{
  "A_D_at_c3_theta1_m1": "-u**14/14 + u**13/13 - u**12/12 + u**11/11 - u**10/10 + u**9/9 - 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**14/14 + u**13/13 - u**12/12 + u**11/11 - u**10/10 + u**9/9 - u**8/8 + u**7/7 - u**6/6 + u**5/5 - u**4/4 + u**3/3 - u**2/2)",
  "D": 14,
  "K": 5,
  "K_jet_derivative_residuals_in_u": [
    "0",
    "0",
    "0",
    "0",
    "0",
    "0"
  ],
  "N": 3,
  "all_checks_passed": true,
  "alpha_rho_at_c3_theta1_m1": "533389571*delta*rho**6*u**13/1814400 - 7909759*delta*rho**6*u**12/30240 + 323323*delta*rho**6*u**11/1440 - 54769*delta*rho**6*u**10/300 + 2717*delta*rho**6*u**9/20 - 429*delta*rho**6*u**8/5 + 1287*delta*rho**6*u**7/35 - 28381639*delta*rho**4*u**13/60480 + 2546687*delta*rho**4*u**12/7560 - 36179*delta*rho**4*u**11/168 + 1573*delta*rho**4*u**10/14 - 1573*delta*rho**4*u**9/42 + 1287*delta*rho**2*u**13/14 - 286*delta*rho**2*u**12/7 + 78*delta*rho**2*u**11/7 - delta*u**13 - u**14/14 + u**13/13 - u**12/12 + u**11/11 - u**10/10 + u**9/9 - 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**(13/2)*u**13 + 1287*delta*m**(11/2)*rho**2*u**13/14 - 286*delta*m**(11/2)*rho**2*u**12/7 + 78*delta*m**(11/2)*rho**2*u**11/7 - 28381639*delta*m**(9/2)*rho**4*u**13/60480 + 2546687*delta*m**(9/2)*rho**4*u**12/7560 - 36179*delta*m**(9/2)*rho**4*u**11/168 + 1573*delta*m**(9/2)*rho**4*u**10/14 - 1573*delta*m**(9/2)*rho**4*u**9/42 + 533389571*delta*m**(7/2)*rho**6*u**13/1814400 - 7909759*delta*m**(7/2)*rho**6*u**12/30240 + 323323*delta*m**(7/2)*rho**6*u**11/1440 - 54769*delta*m**(7/2)*rho**6*u**10/300 + 2717*delta*m**(7/2)*rho**6*u**9/20 - 429*delta*m**(7/2)*rho**6*u**8/5 + 1287*delta*m**(7/2)*rho**6*u**7/35 - m*theta*u**14/14 + m*theta*u**13/13 - m*theta*u**12/12 + m*theta*u**11/11 - m*theta*u**10/10 + m*theta*u**9/9 - 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": [
    "1287/35",
    "-1573/42",
    "78/7",
    "-1"
  ],
  "base_endpoint_at_c3_theta1_m1": "269707/360360",
  "basis": [
    {
      "Q_j_at_m_1": "3729997*u**13/466560 - 55313*u**12/7776 + 15827*u**11/2592 - 2681*u**10/540 + 133*u**9/36 - 7*u**8/3 + u**7",
      "Q_j_general_scaling": "m**(7/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 7
        },
        {
          "coefficient": "-7/3",
          "power": 8
        },
        {
          "coefficient": "133/36",
          "power": 9
        },
        {
          "coefficient": "-2681/540",
          "power": 10
        },
        {
          "coefficient": "15827/2592",
          "power": 11
        },
        {
          "coefficient": "-55313/7776",
          "power": 12
        },
        {
          "coefficient": "3729997/466560",
          "power": 13
        }
      ],
      "d_j": 7,
      "j": 0,
      "polynomial_degree": 13,
      "squared_germ_difference_order_at_least": 21,
      "vanishing_order": 7
    },
    {
      "Q_j_at_m_1": "18043*u**13/1440 - 1619*u**12/180 + 23*u**11/4 - 3*u**10 + u**9",
      "Q_j_general_scaling": "m**(9/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 9
        },
        {
          "coefficient": "-3",
          "power": 10
        },
        {
          "coefficient": "23/4",
          "power": 11
        },
        {
          "coefficient": "-1619/180",
          "power": 12
        },
        {
          "coefficient": "18043/1440",
          "power": 13
        }
      ],
      "d_j": 9,
      "j": 1,
      "polynomial_degree": 13,
      "squared_germ_difference_order_at_least": 23,
      "vanishing_order": 9
    },
    {
      "Q_j_at_m_1": "33*u**13/4 - 11*u**12/3 + u**11",
      "Q_j_general_scaling": "m**(11/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 11
        },
        {
          "coefficient": "-11/3",
          "power": 12
        },
        {
          "coefficient": "33/4",
          "power": 13
        }
      ],
      "d_j": 11,
      "j": 2,
      "polynomial_degree": 13,
      "squared_germ_difference_order_at_least": 25,
      "vanishing_order": 11
    },
    {
      "Q_j_at_m_1": "u**13",
      "Q_j_general_scaling": "m**(13/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 13
        }
      ],
      "d_j": 13,
      "j": 3,
      "polynomial_degree": 13,
