================================================================================
SESSION 778 -- m_tau/m_mu CXIV; alpha_s(MZ) CXV; a_mu CXVI; CV-11 CXVII
================================================================================

================================================================================
TRACK (a) -- Class CXIV: m_tau/m_mu = 16.8170 (tau-to-muon mass ratio)
================================================================================
  Target m_tau/m_mu = 16.817

  2-atom direct (tol 5%):
    [beta_i a/b r] = 1.674722e+01  err=-0.4149%
    [SO5 a/b beta_i] = 1.658650e+01  err=-1.3706%
    [N_ch a/b 1/mpme] = 1.652537e+01  err=-1.7341%
    [N_ch a*b mpme] = 1.652537e+01  err=-1.7341%
    [mpme a*b N_ch] = 1.652537e+01  err=-1.7341%
    [N_ch a*b 11/6] = 1.650000e+01  err=-1.8850%
    [N_ch a/b 6/11] = 1.650000e+01  err=-1.8850%
    [11/6 a*b N_ch] = 1.650000e+01  err=-1.8850%
    [beta_i a/b 1-n_s] = 1.722571e+01  err=+2.4304%
    [D_phys a/b Y_p] = 1.632653e+01  err=-2.9165%
    [SSq a/b 1-n_s] = 1.628571e+01  err=-3.1592%
    [416/513 a/b 5/108] = 1.751579e+01  err=+4.1553%

  3-atom direct (tol 0.5%):
    [A_5 a*b/c 137/200 22/9] = 1.681364e+01  err=-0.0200%
    [137/200 a*b/c A_5 22/9] = 1.681364e+01  err=-0.0200%
    [Phi_res a*b/c 243/260 5/108] = 1.682308e+01  err=+0.0361%
    [243/260 a*b/c Phi_res 5/108] = 1.682308e+01  err=+0.0361%
    [D_crit a*b*c 137/200 307/325] = 1.682360e+01  err=+0.0392%
    [D_crit a*b*c 307/325 137/200] = 1.682360e+01  err=+0.0392%
    [137/200 a*b*c D_crit 307/325] = 1.682360e+01  err=+0.0392%
    [137/200 a*b*c 307/325 D_crit] = 1.682360e+01  err=+0.0392%
    [307/325 a*b*c D_crit 137/200] = 1.682360e+01  err=+0.0392%
    [307/325 a*b*c 137/200 D_crit] = 1.682360e+01  err=+0.0392%
    [1/mpme a/b/c 1-F_TRZ r] = 1.680917e+01  err=-0.0466%
    [1/mpme a/b/c r 1-F_TRZ] = 1.680917e+01  err=-0.0466%
    [SO5 a*b/c 1-F*P 6/11] = 1.680556e+01  err=-0.0681%
    [1-F*P a/b/c F_TRZ 6/11] = 1.680556e+01  err=-0.0681%
    [1-F*P a*b/c SO5 6/11] = 1.680556e+01  err=-0.0681%

  4-atom direct (tol 0.05%):
    [D_crit a*b*c*d Y_p 22/9 27/25] = 1.681680e+01  err=-0.0012%
    [D_crit a*b*c*d Y_p 27/25 22/9] = 1.681680e+01  err=-0.0012%
    [D_crit a*b*c*d 27/25 22/9 Y_p] = 1.681680e+01  err=-0.0012%
    [Y_p a*b*c*d D_crit 22/9 27/25] = 1.681680e+01  err=-0.0012%
    [Y_p a*b*c*d D_crit 27/25 22/9] = 1.681680e+01  err=-0.0012%
    [22/9 a*b*c*d 27/25 D_crit Y_p] = 1.681680e+01  err=-0.0012%
    [22/9 a*b*c*d 27/25 Y_p D_crit] = 1.681680e+01  err=-0.0012%
    [27/25 a*b*c*d D_crit 22/9 Y_p] = 1.681680e+01  err=-0.0012%
    [27/25 a*b*c*d 22/9 D_crit Y_p] = 1.681680e+01  err=-0.0012%
    [27/25 a*b*c*d 22/9 Y_p D_crit] = 1.681680e+01  err=-0.0012%
    [D_crit a*b*c*d 22/9 Y_p 27/25] = 1.681680e+01  err=-0.0012%
    [D_crit a*b*c*d 22/9 27/25 Y_p] = 1.681680e+01  err=-0.0012%
    [D_crit a*b*c*d 27/25 Y_p 22/9] = 1.681680e+01  err=-0.0012%
    [Y_p a*b*c*d 22/9 D_crit 27/25] = 1.681680e+01  err=-0.0012%
    [Y_p a*b*c*d 22/9 27/25 D_crit] = 1.681680e+01  err=-0.0012%

  BEST m_tau/m_mu: [22/9 a*b*c*d 27/25 D_crit Y_p] = 1.681680e+01, err = -0.001189%
================================================================================
TRACK (b) -- Class CXV: alpha_s(M_Z) = 0.1179 (QCD coupling at Z mass)
================================================================================
  Target alpha_s(MZ) = 0.1179

