{
  "A_D_at_c3_theta1_m1": "-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**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": 12,
  "K": 2,
  "K_jet_derivative_residuals_in_u": [
    "0",
    "0",
    "0"
  ],
  "N": 4,
  "all_checks_passed": true,
  "alpha_rho_at_c3_theta1_m1": "-1587761527*delta*rho**8*u**11/12441600 + 35473361*delta*rho**8*u**10/259200 - 114747721*delta*rho**8*u**9/777600 + 691559*delta*rho**8*u**8/4320 - 251713*delta*rho**8*u**7/1440 + 34573*delta*rho**8*u**6/180 - 847*delta*rho**8*u**5/4 + 231*delta*rho**8*u**4 - 231*delta*rho**8*u**3 + 95310611*delta*rho**6*u**11/124416 - 2593525*delta*rho**6*u**10/3456 + 2497495*delta*rho**6*u**9/3456 - 97405*delta*rho**6*u**8/144 + 9625*delta*rho**6*u**7/16 - 1925*delta*rho**6*u**6/4 + 1155*delta*rho**6*u**5/4 - 1218679*delta*rho**4*u**11/1728 + 206437*delta*rho**4*u**10/360 - 10241*delta*rho**4*u**9/24 + 539*delta*rho**4*u**8/2 - 231*delta*rho**4*u**7/2 + 1265*delta*rho**2*u**11/12 - 55*delta*rho**2*u**10 + 55*delta*rho**2*u**9/3 - delta*u**11 - 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**(11/2)*u**11 + 1265*delta*m**(9/2)*rho**2*u**11/12 - 55*delta*m**(9/2)*rho**2*u**10 + 55*delta*m**(9/2)*rho**2*u**9/3 - 1218679*delta*m**(7/2)*rho**4*u**11/1728 + 206437*delta*m**(7/2)*rho**4*u**10/360 - 10241*delta*m**(7/2)*rho**4*u**9/24 + 539*delta*m**(7/2)*rho**4*u**8/2 - 231*delta*m**(7/2)*rho**4*u**7/2 + 95310611*delta*m**(5/2)*rho**6*u**11/124416 - 2593525*delta*m**(5/2)*rho**6*u**10/3456 + 2497495*delta*m**(5/2)*rho**6*u**9/3456 - 97405*delta*m**(5/2)*rho**6*u**8/144 + 9625*delta*m**(5/2)*rho**6*u**7/16 - 1925*delta*m**(5/2)*rho**6*u**6/4 + 1155*delta*m**(5/2)*rho**6*u**5/4 - 1587761527*delta*m**(3/2)*rho**8*u**11/12441600 + 35473361*delta*m**(3/2)*rho**8*u**10/259200 - 114747721*delta*m**(3/2)*rho**8*u**9/777600 + 691559*delta*m**(3/2)*rho**8*u**8/4320 - 251713*delta*m**(3/2)*rho**8*u**7/1440 + 34573*delta*m**(3/2)*rho**8*u**6/180 - 847*delta*m**(3/2)*rho**8*u**5/4 + 231*delta*m**(3/2)*rho**8*u**4 - 231*delta*m**(3/2)*rho**8*u**3 - 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": [
    "-231",
    "1155/4",
    "-231/2",
    "55/3",
    "-1"
  ],
  "base_endpoint_at_c3_theta1_m1": "24859/27720",
  "basis": [
    {
      "Q_j_at_m_1": "144341957*u**11/261273600 - 460693*u**10/777600 + 10431611*u**9/16329600 - 62869*u**8/90720 + 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
        },
        {
          "coefficient": "-62869/90720",
          "power": 8
        },
        {
          "coefficient": "10431611/16329600",
          "power": 9
        },
        {
          "coefficient": "-460693/777600",
          "power": 10
        },
        {
          "coefficient": "144341957/261273600",
          "power": 11
        }
      ],
      "d_j": 3,
      "j": 0,
      "polynomial_degree": 11,
      "squared_germ_difference_order_at_least": 15,
      "vanishing_order": 3
    },
    {
      "Q_j_at_m_1": "8664601*u**11/3265920 - 47155*u**10/18144 + 6487*u**9/2592 - 253*u**8/108 + 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
        },
        {
          "coefficient": "-253/108",
          "power": 8
        },
        {
          "coefficient": "6487/2592",
          "power": 9
