# Claim 4

**Result: verified.** The pinned source states B-E (symmetric) has
`σ²∼1/H` and C-D (asymmetric) has `σ²∼H^{-2/ν}`. Direct substitution into the
printed dominance equations gives 1 in every tested H/ν cell. The discriminating
control uses `σ²=H^-1` in ASYM ν>2 and violates C-D.

This is an exact regime-condition check, not a claim that a small numerical
trajectory proves necessity of mean-field feature evolution.

## Registered wording

Mean-field, feature-evolving regimes require the initialization variance to scale as sigma^2 proportional to 1/H (symmetric case) or sigma^2 proportional to 1/H^(2/nu) (asymmetric case), corresponding to edges B-E and C-D of the Pareto polygon respectively (Section 4).