================================================================================
SESSION 714 -- alpha-chain non-Borel c_3 coefficient hunt
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  alpha_inv_2loop                  = 137.0348010753
  alpha_tree                       = 7.276564e-03
  alpha_tree^2                     = 5.294838e-05
  c_2 = pi/8                       = 0.3926990817
  c_3_borel = c_2^2 / 2!           = 0.0771062844
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  CODATA back-solve:
    needed delta_3                 = 8.742368e-06
    c_3_true (from CODATA)         = 0.16511114
    lambda_eff = c_3_true / c_3_borel = 2.14134480
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  Locked-rational candidate panel for lambda:
    name       lambda       predicted          residual       form
    ---------- ------------ ------------------ -------------- ------------------------------
    2          2.000000     137.0359200065          -577.057  D_phys/2 * 1
    9/4        2.250000     137.0360598728          +443.598  (D_BSFG + Phi_res*D_BSFG)/D_phys/...  ad hoc
    K_Mex      2.083333     137.0359666286          -236.839  25/12 -- G1 Mexican-hat anchor
    32/15      2.133333     137.0359946019           -32.708  2*D_phys^2 / (SO5+Phi_res*D_BSFG)
    15/7       2.142857     137.0359999301            +6.174  2/[SO5_ord*F_TRZ*(Phi_res+F_TRZ)]
    131/60     2.183333     137.0360225751          +171.423  K_Mex + Phi_res*F_TRZ/(1-Phi_res)
    13/6       2.166667     137.0360132507          +103.379  K_Mex + Phi_res/SO5_ord  (= c-chain 13/3 / 2)
    55/24      2.291667     137.0360831839          +613.707  K_Mex*(1+F_TRZ)
    13/3       4.333333     137.0372254261         +8949.051  c-chain geometric phase (transplanted)
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  BEST candidate: 15/7  lambda = 2.142857
    predicted alpha_inv          = 137.0359999301
    residual                     = +6.174 ppb
    structural form              = 2/[SO5_ord*F_TRZ*(Phi_res+F_TRZ)]
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  Structural form test  c_3 = pi^2 / X (integer X):
    X      c_3            predicted          residual
    ------ -------------- ------------------ --------------
    60     0.16449341     137.0359946019       -32.708 ppb <-- A_5
    57     0.17315095     137.0360574190      +425.691 ppb
    59     0.16728143     137.0360148311      +114.912 ppb
    61     0.16179679     137.0359750359      -175.488 ppb
    64     0.15421257     137.0359200065      -577.057 ppb
    128    0.07710628     137.0353605409     -4659.674 ppb
    100    0.09869604     137.0355171913     -3516.541 ppb
    60     0.16449341     137.0359946019       -32.708 ppb <-- A_5
    52     0.18980008     137.0361782213     +1307.228 ppb <-- 2*D_crit
    60     0.16449341     137.0359946019       -32.708 ppb <-- A_5
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  CODATA 2018 sigma(alpha_inv) ~ 0.21 ppb
  --> best candidate residual (+6.174 ppb) is OUTSIDE 1-sigma
================================================================================
alpha_c3_backsolve: predicted=1.6511114107e-01 observed=1.6511114107e-01 error_pct=+0.0000000000 status=OK
alpha_c3_locked_candidate_15_7: predicted=1.3703599993e+02 observed=1.3703599908e+02 error_pct=+0.0000006174 status=WARN
Artifact written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session714_alpha_c3_locked_candidate_hunt_result.json
