The whole is finite (Theorem 2) and static (Theorem 3). It cannot extend infinitely into a linear future, nor can it terminate at an arbitrary spatial or temporal edge, as an edge implies a boundary where the universe stops and “nothing else” begins – a structural impossibility (Theorem 1).
The only geometric configuration that satisfies a finite, boundaryless, and self-contained manifold is a closed temporal loop. The final phase of the whole – the Heat Death, where all rest-mass has decayed into massless radiation – maps cleanly to the initial phase – the Big Bang, which is also a state of pure, massless radiation.
At both limits, as the scale factor collapses (a → 0), the metric of spacetime loses its clocks and rulers. Without rest-mass to define scale, the localized thermodynamic distinction between “hyper-compressed concentration” and “maximal diffusion” completely vanishes. Through Conformal Scale Invariance, these two states share identical geometric and informational properties.
By the Identity of Indiscernibles, they are the exact same state. The Heat Death and the Big Bang are a singular coordinate (S), evaluated not as a local thermodynamic intersection, but as a global identification space. The End is the Start.
To reject Theorem 5 is to assert that the universe can possess a physical edge where it ceases to exist without encountering an external boundary – a direct violation of identity. The processor crashes.