(S1) window inequality fails for 459 values of a in [1,1e6]; largest failure a = 527
     holds for all 528 <= a <= 1e6: True
(S2) columns with a pendant vertical edge, |x| <= 1e6: 0
(S3) x in [1,3000): violations of (min dual walk through column x) >= L_x: 0 []
     x=   1  min walk length=  2  L_x=  2  (w(x)+1=3)
     x=   2  min walk length=  3  L_x=  2  (w(x)+1=3)
     x=   5  min walk length=  3  L_x=  3  (w(x)+1=3)
     x=  10  min walk length=  4  L_x=  3  (w(x)+1=4)
     x=  20  min walk length=  4  L_x=  4  (w(x)+1=4)
     x=  50  min walk length=  5  L_x=  4  (w(x)+1=5)
     x= 100  min walk length=  6  L_x=  5  (w(x)+1=6)
     x= 500  min walk length=  9  L_x=  8  (w(x)+1=9)
     x=1000  min walk length= 11  L_x=  9  (w(x)+1=12)
     x=2000  min walk length= 14  L_x= 11  (w(x)+1=14)
     x=2999  min walk length= 16  L_x= 13  (w(x)+1=16)
(S4) window [-2,2]: 24 end-separating sets with both sides connected; 24 have boundary = simple BOTTOM-TOP dual path (one bottom edge, one top edge)
(S4) window [-3,3]: 100 end-separating sets with both sides connected; 100 have boundary = simple BOTTOM-TOP dual path (one bottom edge, one top edge)
(S5) partial sum over 1 <= |x| <=    1000 of (3w(x)+2) 2^(-l_x) = 3.3519e+03
(S5) partial sum over 1 <= |x| <=   10000 of (3w(x)+2) 2^(-l_x) = 9.1039e+03
(S5) partial sum over 1 <= |x| <=  100000 of (3w(x)+2) 2^(-l_x) = 1.0649e+04
(S5) partial sum over 1 <= |x| <= 1000000 of (3w(x)+2) 2^(-l_x) = 1.0662e+04
