{
  "A_D_at_c3_theta1_m1": "-u**8/8 + u**7/7 - u**6/6 + u**5/5 - u**4/4 + u**3/3 - u**2/2 + 3",
  "A_D_general": "c + m*theta*(-u**8/8 + u**7/7 - u**6/6 + u**5/5 - u**4/4 + u**3/3 - u**2/2)",
  "D": 8,
  "K": 2,
  "K_jet_derivative_residuals_in_u": [
    "0",
    "0",
    "0"
  ],
  "N": 2,
  "all_checks_passed": true,
  "alpha_rho_at_c3_theta1_m1": "-22883*delta*rho**4*u**7/5184 + 3143*delta*rho**4*u**6/648 - 385*delta*rho**4*u**5/72 + 35*delta*rho**4*u**4/6 - 35*delta*rho**4*u**3/6 + 175*delta*rho**2*u**7/16 - 35*delta*rho**2*u**6/4 + 21*delta*rho**2*u**5/4 - delta*u**7 - u**8/8 + u**7/7 - u**6/6 + u**5/5 - u**4/4 + u**3/3 - u**2/2 + 3",
  "alpha_rho_general": "c - delta*m**(7/2)*u**7 + 175*delta*m**(5/2)*rho**2*u**7/16 - 35*delta*m**(5/2)*rho**2*u**6/4 + 21*delta*m**(5/2)*rho**2*u**5/4 - 22883*delta*m**(3/2)*rho**4*u**7/5184 + 3143*delta*m**(3/2)*rho**4*u**6/648 - 385*delta*m**(3/2)*rho**4*u**5/72 + 35*delta*m**(3/2)*rho**4*u**4/6 - 35*delta*m**(3/2)*rho**4*u**3/6 - m*theta*u**8/8 + m*theta*u**7/7 - m*theta*u**6/6 + m*theta*u**5/5 - m*theta*u**4/4 + m*theta*u**3/3 - m*theta*u**2/2",
  "b_j": [
    "-35/6",
    "21/4",
    "-1"
  ],
  "base_endpoint_at_c3_theta1_m1": "359/280",
  "basis": [
    {
      "Q_j_at_m_1": "3269*u**7/4320 - 449*u**6/540 + 11*u**5/12 - u**4 + u**3",
      "Q_j_general_scaling": "m**(3/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 3
        },
        {
          "coefficient": "-1",
          "power": 4
        },
        {
          "coefficient": "11/12",
          "power": 5
        },
        {
          "coefficient": "-449/540",
          "power": 6
        },
        {
          "coefficient": "3269/4320",
          "power": 7
        }
      ],
      "d_j": 3,
      "j": 0,
      "polynomial_degree": 7,
      "squared_germ_difference_order_at_least": 11,
      "vanishing_order": 3
    },
    {
      "Q_j_at_m_1": "25*u**7/12 - 5*u**6/3 + u**5",
      "Q_j_general_scaling": "m**(5/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 5
        },
        {
          "coefficient": "-5/3",
          "power": 6
        },
        {
          "coefficient": "25/12",
          "power": 7
        }
      ],
      "d_j": 5,
      "j": 1,
      "polynomial_degree": 7,
      "squared_germ_difference_order_at_least": 13,
      "vanishing_order": 5
    },
    {
      "Q_j_at_m_1": "u**7",
      "Q_j_general_scaling": "m**(7/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 7
        }
      ],
      "d_j": 7,
      "j": 2,
      "polynomial_degree": 7,
      "squared_germ_difference_order_at_least": 15,
      "vanishing_order": 7
    }
  ],
  "checks": {
    "K_jet_matches_center": true,
    "Q0_degree_at_most_D_minus_one": true,
    "Q0_leading_germ_coefficient": true,
    "Q0_squared_log_germ_identity": true,
    "Q0_vanishing_order": true,
    "Q1_degree_at_most_D_minus_one": true,
    "Q1_leading_germ_coefficient": true,
    "Q1_squared_log_germ_identity": true,
    "Q1_vanishing_order": true,
    "Q2_degree_at_most_D_minus_one": true,
    "Q2_leading_germ_coefficient": true,
    "Q2_squared_log_germ_identity": true,
    "Q2_vanishing_order": true,
    "Taylor_curvature_rational_identity": true,
    "Taylor_curvature_sum": true,
    "Taylor_remainder_derivative_identity": true,
    "Taylor_remainder_zero_at_origin": true,
    "b_0_nonzero": true,
    "b_0_parity_sign": true,
    "b_N_equals_minus_one": true,
    "base_D_jet_matches_center": true,
    "base_endpoint_harmonic_identity": true,
