to consciousness only [and name/form]. Today I can understand it as an experience of Prajnanam Brahma. Back then I was Buddhist and thought of it in terms of emptiness/form.
Even modern Science can prove this if I figured it out right. Where are the objects if there is no observer? The error of modern science is that they begin with the physical and take it for granted. Then begin to explain mind… Without observer however there can be no physical. Without observer there is no science at all. This gets even more interesting when studying quantum physics. At that level the observer is directly affecting the outcome of the experiment. My intuition tells me this is Prajnanam Brahma right in the face of science; matter and consciousness are not separated.