        },
        {
          "coefficient": "-47155/18144",
          "power": 10
        },
        {
          "coefficient": "8664601/3265920",
          "power": 11
        }
      ],
      "d_j": 5,
      "j": 1,
      "polynomial_degree": 11,
      "squared_germ_difference_order_at_least": 17,
      "vanishing_order": 5
    },
    {
      "Q_j_at_m_1": "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
        }
      ],
      "d_j": 7,
      "j": 2,
      "polynomial_degree": 11,
      "squared_germ_difference_order_at_least": 19,
      "vanishing_order": 7
    },
    {
      "Q_j_at_m_1": "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
        }
      ],
      "d_j": 9,
      "j": 3,
      "polynomial_degree": 11,
      "squared_germ_difference_order_at_least": 21,
      "vanishing_order": 9
    },
    {
      "Q_j_at_m_1": "u**11",
      "Q_j_general_scaling": "m**(11/2) times Q_j_at_m_1",
      "coefficients": [
        {
          "coefficient": "1",
          "power": 11
        }
      ],
      "d_j": 11,
      "j": 4,
      "polynomial_degree": 11,
      "squared_germ_difference_order_at_least": 23,
      "vanishing_order": 11
    }
  ],
  "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,
    "Q4_degree_at_most_D_minus_one": true,
    "Q4_leading_germ_coefficient": true,
    "Q4_squared_log_germ_identity": true,
    "Q4_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,
    "oscillator_moment_C4": true,
    "oscillator_moment_C5": 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,
    "target_root_4_is_simple": true,
    "target_root_4_is_zero": true,
    "target_root_4_slope_sign": true
  },
  "curvature_rational_denominator": "(1+u)**2",
  "curvature_rational_numerator": "11*u**12 + 12*u**11 + 1",
  "d_j": [
    3,
    5,
    7,
    9,
    11
  ],
  "endpoint_correction": {
    "E_rho": "1265*delta*m**(9/2)*rho**2*u**11/12 - 55*delta*m**(9/2)*rho**2*u**10 + 55*delta*m**(9/2)*rho**2*u**9/3 - 1218679*delta*m**(7/2)*rho**4*u**11/1728 + 206437*delta*m**(7/2)*rho**4*u**10/360 - 10241*delta*m**(7/2)*rho**4*u**9/24 + 539*delta*m**(7/2)*rho**4*u**8/2 - 231*delta*m**(7/2)*rho**4*u**7/2 + 95310611*delta*m**(5/2)*rho**6*u**11/124416 - 2593525*delta*m**(5/2)*rho**6*u**10/3456 + 2497495*delta*m**(5/2)*rho**6*u**9/3456 - 97405*delta*m**(5/2)*rho**6*u**8/144 + 9625*delta*m**(5/2)*rho**6*u**7/16 - 1925*delta*m**(5/2)*rho**6*u**6/4 + 1155*delta*m**(5/2)*rho**6*u**5/4 - 1587761527*delta*m**(3/2)*rho**8*u**11/12441600 + 35473361*delta*m**(3/2)*rho**8*u**10/259200 - 114747721*delta*m**(3/2)*rho**8*u**9/777600 + 691559*delta*m**(3/2)*rho**8*u**8/4320 - 251713*delta*m**(3/2)*rho**8*u**7/1440 + 34573*delta*m**(3/2)*rho**8*u**6/180 - 847*delta*m**(3/2)*rho**8*u**5/4 + 231*delta*m**(3/2)*rho**8*u**4 - 231*delta*m**(3/2)*rho**8*u**3",