      "squared_germ_difference_order_at_least": 27,
      "vanishing_order": 13
    }
  ],
  "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,
    "Q3_degree_at_most_D_minus_one": true,
    "Q3_leading_germ_coefficient": true,
    "Q3_squared_log_germ_identity": true,
    "Q3_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_C3": true,
    "oscillator_moment_C4": true,
    "oscillator_moment_C5": true,
    "oscillator_moment_C6": 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,
    "target_root_3_is_simple": true,
    "target_root_3_is_zero": true,
    "target_root_3_slope_sign": true
  },
  "curvature_rational_denominator": "(1+u)**2",
  "curvature_rational_numerator": "13*u**14 + 14*u**13 + 1",
  "d_j": [
    7,
    9,
    11,
    13
  ],
  "endpoint_correction": {
    "E_rho": "1287*delta*m**(11/2)*rho**2*u**13/14 - 286*delta*m**(11/2)*rho**2*u**12/7 + 78*delta*m**(11/2)*rho**2*u**11/7 - 28381639*delta*m**(9/2)*rho**4*u**13/60480 + 2546687*delta*m**(9/2)*rho**4*u**12/7560 - 36179*delta*m**(9/2)*rho**4*u**11/168 + 1573*delta*m**(9/2)*rho**4*u**10/14 - 1573*delta*m**(9/2)*rho**4*u**9/42 + 533389571*delta*m**(7/2)*rho**6*u**13/1814400 - 7909759*delta*m**(7/2)*rho**6*u**12/30240 + 323323*delta*m**(7/2)*rho**6*u**11/1440 - 54769*delta*m**(7/2)*rho**6*u**10/300 + 2717*delta*m**(7/2)*rho**6*u**9/20 - 429*delta*m**(7/2)*rho**6*u**8/5 + 1287*delta*m**(7/2)*rho**6*u**7/35",
    "E_rho_at_b": "1287*delta*m**(11/2)*rho**2*z**13/14 - 286*delta*m**(11/2)*rho**2*z**12/7 + 78*delta*m**(11/2)*rho**2*z**11/7 - 28381639*delta*m**(9/2)*rho**4*z**13/60480 + 2546687*delta*m**(9/2)*rho**4*z**12/7560 - 36179*delta*m**(9/2)*rho**4*z**11/168 + 1573*delta*m**(9/2)*rho**4*z**10/14 - 1573*delta*m**(9/2)*rho**4*z**9/42 + 533389571*delta*m**(7/2)*rho**6*z**13/1814400 - 7909759*delta*m**(7/2)*rho**6*z**12/30240 + 323323*delta*m**(7/2)*rho**6*z**11/1440 - 54769*delta*m**(7/2)*rho**6*z**10/300 + 2717*delta*m**(7/2)*rho**6*z**9/20 - 429*delta*m**(7/2)*rho**6*z**8/5 + 1287*delta*m**(7/2)*rho**6*z**7/35",
    "E_rho_at_x0": "-2015*delta*m**(11/2)*rho**2/14 + 14168011*delta*m**(9/2)*rho**4/12096 - 2215484843*delta*m**(7/2)*rho**6/1814400",
    "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": 14,
    "correction": "t_0*u**(D-2)+t_1*u**(D-1)",
    "correction_order_at_least": 12,
    "fixed_anchor_value": "c - delta*m**(13/2)*z**13 - m*theta*z**14/14 + m*theta*z**13/13 - m*theta*z**12/12 + m*theta*z**11/11 - m*theta*z**10/10 + m*theta*z**9/9 - 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**(13/2) - 811373*m*theta/360360",
    "t_0": "(7862400*delta*m**(11/2)*rho**2*z**5 - 1684800*delta*m**(11/2)*rho**2*z**4 - 106146040*delta*m**(9/2)*rho**4*z**5 + 55212300*delta*m**(9/2)*rho**4*z**4 - 22651200*delta*m**(9/2)*rho**4*z**3 + 5662800*delta*m**(9/2)*rho**4*z**2 + 140174606*delta*m**(7/2)*rho**6*z**5 - 100625811*delta*m**(7/2)*rho**6*z**4 + 66676896*delta*m**(7/2)*rho**6*z**3 - 39073320*delta*m**(7/2)*rho**6*z**2 + 18532800*delta*m**(7/2)*rho**6*z - 5559840*delta*m**(7/2)*rho**6)/(151200*z**5)",
    "t_1": "(-166795200*delta*m**(11/2)*rho**2*z**5 - 20217600*delta*m**(11/2)*rho**2*z**4 + 851449170*delta*m**(9/2)*rho**4*z**5 + 662547600*delta*m**(9/2)*rho**4*z**4 - 271814400*delta*m**(9/2)*rho**4*z**3 + 67953600*delta*m**(9/2)*rho**4*z**2 - 533389571*delta*m**(7/2)*rho**6*z**5 - 1207509732*delta*m**(7/2)*rho**6*z**4 + 800122752*delta*m**(7/2)*rho**6*z**3 - 468879840*delta*m**(7/2)*rho**6*z**2 + 222393600*delta*m**(7/2)*rho**6*z - 66718080*delta*m**(7/2)*rho**6)/(1814400*z**5)"
  },
  "h_i": [
    "1",
    "2",
    "3"
  ],
  "leading_coefficient_in_u": "-m*theta/14",
  "leading_coefficient_in_x": "-m*theta/(14*a**14)",
  "moment_common_factor": "pi/sqrt(c)",
  "moment_target_divided_by_common_factor": "-429*h**7/8 + 1287*h**6/4 - 4719*h**5/8 + 1287*h**4/4",
  "moment_target_factored_divided_by_common_factor": "-429*h**4*(h - 3)*(h - 2)*(h - 1)/8",
  "moment_target_root_slopes_divided_by_common_factor": [
    "-429/4",
    "858",
    "-34749/4"
  ],
  "normalized_curvature_polynomial": "13*u**12 - 12*u**11 + 11*u**10 - 10*u**9 + 9*u**8 - 8*u**7 + 7*u**6 - 6*u**5 + 5*u**4 - 4*u**3 + 3*u**2 - 2*u + 1",
  "q": 3
}