run 2, own exact verifier for Theorem 1.1
main.tex sha256 757a6c5b062ee60da12b16531eb9c9a57921dfed20ad95ba2ed804ee7d8761ed
generator: m=2, N=6: 120 pairs (I,J), 60 non-zero forms R_IJ, all vanish identically on [I|X]
           for m=2 every R_IJ is 0 or +-Pf_abcd: True
generator: m=2, N=7: 245 pairs (I,J), 140 non-zero forms R_IJ, all vanish identically on [I|X]
           for m=2 every R_IJ is 0 or +-Pf_abcd: True
generator: m=3, N=6: 225 pairs (I,J), 135 non-zero forms R_IJ, all vanish identically on [I|X]
case (2,4)
  cert_24_nice_int.json sha256 d80e490e5ae7659f...; V in main.tex == V in file: True; multipliers in main.tex == file (lexicographic Pf order): True
  minors: 15; max degree 8 (n = 8); number of minors of degree n: 14; gcd of minors constant: True
  rank M(V) = 9 (n+1 = 9); dim U(V) = 7 (C(N,m) - n = 7)
  rank of the leading coefficient V_p = 2 (m = 2)
  Q(y([I|X])) == 0 identically in the 8 entries of X: True; Q = 0 at 25/25 random integer 2x6 matrices
  elimination pivots all > 0: True (smallest 0.386706, largest 9.58229)
  characteristic polynomial: all e_k > 0: True (det of the Gram matrix = 15.9348)
  for a random y in U(V): sum_I V_I(z) y_I = c z^n: True
  RESULT (2,4): PASS
case (2,5)
  cert_25_nice_int.json sha256 b2bebe0b7a483f3b...; V in main.tex == V in file: True; multipliers in main.tex == file (lexicographic Pf order): True
  minors: 21; max degree 10 (n = 10); number of minors of degree n: 20; gcd of minors constant: True
  rank M(V) = 11 (n+1 = 11); dim U(V) = 11 (C(N,m) - n = 11)
  rank of the leading coefficient V_p = 2 (m = 2)
  Q(y([I|X])) == 0 identically in the 10 entries of X: True; Q = 0 at 25/25 random integer 2x7 matrices
  elimination pivots all > 0: True (smallest 0.500764, largest 35.2293)
  characteristic polynomial: all e_k > 0: True (det of the Gram matrix = 6130.16)
  for a random y in U(V): sum_I V_I(z) y_I = c z^n: True
  RESULT (2,5): PASS
case (3,3)
  cert_33_nice.json sha256 2e93da0fd5548347...; V in main.tex == V in file: True
  own list of distinct non-zero R_IJ (up to sign): 45; equals the labels of the readable listing: True; multipliers of the listing == file: True; max |lambda| = 10000000
  minors: 20; max degree 9 (n = 9); number of minors of degree n: 20; gcd of minors constant: True
  rank M(V) = 10 (n+1 = 10); dim U(V) = 11 (C(N,m) - n = 11)
  rank of the leading coefficient V_p = 3 (m = 3)
  Q(y([I|X])) == 0 identically in the 9 entries of X: True; Q = 0 at 25/25 random integer 3x6 matrices
  elimination pivots all > 0: True (smallest 5.77916e-06, largest 0.00255195)
  characteristic polynomial: all e_k > 0: True (det of the Gram matrix = 2.71174e-45)
  for a random y in U(V): sum_I V_I(z) y_I = c z^n: True
  RESULT (3,3): PASS
  (the 45 forms span a space of dimension 35)
ALL: PASS   (0.2 s)
