Under those assumptions, the allowed scalar transformations remain separated from their zero-factor boundary. Configurations that would put a positive measure outside the admitted interval are excluded by the domain definition. The argument concerns the quantities represented within that domain.

The result does not establish null-geodesic completeness, the ability to extend lightlike paths indefinitely in the appropriate affine parameter. Relativistic singularity theorems address spacetime and causal properties that are not determined by a lower bound on a scalar count factor alone.

A regular gravitational-collapse history would additionally require a realized spacetime and a dynamical analysis of its evolution. The October manuscript therefore supplies a bounded-measure theorem with explicit premises. It does not report a completed black-hole collapse solution, a replacement for every mathematical singularity theorem, or an observation of the proposed lower bound.