Table S1.

Runs of the redistricting Markov chain with results of the $\sqrt{𝜺}$ test

Population threshold,%	Compactness measure	Compactness threshold	Initial value	(Steps) k =	Label function	$\epsilon$-Outlier at $\epsilon$ =	Significant at p =
$2$	Perimeter	$\le 125$	$121.2\dots$	$2^{40}$	${\omega }_{\text{var}}$	$3.0974\cdot {10}^{-8}$	$2.4889\cdot {10}^{-4}$
					${\omega }_{\text{MM}}$	$5.7448\cdot {10}^{-10}$	$3.3896\cdot {10}^{-5}$
$2$	$L^1$	$\le 160$	$156.4\dots$	$2^{40}$	${\omega }_{\text{var}}$	$5.0123\cdot {10}^{-11}$	$1.0012\cdot {10}^{-5}$
					${\omega }_{\text{MM}}$	$5.6936\cdot {10}^{-10}$	$3.3745\cdot {10}^{-5}$
$2$	$L^2$	$\le 44$	$43.06\dots$	$2^{40}$	${\omega }_{\text{var}}$	$8.2249\cdot {10}^{-11}$	$1.2826\cdot {10}^{-5}$
					${\omega }_{\text{MM}}$	$6.8038\cdot {10}^{-10}$	$3.6888\cdot {10}^{-5}$
$2$	$L^{\mathrm{\infty }}$	$\le 25$	$24.73\dots$	$2^{40}$	${\omega }_{\text{var}}$	$3.3188\cdot {10}^{-13}$	$8.1472\cdot {10}^{-7}$
					${\omega }_{\text{MM}}$	$6.9485\cdot {10}^{-8}$	$3.7279\cdot {10}^{-4}$