{
  "status": "VERIFIED",
  "sympy_version": "1.14.0",
  "checks": [
    "AM = 0",
    "A pivot minor = 1",
    "M generic minor = -s",
    "M persistent minor = 1",
    "q is nonzero",
    "Mq = -s h",
    "Ah = 0",
    "wM vanishes at s=0",
    "wh = 1",
    "rank-nullity conclusions match the proof"
  ],
  "scope": "Polynomial identities and rank certificate for the specified finite complex"
}