rank-gap cut certificate
  singleton cut determinants: [1, 2, -3, -2]
  balanced-cut kernel vectors: [[0, 1, -1], [-1, 0, -1], [-1, 0, 0]]
  balanced-cut cross determinants: [-2, -3, 1]
  conclusion: P(W) contains no rank-one or rank-two quadric

apolar algebra certificate
  dim A_2: 3
  rank of cubic relation span: 4 (hence A_3=0)
  dim K_(2,4): 18
  rank d_3: 15
  dim H_(2,4) = beta_(2,4): 3

full PG(3,2) positive control
PG(3,2): n=15, rank=4, flats=67, Sylvester=True, third-points-per-pair=[1,1]
  degree 3: dim K2=1575, rank(d2)=510, rank(d3)=455, H2=610, block-sum=610, nonzero-blocks=50
  degree 4: dim K2=3675, rank(d2)=224, rank(d3)=3451, H2=0, block-sum=0, nonzero-blocks=0
  degree 5: dim K2=1575, rank(d2)=15, rank(d3)=1560, H2=0, block-sum=0, nonzero-blocks=0
  degree 6: dim K2=105, rank(d2)=0, rank(d3)=105, H2=0, block-sum=0, nonzero-blocks=0
