Fisher-Consistent Statistical Evidence for Scale-Regulated Accumulation.

The author present a Fisher-consistent statistical analysis of the Additive–Multiplicative (AM) Regulator framework introduced in prior theoretical, numerical, philosophical, experimental, and geometric-extension studies. Rather than testing for universal validity, the author assess whether the AM-regulated formulation demonstrates statistically significant improvement over unregulated baseline models across heterogeneous physical domains. Using likelihood-ratio tests, variance reduction metrics, and goodness-of-fit statistics applied to representative datasets from fluid dynamics, gravitation, cosmology, and number theory, the author finds consistent, positive statistical support for regulated accumulation. These results do not establish ontological necessity but demonstrate that the AM-regulator survives stringent Fisherian hypothesis testing without over fitting, motivating its constrained geometric extension.