Proposition: Severity and count uncertainty

On a fresh block,

with conditional probability at least $1-{{\delta }_t}^H$.

For a predeclared $L_s$-Lipschitz severity-fraction map $s:[0,K]\to [0,1]$,

For $A$ eligible active coordinates, the population-rule floor count lies between

and

For the source's fraction map at fixed gain and base $0.05$, one can take $L_s=0.10$.

Proof. Apply Hoeffding to variables in $[0,K]$. Use Lipschitz continuity and monotonicity of the floor function. The source's two clipping operations are $1$-Lipschitz; the intervening slope in the activation mean is $0.05\cdot 2$.