{
  "distinct_products_lcm_checks": 52,
  "fundamental_matrix_route_comparisons": 2304,
  "nonzero_coefficients_compared": 1204,
  "taylor_depth": 7,
  "max_taylor_order": 36,
  "enlarged_system_symbolic_identities": 100,
  "pullback_and_residue_checks": 3,
  "descending_residue_identities": 12,
  "constant_certificate": {
    "log_lower": "753114459111884487225644939696932713875971793033276834896775552/553363288220835205777494909307713877862954255822400617330837775",
    "log_upper": "3012457842721143971927901689146116259358437248288124914612635873/2213453152883340823109979637230855511451817023289602469323351100",
    "sqrt_upper": "1167/1000",
    "constant_lower": "3765572295559422436128224698484663569379858965166384174483877760000/17328482349264545011398169914510522305545167570803145333968630899719",
    "constant_lower_decimal_diagnostic": 0.21730537156470836,
    "greater_than_0_21_exact": true,
    "rank_slope_greater_than_1_exact": true
  },
  "status": "Exact finite supporting checks; same assistant; not formal or independent mathematical verification."
}