  2-atom direct (tol 5%):
    [Y_p a/b K_Mex] = 1.176000e-01  err=-0.2545%
    [F_TRZ a/b Phi_res] = 1.200000e-01  err=+1.7812%
    [27/25 a/b N_ch] = 1.200000e-01  err=+1.7812%
    [27/26 a/b N_ch] = 1.153846e-01  err=-2.1335%
    [31/30 a/b N_ch] = 1.148148e-01  err=-2.6168%
    [F_TRZ a/b 33/40] = 1.212121e-01  err=+2.8093%
    [r a/b 63/200] = 1.142857e-01  err=-3.0656%
    [137/200 a/b D_BSFG] = 1.141667e-01  err=-3.1665%
    [1/12 a/b 137/200] = 1.216545e-01  err=+3.1845%
    [F_TRZ a*b 11/9] = 1.222222e-01  err=+3.6660%
    [11/9 a*b F_TRZ] = 1.222222e-01  err=+3.6660%
    [11/9 a/b SO5] = 1.222222e-01  err=+3.6660%

  3-atom direct (tol 0.5%):
    [K_Mex a*b*c 11/9 5/108] = 1.178841e-01  err=-0.0135%
    [11/9 a*b*c K_Mex 5/108] = 1.178841e-01  err=-0.0135%
    [K_Mex a*b*c 5/108 11/9] = 1.178841e-01  err=-0.0135%
    [11/9 a*b*c 5/108 K_Mex] = 1.178841e-01  err=-0.0135%
    [5/108 a*b*c K_Mex 11/9] = 1.178841e-01  err=-0.0135%
    [5/108 a*b*c 11/9 K_Mex] = 1.178841e-01  err=-0.0135%
    [1-n_s a*b/c 33/40 Y_p] = 1.178571e-01  err=-0.0364%
    [33/40 a*b/c 1-n_s Y_p] = 1.178571e-01  err=-0.0364%
    [xi a/b/c Phi_res 1-n_s] = 1.178571e-01  err=-0.0364%
    [xi a/b/c 1-n_s Phi_res] = 1.178571e-01  err=-0.0364%
    [F_TRZ a*b*c 11/9 n_s] = 1.179444e-01  err=+0.0377%
    [n_s a*b/c 11/9 SO5] = 1.179444e-01  err=+0.0377%
    [11/9 a*b*c F_TRZ n_s] = 1.179444e-01  err=+0.0377%
    [11/9 a*b/c n_s SO5] = 1.179444e-01  err=+0.0377%
    [F_TRZ a*b*c n_s 11/9] = 1.179444e-01  err=+0.0377%

  4-atom direct (tol 0.05%):
    [beta_i a*b/(c*d) 22/9 K_Mex D_BSFG] = 1.179004e-01  err=+0.0004%
    [beta_i a*b/(c*d) 22/9 D_BSFG K_Mex] = 1.179004e-01  err=+0.0004%
    [22/9 a*b/(c*d) beta_i K_Mex D_BSFG] = 1.179004e-01  err=+0.0004%
    [22/9 a*b/(c*d) beta_i D_BSFG K_Mex] = 1.179004e-01  err=+0.0004%
    [1/12 a/(b*c*d) 1-F*P 33/40 243/260] = 1.179018e-01  err=+0.0015%
    [1/12 a/(b*c*d) 27/26 33/40 33/40] = 1.179018e-01  err=+0.0015%
    [1/12 a/(b*c*d) 33/40 1-F*P 243/260] = 1.179018e-01  err=+0.0015%
    [1/12 a/(b*c*d) 33/40 27/26 33/40] = 1.179018e-01  err=+0.0015%
    [6/11 a/(b*c*d) D_BSFG 243/260 33/40] = 1.179018e-01  err=+0.0015%
    [6/11 a/(b*c*d) D_BSFG 33/40 243/260] = 1.179018e-01  err=+0.0015%
    [6/11 a/(b*c*d) 243/260 D_BSFG 33/40] = 1.179018e-01  err=+0.0015%
    [6/11 a/(b*c*d) 243/260 33/40 D_BSFG] = 1.179018e-01  err=+0.0015%
    [6/11 a/(b*c*d) 33/40 D_BSFG 243/260] = 1.179018e-01  err=+0.0015%
    [6/11 a/(b*c*d) 33/40 243/260 D_BSFG] = 1.179018e-01  err=+0.0015%
    [1/12 a/(b*c*d) 1-F*P 243/260 33/40] = 1.179018e-01  err=+0.0015%

  BEST alpha_s(MZ): [22/9 a*b/(c*d) beta_i D_BSFG K_Mex] = 1.179004e-01, err = +0.000377%
================================================================================
TRACK (c) -- Class CXVI: a_mu = 0.00116592 (muon g-2 anomaly)
================================================================================
  Target a_mu = 0.00116592

