The factor of two reflects the different conventional energy conditions used in those speed expressions. Circular motion and escape are not interchangeable definitions of gravitational binding. Their count reductions therefore answer different questions even when they use the same underlying source and radius.

These restrictions describe particular mathematical comparisons. A galaxy’s observed stellar population also contains velocity dispersion, noncircular motion, and a spatially extended baryonic distribution. A point-source count boundary alone does not predict that full population.

The September source version preserves both inequalities as separate results. Their historical role is to organize the domain of the gravitational construction, rather than to supply two independent observational confirmations. Applying either restriction to a measured system requires its source model, operational speed definition, and uncertainty treatment.