The apparatus is the metal and crystal device you already found, that can travel through seals and barriers. It’s just far more powerful than you thought.
There is also way more math involved to calculate the right angles and power into each crystal than Parsley first realized (especially to open a sealed door to the cosmic leylines, which Auroc has notes for on page 4). There are over two dozen pages of complicated mathematical theorem Auroc created so as to work the Apparatus. At full size it can unfold into something over seven feet by seven feet, at its smallest it’s barely over a foot. For regular travel between planets it’s easier, apparently, but things like planetary spin and rotation need to be taken into account, alongside other factors.
Apparently, despite his arrogance, Auroc was quite a brilliant mathematician.