Singularity Resolution

Standard general relativity predicts singularities: points of infinite curvature, infinite density, zero volume. The Penrose-Hawking theorems show they are generic whenever matter satisfies reasonable energy conditions and gravity is purely classical.

In the record algebra, infinite curvature means infinite record density — infinitely many records in a finite volume. But each record has minimum volume ℓ_P⁴ (Axiom B) and finite propagation (Axiom C). Infinite record density in finite volume is impossible. The monoid cannot be compressed below the Planck density. You cannot squeeze the records tighter than one per Planck cell.

What happens instead: as record density approaches the Planck density, the available cells approach saturation. The geometry approaches maximum curvature. The eye approaches closing. The loop (AP09 §4.4): closing IS opening. When all ε are coupled, the 1:1 restores. κ is exceeded. The break begins again. The singularity is not a point of infinite density. It is the loop point — where the monoid saturates, defragments (forgetful functor U: Mon → Set; AP09 §4.4), and the break restarts. Defragmentation strips composition but preserves elements: the records survive, their ordering dissolves, and the next cycle starts from the full defragmented content of all prior cycles, carried as probability and possibility.

The singularity is resolved by topology, not by fiat. The loop is not imposed to avoid infinities. It is a structural consequence of the axiom: 1:1 + 1×ε is the beginning condition. When conditions return to the beginning, the structure begins again. The eye is the topology. The loop is the eye closing and opening. The singularity is the hinge.