{
  "method": "exact symbolic polynomial arithmetic; local certificates only",
  "sympy_version": "1.14.0",
  "source_sha256": "60993c0b524291b7f707e42eec89ec7e910c22760d81f1d3af007c229228c13c",
  "checks": {
    "cusp_identity": true,
    "shift_identity": true,
    "linearized_S_mod_relation": true,
    "compatibility_identity": true,
    "explicit_bezout_certificate": true,
    "squared_coefficient_certificate": true,
    "UG_relation_certificate": true,
    "T_composite_certificate": true,
    "critical_gradient_exact": true,
    "critical_fibre_exact": true
  },
  "critical_gradient": [
    "0",
    "0",
    "0",
    "0"
  ],
  "critical_fibre": "-1"
}