================================================================================
SESSION 782 -- lambda_H CXXX; y_t CXXXI; log eta_B CXXXII; CV-15 -> 1/alpha=137 CXXXIII
================================================================================

================================================================================
TRACK (a) -- Class CXXX: Higgs self-coupling lambda_H ~ 0.129
================================================================================
  Target lambda_H = 0.129

  2-atom direct (tol 5%):
    [63/200 a/b 22/9] = 1.288636e-01  err=-0.1057%
    [Y_p a*b 1/mpme] = 1.334312e-01  err=+3.4350%
    [Y_p a/b mpme] = 1.334312e-01  err=+3.4350%
    [1/mpme a*b Y_p] = 1.334312e-01  err=+3.4350%
    [Y_p a/b 11/6] = 1.336364e-01  err=+3.5941%
    [Y_p a*b 6/11] = 1.336364e-01  err=+3.5941%
    [6/11 a*b Y_p] = 1.336364e-01  err=+3.5941%
    [F_TRZ a/b 416/513] = 1.233173e-01  err=-4.4052%
    [416/513 a/b D_BSFG] = 1.351527e-01  err=+4.7695%

  3-atom direct (tol 0.5%):
    [1/137 a/b/c 11/9 5/108] = 1.289980e-01  err=-0.0015%
    [1/137 a/b/c 5/108 11/9] = 1.289980e-01  err=-0.0015%
    [alpha a/b/c 11/9 5/108] = 1.289641e-01  err=-0.0278%
    [alpha a/b/c 5/108 11/9] = 1.289641e-01  err=-0.0278%
    [n_s a*b/c Y_p 11/6] = 1.289591e-01  err=-0.0317%
    [Y_p a*b/c n_s 11/6] = 1.289591e-01  err=-0.0317%
    [Y_p a*b*c 6/11 n_s] = 1.289591e-01  err=-0.0317%
    [6/11 a*b*c Y_p n_s] = 1.289591e-01  err=-0.0317%
    [n_s a*b*c Y_p 6/11] = 1.289591e-01  err=-0.0317%
    [n_s a*b*c 6/11 Y_p] = 1.289591e-01  err=-0.0317%
    [Y_p a*b*c n_s 6/11] = 1.289591e-01  err=-0.0317%
    [6/11 a*b*c n_s Y_p] = 1.289591e-01  err=-0.0317%
    [Y_p a*b/c 1/mpme 31/30] = 1.291269e-01  err=+0.0984%
    [Y_p a/b/c mpme 31/30] = 1.291269e-01  err=+0.0984%
    [1/mpme a*b/c Y_p 31/30] = 1.291269e-01  err=+0.0984%

  4-atom direct (tol 0.05%):
    [1-F*P a*b/(c*d) 11/9 N_ch n_s] = 1.290006e-01  err=+0.0005%
    [1-F*P a*b/(c*d) 11/9 n_s N_ch] = 1.290006e-01  err=+0.0005%
    [11/9 a*b/(c*d) 1-F*P N_ch n_s] = 1.290006e-01  err=+0.0005%
    [11/9 a*b/(c*d) 1-F*P n_s N_ch] = 1.290006e-01  err=+0.0005%
    [11/9 a*b*c/d 11/9 1/12 n_s] = 1.290006e-01  err=+0.0005%
    [11/9 a*b*c/d 1/12 11/9 n_s] = 1.290006e-01  err=+0.0005%
    [1/12 a*b*c/d 11/9 11/9 n_s] = 1.290006e-01  err=+0.0005%
    [n_s a*b*c*d 1-n_s 11/6 K_Mex] = 1.290017e-01  err=+0.0013%
    [1-n_s a*b*c*d n_s 11/6 K_Mex] = 1.290017e-01  err=+0.0013%
    [1-n_s a*b*c*d 11/6 K_Mex n_s] = 1.290017e-01  err=+0.0013%
    [1-n_s a*b*c*d 11/6 n_s K_Mex] = 1.290017e-01  err=+0.0013%
    [11/6 a*b*c*d 1-n_s K_Mex n_s] = 1.290017e-01  err=+0.0013%
    [11/6 a*b*c*d 1-n_s n_s K_Mex] = 1.290017e-01  err=+0.0013%
    [K_Mex a*b*c*d n_s 11/6 1-n_s] = 1.290017e-01  err=+0.0013%
    [K_Mex a*b*c*d 1-n_s 11/6 n_s] = 1.290017e-01  err=+0.0013%

