Symbolism, Imagery, Allegory
In some ways, the Integral is the perfect embodiment of the State: mechanical and made of glass, constructed through the twin disciplines of mathematics and engineering. Its purpose is to spread the will of the State to other planets: something that D-503 thinks is great (at least initially), but fills most readers' hearts with dread. On the one hand, it's starkly beautiful. On the other hand, it represents a dire threat to everything else in the universe.
In that sense, it becomes an embodiment not just of the State, but also of humanity itself and where it's headed. That's why it's so important for MEPHI to take it over, after all. It can determine what side of humanity is going to be shown the universe, and conversely, what side will ultimately prevail:
"The Integral must be ours. And it will be ours. On the day when it first sets sail into the sky we shall be on board." (27.29)
The future—with all its promises and all its threats—is wrapped up in that ship, which is what makes it such an important point of contention between the State and MEPHI.