PASS: exact running-mean identities and normalized-weight variance-gap identity, T=1,2,7,29.
PASS: exact recursive-kernel integral algebra at c=3/4,3/2,2,5; c=1 has log-square integral 2.
T=100: mean-square cumulative-weight gap=0.335780217, max-weight/sqrt(T)=0.359290116
T=1000: mean-square cumulative-weight gap=0.151419034, max-weight/sqrt(T)=0.114938441
T=10000: mean-square cumulative-weight gap=0.0736136618, max-weight/sqrt(T)=0.0363474912
T=100000: mean-square cumulative-weight gap=0.0383324989, max-weight/sqrt(T)=0.0114940859
PASS: polynomial-gain finite-T normalization and variance gaps, a=0.8, rho=0.75.
Scope: finite checks support identities but do not prove the asymptotic rate or reproduce the paper experiments.