{
  "physical_measurements": 0,
  "required_rear_cornering_stiffness_each_N_rad_for_nonnegative_understeer": 76363.63636363637,
  "selected_rear_cornering_stiffness_each_N_rad_target": 90000.0,
  "linear_lateral_models": [
    {
      "rear_cornering_stiffness_each_N_rad": 70000.0,
      "understeer_coefficient_s2_m": -0.0008214505660377375,
      "critical_speed_kmh_in_linear_model": 210.17971549750828,
      "states": [
        {
          "speed_kmh": 100,
          "eigenvalues_per_s": [
            [
              -2.1221654119382025,
              0.0
            ],
            [
              -6.0630684849517085,
              0.0
            ]
          ],
          "maximum_real_eigenvalue_per_s": -2.1221654119382025,
          "trace_negative": true,
          "determinant_positive": true
        },
        {
          "speed_kmh": 200,
          "eigenvalues_per_s": [
            [
              -0.09839529515164092,
              0.0
            ],
            [
              -3.994221653293314,
              0.0
            ]
          ],
          "maximum_real_eigenvalue_per_s": -0.09839529515164092,
          "trace_negative": true,
          "determinant_positive": true
        },
        {
          "speed_kmh": 300,
          "eigenvalues_per_s": [
            [
              0.5795050801559218,
              0.0
            ],
            [
              -3.3079163791192254,
              0.0
            ]
          ],
          "maximum_real_eigenvalue_per_s": 0.5795050801559218,
          "trace_negative": true,
          "determinant_positive": false
        },
        {
          "speed_kmh": 400,
          "eigenvalues_per_s": [
            [
              0.9190834870273026,
              0.0
            ],
            [
              -2.9653919612497806,
              0.0
            ]
          ],
          "maximum_real_eigenvalue_per_s": 0.9190834870273026,
          "trace_negative": true,
          "determinant_positive": false
        }
      ]
    },
    {
      "rear_cornering_stiffness_each_N_rad": 90000.0,
      "understeer_coefficient_s2_m": 0.0013690842767295594,
      "critical_speed_kmh_in_linear_model": null,
      "states": [
        {
          "speed_kmh": 100,
          "eigenvalues_per_s": [
            [
              -4.647183454633563,
              2.8026920648907456
            ],
            [
              -4.647183454633563,
              -2.8026920648907456
            ]
          ],
          "maximum_real_eigenvalue_per_s": -4.647183454633563,
          "trace_negative": true,
          "determinant_positive": true
        },
        {
          "speed_kmh": 200,
          "eigenvalues_per_s": [
            [
              -2.3235917273167814,
              2.830997653530431
            ],
            [
              -2.3235917273167814,
              -2.830997653530431
            ]
          ],
          "maximum_real_eigenvalue_per_s": -2.3235917273167814,
          "trace_negative": true,
          "determinant_positive": true
        },
        {
          "speed_kmh": 300,
          "eigenvalues_per_s": [
            [
              -1.5490611515445212,
              2.8362084288739755
            ],
            [
              -1.5490611515445212,
              -2.8362084288739755
            ]
          ],
          "maximum_real_eigenvalue_per_s": -1.5490611515445212,
          "trace_negative": true,
          "determinant_positive": true
        },
        {
          "speed_kmh": 400,
          "eigenvalues_per_s": [
            [
              -1.1617958636583907,
              2.8380299399791618
            ],
            [
              -1.1617958636583907,
              -2.8380299399791618
            ]
          ],
          "maximum_real_eigenvalue_per_s": -1.1617958636583907,
          "trace_negative": true,
          "determinant_positive": true
        }
      ]
    }
  ],
  "ideal_LQR_closed_loop_checks": [
    {
      "speed_kmh": 25,
      "maximum_ideal_linear_closed_loop_eigenvalue_per_s": -0.9240539302577921
    },
    {
      "speed_kmh": 100,
      "maximum_ideal_linear_closed_loop_eigenvalue_per_s": -2.267757388891409
    },
    {
      "speed_kmh": 200,
      "maximum_ideal_linear_closed_loop_eigenvalue_per_s": -1.6137147801017013
    },
    {
      "speed_kmh": 300,
      "maximum_ideal_linear_closed_loop_eigenvalue_per_s": -1.3106993915232446
    },
    {
      "speed_kmh": 400,
      "maximum_ideal_linear_closed_loop_eigenvalue_per_s": -1.1343626836238123
    }
  ],
  "maximum_contact_force_power_identity_error_W": 5.020410753786564e-10,
  "classification": "Formal checks within the stated linear/force model, not physical vehicle validation.",
  "interpretation": [
    "For positive cornering stiffness the two-state lateral subsystem has negative trace. If b*Cr >= a*Cf its determinant is positive for every finite positive speed in this model.",
    "The initial 70 kN/rad-per-rear-tyre target falls below the 76.4 kN/rad threshold for the assumed geometry. The revised 90 kN/rad target is a hardware requirement to measure, not a measured tyre specification.",
    "The linear proof omits combined braking saturation, load transfer, actuator delays and nonlinear tyres. Those are addressed only by the explicit scenario screen, not covered by this proof."
  ]
}