  BEST lambda_H: [1-F*P a*b/(c*d) 11/9 N_ch n_s] = 1.290006e-01, err = +0.000479%
================================================================================
TRACK (b) -- Class CXXXI: top Yukawa y_t ~ 0.993
================================================================================
  Target y_t = 0.993

  2-atom direct (tol 5%):
    [11/9 a*b 416/513] = 9.911198e-01  err=-0.1893%
    [416/513 a*b 11/9] = 9.911198e-01  err=-0.1893%
    [31/30 a/b 27/26] = 9.950617e-01  err=+0.2076%
    [1-F*P a*b 27/25] = 9.900000e-01  err=-0.3021%
    [27/25 a*b 1-F*P] = 9.900000e-01  err=-0.3021%
    [33/40 a/b Phi_res] = 9.900000e-01  err=-0.3021%
    [243/260 a/b 307/325] = 9.894137e-01  err=-0.3612%
    [n_s a*b 31/30] = 9.971667e-01  err=+0.4196%
    [31/30 a*b n_s] = 9.971667e-01  err=+0.4196%
    [1/mpme a*b 11/6] = 9.984645e-01  err=+0.5503%
    [11/6 a*b 1/mpme] = 9.984645e-01  err=+0.5503%
    [1/mpme a/b 6/11] = 9.984645e-01  err=+0.5503%

  3-atom direct (tol 0.5%):
    [D_crit a*b*c 33/40 5/108] = 9.930556e-01  err=+0.0056%
    [D_crit a*b*c 5/108 33/40] = 9.930556e-01  err=+0.0056%
    [33/40 a*b*c D_crit 5/108] = 9.930556e-01  err=+0.0056%
    [33/40 a*b*c 5/108 D_crit] = 9.930556e-01  err=+0.0056%
    [5/108 a*b*c D_crit 33/40] = 9.930556e-01  err=+0.0056%
    [5/108 a*b*c 33/40 D_crit] = 9.930556e-01  err=+0.0056%
    [n_s a/b/c 1-F_TRZ 27/25] = 9.927984e-01  err=-0.0203%
    [n_s a/b/c 27/25 1-F_TRZ] = 9.927984e-01  err=-0.0203%
    [D_crit a*b/c 1-n_s 1-F*P] = 9.927273e-01  err=-0.0275%
    [1-n_s a*b/c D_crit 1-F*P] = 9.927273e-01  err=-0.0275%
    [Y_p a*b/c 22/9 beta_i] = 9.933470e-01  err=+0.0349%
    [22/9 a*b/c Y_p beta_i] = 9.933470e-01  err=+0.0349%
    [n_s a*b/c r 1-n_s] = 9.925714e-01  err=-0.0432%
    [r a*b/c n_s 1-n_s] = 9.925714e-01  err=-0.0432%
    [27/26 a*b/c 31/30 27/25] = 9.935897e-01  err=+0.0594%

  4-atom direct (tol 0.05%):
    [1-F_TRZ a*b*c/d n_s 27/25 307/325] = 9.929756e-01  err=-0.0025%
    [1-F_TRZ a*b*c/d 27/25 n_s 307/325] = 9.929756e-01  err=-0.0025%
    [n_s a*b*c/d 1-F_TRZ 27/25 307/325] = 9.929756e-01  err=-0.0025%
    [n_s a*b*c/d 27/25 1-F_TRZ 307/325] = 9.929756e-01  err=-0.0025%
    [27/25 a*b*c/d 1-F_TRZ n_s 307/325] = 9.929756e-01  err=-0.0025%
    [27/25 a*b*c/d n_s 1-F_TRZ 307/325] = 9.929756e-01  err=-0.0025%
    [31/30 a*b*c*d 31/30 31/30 1-F_TRZ] = 9.930333e-01  err=+0.0034%
    [31/30 a*b*c*d 31/30 1-F_TRZ 31/30] = 9.930333e-01  err=+0.0034%
    [1-F_TRZ a*b*c*d 31/30 31/30 31/30] = 9.930333e-01  err=+0.0034%
    [31/30 a*b*c*d 1-F_TRZ 31/30 31/30] = 9.930333e-01  err=+0.0034%
    [31/30 a/(b*c*d) n_s 27/26 27/26] = 9.929612e-01  err=-0.0039%
    [31/30 a/(b*c*d) 27/26 n_s 27/26] = 9.929612e-01  err=-0.0039%
    [31/30 a/(b*c*d) 27/26 27/26 n_s] = 9.929612e-01  err=-0.0039%
    [416/513 a/(b*c*d) Phi_res D_phys Y_p] = 9.929586e-01  err=-0.0042%
    [416/513 a/(b*c*d) Phi_res Y_p D_phys] = 9.929586e-01  err=-0.0042%

