(1) terminology: maximal minors and elementary divisors of the incidence matrix B
    all 8 corner patterns of 2x2x2: (|maximal minors|, gcd, elementary divisors) = [((0, 1, 2), 1, (1, 1, 1))]
ok   corner patterns of 2x2x2 are saturated but have a maximal minor +-2
    all 16 corner patterns of 2x2x2x2: (|maximal minors|, gcd, elementary divisors) = [((0, 1, 2, 3), 1, (1, 1, 1, 1))]
ok   corner patterns of 2x2x2x2 are saturated but have a maximal minor +-3
    2x2x2 {111,112,221}: |maximal minors| [0, 1], gcd 1, elementary divisors [1, 1, 1]
ok   {111,112,221}: unimodular in the usual sense
    2x2x2x2 {1111,1122,2212,2221}: |maximal minors| [0, 2], gcd 2, elementary divisors [1, 1, 1, 2]
ok   {1111,1122,2212,2221}: not saturated (gcd 2, elementary divisors 1,1,1,2)
(2) Corollary 1.4: largest degree 2 + 2P(d1,d2)
ok   closed forms equal 2+2P for all 2 <= d1 <= d2 <= 40 (the case 2x2 gives 2); mismatches: []
ok   without the new case, 2(d1+d2-4) would give 0 for 2x2
(3) Lemma 5.2 inequalities
ok   for 1 <= p <= p' <= 30: t+3 <= 2p+1, t+3 <= p+p' <= 2p', floor((t+3)/2) <= p, ceil((t+3)/2) <= p'
(4) diagonal patterns
ok   |E| = d equals m = n(d-1) only for (n, d) = (2, 2): [(2, 2)]
ok   the 2x2 diagonal {11,22} is the corner pattern E*(12)
ok   degree n^(d-1) = 2 = n(n-1) for n = d = 2
(5) Cai-Recke-Yahl correspondence and ranks
ok   2x2x2 {111,112,221}: rank A = 4 = m+1, rank A_E = 3 = |E| = m = 3
ok   2x2x2 {111,112,221}: sum w(kappa) p_kappa = <w,theta>, slice sums = theta_(j,k), w = 0 on E
ok   2x2x2 {111,122,212}: rank A = 4 = m+1, rank A_E = 3 = |E| = m = 3
ok   2x2x2 {111,122,212}: sum w(kappa) p_kappa = <w,theta>, slice sums = theta_(j,k), w = 0 on E
ok   2x2x3 {111,122,212,223}: rank A = 5 = m+1, rank A_E = 4 = |E| = m = 4
ok   2x2x3 {111,122,212,223}: sum w(kappa) p_kappa = <w,theta>, slice sums = theta_(j,k), w = 0 on E
ok   2x2x2x2 {1111,1122,1212,2221}: rank A = 5 = m+1, rank A_E = 4 = |E| = m = 4
ok   2x2x2x2 {1111,1122,1212,2221}: sum w(kappa) p_kappa = <w,theta>, slice sums = theta_(j,k), w = 0 on E
ok   2x3x3 {111,122,133,212,223}: rank A = 6 = m+1, rank A_E = 5 = |E| = m = 5
ok   2x3x3 {111,122,133,212,223}: sum w(kappa) p_kappa = <w,theta>, slice sums = theta_(j,k), w = 0 on E
(6) Step 1 of Theorem 1.1 for n = 3
ok   <w,theta> = 3(a1+a2+a3-2) = -3 l_E with l_E = 2 - a1 - a2 - a3
ALL CHECKS PASSED
