@avehtari – the sum of neighboring pairs of autocorrelations should always be positive (even if the odd lags are negative due to super-efficiency), and if they end up negative due to noise then the stopping rule should trigger, leaving only the previous positive autocorrelation-pair-sums. Consequently any of the Geyer-based algorithms should always return N_eff < N, no?
We shouldn’t simply report min(N_eff, N). If we don’t want to report super efficient results then we should use one of the Geyer sum-pair methods.