The whole is finite (Step 3). It is static (Step 4). It cannot extend infinitely into the future – that would violate finitude. It cannot simply terminate at a boundary, because a boundary is a coordinate where the universe stops and “something else” begins. But there is no something else (Step 2). A boundary would be a point where identity breaks – where A becomes not‑A.
The only remaining possibility is that the temporal dimension curves back upon itself. The final coordinate – the Heat Death, where all mass has decayed into massless radiation – must connect seamlessly to the initial coordinate – the Big Bang, where all energy is also massless radiation. At both coordinates, the metric has no scale. Massless particles experience no distance and no duration. The two ends are geometrically indistinguishable.
By the identity of indiscernibles, if two states share every geometric property, they are the same state. The Heat Death is the Big Bang. The End is the Start. The loop is closed.
To reject Step 6 is to assert that the whole can have an edge where it ceases to be itself without becoming anything else – a violation of identity. The processor crashes.