==========================================================================================
SOLUTION flip3 (involutive control) N = 3
 eps = 1
   dims B_n / K_n                    : [1, 3, 3, 1, 0, 0] [1, 3, 3, 1, 0, 0]
   H_n(TV, d_br)   rack/braided hom. : [1, 3, 9, 27, 81]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 3, 3, 1, 0]
   H_n(B, del)     Im QS             : [1, 3, 3, 1, 0]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 3, 3, 1, 0]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 eps = 0
   dims B_n / K_n                    : [1, 3, 3, 1, 0, 0] [1, 3, 3, 1, 0, 0]
   H_n(TV, d_br)   rack/braided hom. : [1, 3, 9, 27, 81]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 3, 3, 1, 0]
   H_n(B, del)     Im QS             : [1, 3, 3, 1, 0]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 3, 3, 1, 0]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 time 0.0s
==========================================================================================
SOLUTION dihedral quandle R3 (control) N = 3
 eps = 1
   dims B_n / K_n                    : [1, 3, 4, 3, 1, 0] [1, 3, 4, 3, 1, 0]
   H_n(TV, d_br)   rack/braided hom. : [1, 1, 1, 1, 1]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 1, 0, 1, 1]
   H_n(B, del)     Im QS             : [1, 1, 0, 1, 1]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 1, 0, 1, 1]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 eps = 0
   dims B_n / K_n                    : [1, 3, 4, 3, 1, 0] [1, 3, 4, 3, 1, 0]
   H_n(TV, d_br)   rack/braided hom. : [1, 3, 9, 27, 81]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 3, 4, 3, 1]
   H_n(B, del)     Im QS             : [1, 3, 4, 3, 1]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 3, 4, 3, 1]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 time 0.0s
==========================================================================================
SOLUTION permrack2_10 N = 2
 eps = 1
   dims B_n / K_n                    : [1, 2, 3, 5, 8, 13, 21, 34] [1, 2, 3, 5, 8, 13, 21, 34]
   H_n(TV, d_br)   rack/braided hom. : [1, 1, 1, 1, 1, 1, 1]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 1, 0, 0, 0, 0, 0]
   H_n(B, del)     Im QS             : [1, 1, 0, 0, 0, 0, 0]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 1, 0, 0, 0, 0, 0]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 eps = 0
   dims B_n / K_n                    : [1, 2, 3, 5, 8, 13, 21, 34] [1, 2, 3, 5, 8, 13, 21, 34]
   H_n(TV, d_br)   rack/braided hom. : [1, 2, 4, 8, 16, 32, 64]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 2, 3, 5, 8, 13, 21]
   H_n(B, del)     Im QS             : [1, 2, 3, 5, 8, 13, 21]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 2, 3, 5, 8, 13, 21]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 time 0.0s
==========================================================================================
SOLUTION permrack3_120 N = 3
 eps = 1
   dims B_n / K_n                    : [1, 3, 7, 16, 33, 64, 113] [1, 3, 7, 16, 36, 81, 182]
   H_n(TV, d_br)   rack/braided hom. : [1, 1, 1, 1, 1, 1]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 1, 0, 1, 2, 1]
   H_n(B, del)     Im QS             : [1, 1, 0, 1, 1, 2]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 1, 0, 0, 0, 0]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 eps = 0
   dims B_n / K_n                    : [1, 3, 7, 16, 33, 64, 113] [1, 3, 7, 16, 36, 81, 182]
   H_n(TV, d_br)   rack/braided hom. : [1, 3, 9, 27, 81, 243]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 3, 7, 16, 36, 81]
   H_n(B, del)     Im QS             : [1, 3, 7, 16, 33, 64]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 3, 7, 16, 36, 81]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 time 0.9s
==========================================================================================
SOLUTION permrack4_1230 N = 4
 eps = 1
   dims B_n / K_n                    : [1, 4, 14, 47, 152, 489] [1, 4, 14, 49, 171, 597]
   H_n(TV, d_br)   rack/braided hom. : [1, 1, 1, 1, 1]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 1, 0, 1, 2]
   H_n(B, del)     Im QS             : [1, 1, 0, 1, 1]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 1, 0, 0, 0]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 eps = 0
   dims B_n / K_n                    : [1, 4, 14, 47, 152, 489] [1, 4, 14, 49, 171, 597]
   H_n(TV, d_br)   rack/braided hom. : [1, 4, 16, 64, 256]
   H_n(TV/J, d_br) R_sigma-quotient  : [1, 4, 14, 49, 171]
   H_n(B, del)     Im QS             : [1, 4, 14, 47, 152]
   H_n(K, del)     Koszul (=H_*(M;k) if A Koszul): [1, 4, 14, 49, 171]
   (last listed degree n = nmax-1 uses B_nmax, K_nmax; all values exact mod P)
 time 5.7s
