(1) lower-bound grids
  five-queens grids on 5x5: concentrations [Fraction(8, 5)]
  five-queens grids on 5x10: concentrations [Fraction(8, 5)]
  five-queens grids on 10x15: concentrations [Fraction(8, 5)]
  five-queens grids on 20x5: concentrations [Fraction(8, 5)]
  5x5, A at (i, 2i mod 5): 40 appearances; per direction: [5, 5, 5, 5, 5, 5, 5, 5]
  5x5 with s = 1 (not a five-queens lattice): concentration 6/5
  5x5 with s = 4 (not a five-queens lattice): concentration 6/5
  5x5 lattice grid: ct(BABBB) = 40  ct(ABBBB) = 40  ct(BBBA) = 40
  hyperplane grids on 3x3x3: 39 distinct grids, concentrations [Fraction(6, 1)]
  hyperplane grids on 3x6x3: 39 distinct grids, concentrations [Fraction(6, 1)]
  hyperplane grids on 3x3x6: 39 distinct grids, concentrations [Fraction(6, 1)]
  3x3x3, A at y1 = 0: appearances 162
  shape 3x4x5: k = 1, admissible grids 3, (3/2)(3^k-1) = 3
  shape 3x3x4: k = 2, admissible grids 12, (3/2)(3^k-1) = 12
  shape 6x2x3: k = 2, admissible grids 12, (3/2)(3^k-1) = 12
  shape 3x1x1: k = 1, admissible grids 3, (3/2)(3^k-1) = 3
  shape 1x6x1: k = 1, admissible grids 3, (3/2)(3^k-1) = 3
  shape 3x3x3: k = 3, admissible grids 39, (3/2)(3^k-1) = 39
(2) the 4x4 grid of Theorem 1.4 and the grid P of Proposition 5.3
  F = AABA/BBAB/ABBB/ABBB: letters A 6  appearances 24
  P = AAAB/BBAB/BBBA/BBAB: letters A 6  appearances 24
  P(r, c) = F^t(r + a, c + b) for (a, b) in [(0, 2)]
  pair (alpha, c) = (Fraction(3, 8), Fraction(3, 2))  delta = 1/16  distance alpha - 1/5 = 7/40
(3) the strip family of Proposition 5.3: all multiples L, N of 20 with 20 <= L <= N - 20, N <= 400
  pairs (L, N) counted from the definition: 190  mismatches with #A = 4N + 7L/2, ct = 32N - 2L - 54: 0
  Gamma_{20,40}: letters A 230  appearances 1186
  Gamma_{40,60}: delta = 67/960, alpha - 1/5 = 7/60, ratio = 112/67
  Gamma_{40,80}: delta = 67/1280, alpha - 1/5 = 7/80, ratio = 112/67
  Gamma_{40,100}: delta = 67/1600, alpha - 1/5 = 7/100, ratio = 112/67
  Gamma_{40,200}: delta = 67/3200, alpha - 1/5 = 7/200, ratio = 112/67
  (not admissible) L = 4, N = 20: ct = 578, 32N - 2L - 54 = 578
  (not admissible) L = 8, N = 40: ct = 1210, 32N - 2L - 54 = 1210
  (not admissible) L = 20, N = 30: ct = 866, 32N - 2L - 54 = 866
  (not admissible) L = 40, N = 45: ct = 1306, 32N - 2L - 54 = 1306
(4) Lemma 4.2 by enumeration
  ten distinct lattice windows; numbers of entries 1: [3, 3, 3, 3, 3, 3, 3, 3, 4, 4]
  Lemma 4.2(b): the lattice window that continues W_{s,t} to the right / downwards is unique and equals W_{s,t-1} / W_{s,t+s}: True
  Lemma 4.2(c): True
(5) arrays without wraparound
  Corollary 1.2(b), construction A at j = 2i mod 5, n = 1..40: occurrences >= (8/5)(n-6)(n-10) for n >= 6 and <= (8/5)n^2: True
    (n, occurrences, lower, upper): [(4, 4, '96/5', '128/5'), (5, 11, '8', '40'), (6, 24, '0', '288/5'), (10, 95, '0', '160'), (20, 503, '224', '640'), (40, 2279, '1632', '2560')]
    M(1) = 0 by enumeration of all two-letter arrays; (8/5)(n-6)(n-10) = 72
    M(2) = 0 by enumeration of all two-letter arrays; (8/5)(n-6)(n-10) = 256/5
    M(3) = 0 by enumeration of all two-letter arrays; (8/5)(n-6)(n-10) = 168/5
    M(4) = 7 by enumeration of all two-letter arrays; (8/5)(n-6)(n-10) = 96/5
  Corollary 1.7, construction A at y1 = 0 mod 3, n = 1..18: occurrences >= 6(n-4)^2(n-6) for n >= 6 and <= 6n^3: True
    (n, occurrences, lower, upper): [(5, 242, -6, 750), (6, 588, 0, 1296), (7, 1156, 54, 2058), (12, 7168, 2304, 10368), (18, 27500, 14112, 34992)]
RESULT PASS