    "E_rho_at_b": "1265*delta*m**(9/2)*rho**2*z**11/12 - 55*delta*m**(9/2)*rho**2*z**10 + 55*delta*m**(9/2)*rho**2*z**9/3 - 1218679*delta*m**(7/2)*rho**4*z**11/1728 + 206437*delta*m**(7/2)*rho**4*z**10/360 - 10241*delta*m**(7/2)*rho**4*z**9/24 + 539*delta*m**(7/2)*rho**4*z**8/2 - 231*delta*m**(7/2)*rho**4*z**7/2 + 95310611*delta*m**(5/2)*rho**6*z**11/124416 - 2593525*delta*m**(5/2)*rho**6*z**10/3456 + 2497495*delta*m**(5/2)*rho**6*z**9/3456 - 97405*delta*m**(5/2)*rho**6*z**8/144 + 9625*delta*m**(5/2)*rho**6*z**7/16 - 1925*delta*m**(5/2)*rho**6*z**6/4 + 1155*delta*m**(5/2)*rho**6*z**5/4 - 1587761527*delta*m**(3/2)*rho**8*z**11/12441600 + 35473361*delta*m**(3/2)*rho**8*z**10/259200 - 114747721*delta*m**(3/2)*rho**8*z**9/777600 + 691559*delta*m**(3/2)*rho**8*z**8/4320 - 251713*delta*m**(3/2)*rho**8*z**7/1440 + 34573*delta*m**(3/2)*rho**8*z**6/180 - 847*delta*m**(3/2)*rho**8*z**5/4 + 231*delta*m**(3/2)*rho**8*z**4 - 231*delta*m**(3/2)*rho**8*z**3",
    "E_rho_at_x0": "-715*delta*m**(9/2)*rho**2/4 + 18061043*delta*m**(7/2)*rho**4/8640 - 533389571*delta*m**(5/2)*rho**6/124416 + 20065150391*delta*m**(3/2)*rho**8/12441600",
    "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": 12,
    "correction": "t_0*u**(D-2)+t_1*u**(D-1)",
    "correction_order_at_least": 10,
    "fixed_anchor_value": "c - delta*m**(11/2)*z**11 - 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**(11/2) - 58301*m*theta/27720",
    "t_0": "(57024000*delta*m**(9/2)*rho**2*z**7 - 14256000*delta*m**(9/2)*rho**2*z**6 - 1077088320*delta*m**(7/2)*rho**4*z**7 + 631184400*delta*m**(7/2)*rho**4*z**6 - 299376000*delta*m**(7/2)*rho**4*z**5 + 89812800*delta*m**(7/2)*rho**4*z**4 + 2737993500*delta*m**(5/2)*rho**6*z**7 - 2154450375*delta*m**(5/2)*rho**6*z**6 + 1592514000*delta*m**(5/2)*rho**6*z**5 - 1066527000*delta*m**(5/2)*rho**6*z**4 + 598752000*delta*m**(5/2)*rho**6*z**3 - 224532000*delta*m**(5/2)*rho**6*z**2 - 1154836804*delta*m**(3/2)*rho**8*z**7 + 1048416721*delta*m**(3/2)*rho**8*z**6 - 933669000*delta*m**(3/2)*rho**8*z**5 + 809188380*delta*m**(3/2)*rho**8*z**4 - 673263360*delta*m**(3/2)*rho**8*z**3 + 523908000*delta*m**(3/2)*rho**8*z**2 - 359251200*delta*m**(3/2)*rho**8*z + 179625600*delta*m**(3/2)*rho**8)/(777600*z**7)",
    "t_1": "(-1311552000*delta*m**(9/2)*rho**2*z**7 - 228096000*delta*m**(9/2)*rho**2*z**6 + 8774488800*delta*m**(7/2)*rho**4*z**7 + 10098950400*delta*m**(7/2)*rho**4*z**6 - 4790016000*delta*m**(7/2)*rho**4*z**5 + 1437004800*delta*m**(7/2)*rho**4*z**4 - 9531061100*delta*m**(5/2)*rho**6*z**7 - 34471206000*delta*m**(5/2)*rho**6*z**6 + 25480224000*delta*m**(5/2)*rho**6*z**5 - 17064432000*delta*m**(5/2)*rho**6*z**4 + 9580032000*delta*m**(5/2)*rho**6*z**3 - 3592512000*delta*m**(5/2)*rho**6*z**2 + 1587761527*delta*m**(3/2)*rho**8*z**7 + 16774667536*delta*m**(3/2)*rho**8*z**6 - 14938704000*delta*m**(3/2)*rho**8*z**5 + 12947014080*delta*m**(3/2)*rho**8*z**4 - 10772213760*delta*m**(3/2)*rho**8*z**3 + 8382528000*delta*m**(3/2)*rho**8*z**2 - 5748019200*delta*m**(3/2)*rho**8*z + 2874009600*delta*m**(3/2)*rho**8)/(12441600*z**7)"
  },
  "h_i": [
    "1",
    "2",
    "3",
    "4"
  ],
  "leading_coefficient_in_u": "-m*theta/12",
  "leading_coefficient_in_x": "-m*theta/(12*a**12)",
  "moment_common_factor": "pi/sqrt(c)",
  "moment_target_divided_by_common_factor": "-231*h**6/8 + 1155*h**5/4 - 8085*h**4/8 + 5775*h**3/4 - 693*h**2",
  "moment_target_factored_divided_by_common_factor": "-231*h**2*(h - 4)*(h - 3)*(h - 2)*(h - 1)/8",
  "moment_target_root_slopes_divided_by_common_factor": [
    "693/4",
    "-231",
    "2079/4",
    "-2772"
  ],
  "normalized_curvature_polynomial": "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": 1
}