    "base_endpoint_positive_at_c3_theta1_m1": true,
    "corrected_K_jet_matches_center": true,
    "corrected_exact_degree": true,
    "corrected_leading_coefficient": true,
    "corrected_left_endpoint_identity": true,
    "corrected_right_anchor_identity": true,
    "correction_vanishes_to_order_at_least_D_minus_two": true,
    "degree_formula": true,
    "degree_is_even": true,
    "endpoint_correction_matrix_determinant": true,
    "exact_degree": true,
    "first_perturbation_order_above_K": true,
    "harmonic_moment_target_identity": true,
    "last_basis_exact_monomial": true,
    "leading_coefficient": true,
    "linear_degree_bound": true,
    "oscillator_moment_C1": true,
    "oscillator_moment_C2": true,
    "oscillator_moment_C3": true,
    "t0_divisible_by_rho_squared": true,
    "t0_is_polynomial_in_rho": true,
    "t1_divisible_by_rho_squared": true,
    "t1_is_polynomial_in_rho": true,
    "target_root_1_is_simple": true,
    "target_root_1_is_zero": true,
    "target_root_1_slope_sign": true,
    "target_root_2_is_simple": true,
    "target_root_2_is_zero": true,
    "target_root_2_slope_sign": true
  },
  "curvature_rational_denominator": "(1+u)**2",
  "curvature_rational_numerator": "7*u**8 + 8*u**7 + 1",
  "d_j": [
    3,
    5,
    7
  ],
  "endpoint_correction": {
    "E_rho": "175*delta*m**(5/2)*rho**2*u**7/16 - 35*delta*m**(5/2)*rho**2*u**6/4 + 21*delta*m**(5/2)*rho**2*u**5/4 - 22883*delta*m**(3/2)*rho**4*u**7/5184 + 3143*delta*m**(3/2)*rho**4*u**6/648 - 385*delta*m**(3/2)*rho**4*u**5/72 + 35*delta*m**(3/2)*rho**4*u**4/6 - 35*delta*m**(3/2)*rho**4*u**3/6",
    "E_rho_at_b": "175*delta*m**(5/2)*rho**2*z**7/16 - 35*delta*m**(5/2)*rho**2*z**6/4 + 21*delta*m**(5/2)*rho**2*z**5/4 - 22883*delta*m**(3/2)*rho**4*z**7/5184 + 3143*delta*m**(3/2)*rho**4*z**6/648 - 385*delta*m**(3/2)*rho**4*z**5/72 + 35*delta*m**(3/2)*rho**4*z**4/6 - 35*delta*m**(3/2)*rho**4*z**3/6",
    "E_rho_at_x0": "-399*delta*m**(5/2)*rho**2/16 + 45409*delta*m**(3/2)*rho**4/1728",
    "anchor": "b=a*(1+z), with z>0",
    "anchor_value_scope": "The identity is P_hat_rho(b)=P_0(b). It equals zero when b is chosen as a root of P_0 in the analytic construction.",
    "corrected_degree": 8,
    "correction": "t_0*u**(D-2)+t_1*u**(D-1)",
    "correction_order_at_least": 6,
    "fixed_anchor_value": "c - delta*m**(7/2)*z**7 - m*theta*z**8/8 + m*theta*z**7/7 - m*theta*z**6/6 + m*theta*z**5/5 - m*theta*z**4/4 + m*theta*z**3/3 - m*theta*z**2/2",
    "fixed_left_value": "c + delta*m**(7/2) - 481*m*theta/280",
    "t_0": "(9072*delta*m**(5/2)*rho**2*z**3 - 3402*delta*m**(5/2)*rho**2*z**2 - 14168*delta*m**(3/2)*rho**4*z**3 + 11025*delta*m**(3/2)*rho**4*z**2 - 7560*delta*m**(3/2)*rho**4*z + 3780*delta*m**(3/2)*rho**4)/(648*z**3)",
    "t_1": "(-56700*delta*m**(5/2)*rho**2*z**3 - 27216*delta*m**(5/2)*rho**2*z**2 + 22883*delta*m**(3/2)*rho**4*z**3 + 88200*delta*m**(3/2)*rho**4*z**2 - 60480*delta*m**(3/2)*rho**4*z + 30240*delta*m**(3/2)*rho**4)/(5184*z**3)"
  },
  "h_i": [
    "1",
    "2"
  ],
  "leading_coefficient_in_u": "-m*theta/8",
  "leading_coefficient_in_x": "-m*theta/(8*a**8)",
  "moment_common_factor": "pi/sqrt(c)",
  "moment_target_divided_by_common_factor": "-35*h**4/4 + 105*h**3/4 - 35*h**2/2",
  "moment_target_factored_divided_by_common_factor": "-35*h**2*(h - 2)*(h - 1)/4",
  "moment_target_root_slopes_divided_by_common_factor": [
    "35/4",
    "-35"
  ],
  "normalized_curvature_polynomial": "7*u**6 - 6*u**5 + 5*u**4 - 4*u**3 + 3*u**2 - 2*u + 1",
  "q": 1
}