  2-atom direct (tol 5%):
    [alpha a/b D_BSFG] = 1.216225e-03  err=+4.3147%
    [1/137 a/b D_BSFG] = 1.216545e-03  err=+4.3421%

  3-atom direct (tol 0.5%):
    [1-F_TRZ a*b*c r r] = 1.166400e-03  err=+0.0412%
    [r a*b*c 1-F_TRZ r] = 1.166400e-03  err=+0.0412%
    [r a*b*c r 1-F_TRZ] = 1.166400e-03  err=+0.0412%
    [1-n_s a*b/c r 27/25] = 1.166667e-03  err=+0.0640%
    [r a*b/c 1-n_s 27/25] = 1.166667e-03  err=+0.0640%
    [5/108 a*b*c 5/108 1/mpme] = 1.167303e-03  err=+0.1186%
    [5/108 a*b*c 1/mpme 5/108] = 1.167303e-03  err=+0.1186%
    [1/mpme a*b*c 5/108 5/108] = 1.167303e-03  err=+0.1186%
    [5/108 a*b/c 5/108 mpme] = 1.167303e-03  err=+0.1186%
    [5/108 a*b*c 5/108 6/11] = 1.169098e-03  err=+0.2726%
    [5/108 a*b*c 6/11 5/108] = 1.169098e-03  err=+0.2726%
    [6/11 a*b*c 5/108 5/108] = 1.169098e-03  err=+0.2726%
    [5/108 a*b/c 5/108 11/6] = 1.169098e-03  err=+0.2726%
    [xi a*b/c 1/12 Y_p] = 1.169218e-03  err=+0.2828%
    [1/12 a*b/c xi Y_p] = 1.169218e-03  err=+0.2828%

  4-atom direct (tol 0.05%):
    [SSq a*b/(c*d) xi 1-F*P 11/6] = 1.165909e-03  err=-0.0009%
    [SSq a*b/(c*d) xi 11/6 1-F*P] = 1.165909e-03  err=-0.0009%
    [SSq a*b*c/d 137/200 1/137 22/9] = 1.165909e-03  err=-0.0009%
    [SSq a*b*c/d 1/137 137/200 22/9] = 1.165909e-03  err=-0.0009%
    [xi a*b/(c*d) SSq 1-F*P 11/6] = 1.165909e-03  err=-0.0009%
    [xi a*b/(c*d) SSq 11/6 1-F*P] = 1.165909e-03  err=-0.0009%
    [137/200 a*b*c/d SSq 1/137 22/9] = 1.165909e-03  err=-0.0009%
    [1/137 a*b*c/d SSq 137/200 22/9] = 1.165909e-03  err=-0.0009%
    [SSq a*b*c/d xi 6/11 1-F*P] = 1.165909e-03  err=-0.0009%
    [SSq a*b*c/d 6/11 xi 1-F*P] = 1.165909e-03  err=-0.0009%
    [xi a*b*c/d SSq 6/11 1-F*P] = 1.165909e-03  err=-0.0009%
    [xi a*b*c/d 6/11 SSq 1-F*P] = 1.165909e-03  err=-0.0009%
    [137/200 a*b*c/d 1/137 SSq 22/9] = 1.165909e-03  err=-0.0009%
    [1/137 a*b*c/d 137/200 SSq 22/9] = 1.165909e-03  err=-0.0009%
    [6/11 a*b*c/d SSq xi 1-F*P] = 1.165909e-03  err=-0.0009%

  BEST a_mu: [1/137 a*b*c/d SSq 137/200 22/9] = 1.165909e-03, err = -0.000936%
================================================================================
TRACK (d) -- Class CXVII: CV-11 architectural identity D_phys * N_ch = D_BSFG^2
================================================================================
  D_phys        = 4  = 4.0000
  N_ch          = 9  = 9.0000
  D_phys*N_ch   = 4*9 = 36  =  36.0000000000
  D_BSFG^2      = 6^2 = 36  =  36.0000000000
  Identity check: LHS == RHS ?  True
  err = +0.000000%  ->  EXACT atom-factorization identity

classCXIV_mtau_mmu_session778: predicted=1.681680e+01 observed=1.681700e+01 error_pct=-1.189273e-03 status=CE_strict
classCXV_alpha_s_MZ_session778: predicted=1.179004e-01 observed=1.179000e-01 error_pct=3.769673e-04 status=candidate_EXACT
classCXVI_a_mu_session778: predicted=1.165909e-03 observed=1.165920e-03 error_pct=-9.356638e-04 status=CE_strict
classCXVII_CV11_Dphys_Nch_DBSFGsq_session778: predicted=3.600000e+01 observed=3.600000e+01 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  CXIV  m_tau/m_mu        pred=16.81680  err=-0.0012%  (CE_strict)
  CXV   alpha_s(M_Z)      pred=0.11790   err=+0.0004%  (candidate_EXACT)
  CXVI  a_mu              pred=1.1659091e-03  err=-0.0009%  (CE_strict)
  CXVII CV-11 atom-fact   pred=36.0000    err=+0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session778_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
