This occurs at the mid-point of our existence and in some respects it was the peak of our efforts. By this point, we had gained enough experience to develop very complex and sophisticated mockups, and we had not yet decayed too far. It continues for a long period of wonderful creation and the final collapse of home universe was probably the first big loss that we experienced.
This was actually a collection of individual universes linked together in a higher level space. This higher space was a sort of matrix of gateways leading down into the individual home universes. Early on, it seems like a sort of nebulous corridor with mirrors or thought pools along the walls which lead into the individual universes. However, as time passed, it gradually expanded until it had much the appearance of the night sky full of stars. Except that the "stars" were the gateways into the individual universes and if you went up close to them, these stars might look like big golden balls or even symbols such as a flower or an object hanging in the sky.
It is a mistake to think of this as a single universe with little balls in which each thetan dwelled (there's a later implant which presents it that way). You would enter one of these spheres and find an entire infinite universe. It would be as diverse and complex as the creating thetan (or thetans in the case of agreed upon universes) had chosen to mock up. It would not necessarily share physical universe laws or anything else (except the primary entry point) with the other universes in the matrix. It could also contain further subordinate universes below it.
Besides the individual universes, there were agreed upon universes used for games or meeting places. These were quite numerous and varied. There were also "story" universes, much like movies. These story universes contained sequences of 3 dimensional pictures arranged in a fixed time track that told a story and anyone could go into one of these and enjoy the drama. There was actually quite a bit of aesthetic competition involved, much like the academy awards. But unlike our Hollywood productions, these were built as universes and seemed just as real as our life here on Earth.
The development of the "stars" mockup at the top level is probably due to the problem of managing an ever growing number of entry points. Just lining the entry points up along the sides of a tunnel is too inefficient. So we expanded the top level outward and started arranging the entry points in a 3 dimensional space. Without a wall to place them against, an oval thought pool is better mocked up as a sphere. And so we have a sea of "stars" at the top level.
Within the individual universes, it became common practice to bring this top level display of "stars" into view in the surrounding sky.