file cert_33_nice.json  (m,p,n) = (3, 3, 9)  N' = 20
 (A) minors: max degree 9  #minors of degree n: 20  gcd degree 0 -> True
 (B) rank M = 10 (n+1 = 10 )
 (C) dim U = 11 (N'-n = 11 )
 (D) #quadrics generated 45 ; Q == 0 on Grassmannian chart (polynomial identity): True ; each generated quadric vanishes: True
 (E) Bareiss leading minors all > 0: True ; LDL pivots all > 0: True ; float eigen range on U (orthonormal basis): (1.3341779886528064e-06, 0.00031877556321652256)
 (F) complex non-degeneracy: True dim ker M = 10, degree 5, rank mod 2147483587 = 2002 of 2002
 ==> INDEPENDENT VERDICT: PASS
