"Ok, let me explain."

I'd love it if you did, Ornlu but, or course, you didn't.

Sadly, you ignored my first question, which is important. Let me ask more directly. Are you relaying information that you have gained by interacting with Bryce 'personnel' who know; or are you drawing your own conclusions?

Now, let's go back to the beginning. The Bryce5 manual states:

True Ambience - Computes the ambient light
for a surface using the color and intensity of
nearby surfaces, resulting in color blending
from one surface to another.

This statement has been quoted several times (including by no less than AgentSmith) to pooh-pooh various suggestions about the nature of True Ambience. There's some laughing, and a "that's all it is" response, as if the manual statement was the full and final word of God on the matter.

Examine the manual statement for the first premium effect listed:

Soft Shadows - Softens the edges of the shadows.

Whoopee. Does that actually say anything about how shadow softening happens? If there were some debate over the process of how Bryce soft shadows occur, would anyone have any respect for someone who said, "it's just the softening of the edges of shadows, lol"?
The manual statement about True Ambience is equally shallow and vague, yet appears to carry sufficient weight to deter further thought for some.

Why is this relevant? Because what you said, Ornlu, is no more an explanation than the Bryce manual. You offer no detail of the processes involved. I don't mean to sound harsh, but I don't think you have any more idea of the specifics of how True Ambience works than I do, or anyone else outside the Bryce coding fraternity does. And the details and specifics of how it works are fundamental to these discussions. They would resolve all the notions of 'radiosity', 'caustics' or whatever.

To deal with what you said (not in order):
"The only two values taken into account by the true ambience render is the value for ambience and the color ."

This is not true. For example, in post 6 of the thread I linked to, the only ambient materials are on the ground plane and the purple cylinder. If ambience and colour are the only values taken into account, why is the scene (apart from the bright white diffuse surface) visible at all?

"Any object with an ambient value on the surface is immediately calculated."
Er, what does this mean? Calculated? Immediately?

"At any location where this object is reflected it is also calculated. Therefore, if the light is seen in a mirror it will have an 'ambient' value where the reflection is in the mirror."
This has important implications, so I hope you're not just making it up as you go along.
From what perspective is this reflected ambience 'seen'? Does the render engine interpret the reflection from the 'point of view' of the reflective object, or from the 'point of view' of the camera? What process does the render engine use to 'see' the ambient surface reflected in the mirror, and to treat the reflection as another ambient surface?

"'sphere' of influence is created at however many RPP..."
This is interesting. You've brought rays into the discussion. In what way do rays operate in True Ambience?

"You will notice that the same effect is generated with a white opaque surface.."
No, I notice that a white, opaque surface generates an entirely different effect. Look at posts 3 and 5 in the link. The big sphere has an opaque material the same as the ground plane. No 'caustics' seen as via the reflective spheres there. Setting the big sphere material to maximum white, maximum ambience has no effect with regard to the appearance of 'caustics' on the floor. An opaque surface does not deliver the 'caustic' effect.

"Now, you mentioned that there is a 'caustics' effect on the transparent sphere. This is caused by the same phenomenon, look at the sphere, you will see that the basic 'refractions' in bryce cause the incident reflection/refraction of your white planeto be projected on both sides of the sphere."
Do you see the enormity of what you are saying here? You are suggesting that the render engine can take account of an internal reflection caused by refraction, and then use that internal reflection to create a 'sphere of influence' for another effect. That's pretty major, even in the absence of an explanation of how it actually occurs. If you read my thread carefully, you will note that the scene in post 6 has reflections disabled. This makes your explanation even more amazing.

"...the light in your scene would probably act very similarly with a plain plane without reflection as it does with the mirror."
No. The light in my scene most certainly acts entirely dissimilarly under such conditions.

As an 'explanation', you've offered a mix of mistakes and generalisations. It's certainly a leap from the "proximity of ambient surfaces", but looks very much like a leap in the dark. You've offered nothing in the way of a process by which these generalised notions might occur. In the absence of such a description, you might as well say that draculaz's robot "immediately" wonders through the scene and paints the ambient 'spheres of influence' in watercolour.

But you did mention rays. And that mention, inadvertent as I suspect it was, is pleasing to me. Since Bryce is a raytrace renderer, it is entirely reasonable to assume that the process of True Ambience operates via 'rays', much as every other effect in a Bryce render is facilitated. And if True Ambience operates via rays, I regard my ideas about it being 'illumination' having virtual optical properties as being as valid as anyone else's ideas about it being nothing more than (magic?) 'color blending'.

Only a detailed, 'official' explanation will settle it.