{
  "inputs": {
    "T": "100",
    "L": "100",
    "s": "1",
    "dilution": "1"
  },
  "molecularity": {
    "reactants": [
      2,
      2,
      2,
      2,
      0,
      0
    ],
    "products": [
      2,
      0,
      1,
      9,
      1,
      1
    ],
    "catalyst_free": true
  },
  "rates": [
    "10000",
    "4",
    "100",
    "10000",
    "99",
    "2"
  ],
  "equilibrium": [
    "1",
    "1",
    "1",
    "1/100"
  ],
  "flux": [
    "100",
    "4",
    "100",
    "1",
    "99",
    "2"
  ],
  "jacobian": [
    [
      "-100",
      "0",
      "0",
      "-9800"
    ],
    [
      "0",
      "-4",
      "-4",
      "800"
    ],
    [
      "200",
      "-4",
      "-404",
      "20800"
    ],
    [
      "-100",
      "0",
      "200",
      "-10400"
    ]
  ],
  "operating_classification": {
    "status": "unstable_complex_pair",
    "coefficients": [
      "10908",
      "185600",
      "1280000",
      "64000000"
    ],
    "H": "-5025252352000000",
    "second_hurwitz": "2023244800"
  },
  "source_100_100_root_certificate": {
    "certified": true,
    "real_part_bracket": [
      "2",
      "4"
    ],
    "H_at_endpoints": [
      "-2133097221521408",
      "2676722101092352"
    ],
    "shifted_coefficients": [
      "4*t + 10908",
      "6*t**2 + 32724*t + 185600",
      "4*t**3 + 32724*t**2 + 371200*t + 1280000",
      "t**4 + 10908*t**3 + 185600*t**2 + 1280000*t + 64000000"
    ],
    "H_shift": "64*t**6 + 1047168*t**5 + 5717193472*t**4 + 10447845060096*t**3 + 176860746547200*t**2 + 1050518937600000*t - 5025252352000000",
    "root_construction": "At an intervening zero of H(t), omega=sqrt(C(t)/A(t)); p(t+i*omega)=0."
  },
  "family_certificate": {
    "family_coefficients": [
      "L*(T + 4) + 5*T + 8",
      "2*L*(7*T + 16) + 4*T*(T + 6)",
      "16*T*(7*L + T)",
      "64*L*T**2"
    ],
    "H": "-64*L**3*T**4 + 1056*L**3*T**3 + 8832*L**3*T**2 + 14336*L**3*T + 32*L**2*T**4 + 10144*L**2*T**3 + 26624*L**2*T**2 + 28672*L**2*T + 64*L*T**5 + 2400*L*T**4 + 14208*L*T**3 + 21504*L*T**2 + 320*T**5 + 2176*T**4 + 3072*T**3",
    "negative_ray_coefficients_descending": [
      "-5254246400",
      "-1562660812800",
      "-154010347520000",
      "-5025252352000000"
    ],
    "large_L_leading_coefficient": "-32*T*(T + 4)*(2*T**2 - 41*T - 112)",
    "fast_D_matrix": [
      [
        "-6*T/(T + 4)",
        "0",
        "-2*T*(T - 2)/(T + 4)"
      ],
      [
        "-8*T/(T + 4)",
        "-4",
        "4*(3*T - 4)/(T + 4)"
      ],
      [
        "0",
        "-4",
        "-4"
      ]
    ],
    "fast_D_cubic_coefficients": [
      "2*(7*T + 16)/(T + 4)",
      "112*T/(T + 4)",
      "64*T**2/(T + 4)"
    ],
    "fast_D_hurwitz": "-32*T*(2*T**2 - 41*T - 112)/(T + 4)**2",
    "large_L_threshold": "41/4 + sqrt(2577)/4",
    "large_L_threshold_numeric": 22.941040146497055
  },
  "stable_control": {
    "status": "strictly_stable",
    "coefficients": [
      "24",
      "124",
      "288",
      "256"
    ],
    "H": "626688",
    "second_hurwitz": "2688"
  },
  "child_count": 25,
  "singular_children": 4,
  "maximal_assignments": [
    [
      null,
      null,
      1,
      0
    ],
    [
      null,
      1,
      2,
      0
    ],
    [
      0,
      null,
      1,
      3
    ],
    [
      0,
      1,
      2,
      3
    ]
  ],
  "completion": {
    "reaction_count": 12,
    "feed_concentrations": [
      "100",
      "1",
      "1",
      "201/100"
    ],
    "child_count": 121,
    "all_children_transported": true,
    "spectral_classification": {
      "status": "unstable_complex_pair",
      "coefficients": [
        "10912",
        "218330",
        "1683928",
        "65476509"
      ],
      "H": "-3787419104552000",
      "second_hurwitz": "2380733032"
    },
    "source_margin_applies": true
  },
  "local_dynamics": {
    "eigenvalue_real": 2.999746757992079,
    "eigenvalue_imag": 15.68952573460232,
    "relative_linear_error": 4.920166074674216e-06,
    "independent_solver_error_relative_to_mode": 0.0008229080944758257,
    "scope": "Short-time numerical departure only; no periodic-orbit or long-time claim."
  },
  "mass_obstruction": "2C->D and 2D->A+4B+4C imply mass_A+4*mass_B=0, impossible with positive masses.",
  "scope": "Kinetic abstract-species counterexample; products can have nine molecules. No atom-balanced mechanism, Hopf theorem or Lean rerun."
}