  BEST y_t: [1-F_TRZ a*b*c/d 27/25 n_s 307/325] = 9.929756e-01, err = -0.002460%
================================================================================
TRACK (c) -- Class CXXXII: log10(eta_B) ~ -9.215 (search on |val|)
================================================================================
  Target |log10(eta_B)| = 9.215

  2-atom direct (tol 5%):
    [SO5 a/b 27/25] = 9.259259e+00  err=+0.4803%
    [SO5 a*b 1-F*P] = 9.166667e+00  err=-0.5245%
    [1-F*P a/b F_TRZ] = 9.166667e+00  err=-0.5245%
    [1-F*P a*b SO5] = 9.166667e+00  err=-0.5245%
    [N_ch a*b 31/30] = 9.300000e+00  err=+0.9224%
    [31/30 a*b N_ch] = 9.300000e+00  err=+0.9224%
    [N_ch a/b n_s] = 9.326425e+00  err=+1.2092%
    [243/260 a/b F_TRZ] = 9.346154e+00  err=+1.4233%
    [N_ch a*b 27/26] = 9.346154e+00  err=+1.4233%
    [SO5 a*b 243/260] = 9.346154e+00  err=+1.4233%
    [27/26 a*b N_ch] = 9.346154e+00  err=+1.4233%
    [243/260 a*b SO5] = 9.346154e+00  err=+1.4233%

  3-atom direct (tol 0.5%):
    [416/513 a/b/c r 22/9] = 9.214957e+00  err=-0.0005%
    [416/513 a/b/c 22/9 r] = 9.214957e+00  err=-0.0005%
    [D_BSFG a/b/c beta_i 27/25] = 9.214721e+00  err=-0.0030%
    [D_BSFG a/b/c 27/25 beta_i] = 9.214721e+00  err=-0.0030%
    [N_ch a/b/c 307/325 31/30] = 9.220343e+00  err=+0.0580%
    [N_ch a/b/c 31/30 307/325] = 9.220343e+00  err=+0.0580%
    [5/108 a*b/c 137/200 xi] = 9.225589e+00  err=+0.1149%
    [137/200 a*b/c 5/108 xi] = 9.225589e+00  err=+0.1149%
    [11/6 a/b/c Y_p 416/513] = 9.227826e+00  err=+0.1392%
    [11/6 a/b/c 416/513 Y_p] = 9.227826e+00  err=+0.1392%
    [D_phys a*b/c A_5 D_crit] = 9.230769e+00  err=+0.1711%
    [A_5 a*b/c D_phys D_crit] = 9.230769e+00  err=+0.1711%
    [33/40 a/b/c D_crit xi] = 9.230769e+00  err=+0.1711%
    [33/40 a/b/c xi D_crit] = 9.230769e+00  err=+0.1711%
    [N_ch a*b/c n_s 307/325] = 9.194218e+00  err=-0.2255%

  4-atom direct (tol 0.05%):
    [D_crit a/(b*c*d) SSq 33/40 D_BSFG] = 9.214957e+00  err=-0.0005%
    [D_crit a/(b*c*d) D_BSFG 33/40 SSq] = 9.214957e+00  err=-0.0005%
    [D_crit a/(b*c*d) 33/40 SSq D_BSFG] = 9.214957e+00  err=-0.0005%
    [D_crit a/(b*c*d) 33/40 D_BSFG SSq] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b*c/d SO5 416/513 11/6] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b*c*d SO5 416/513 6/11] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b/(c*d) 416/513 F_TRZ 11/6] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b*c/d 416/513 SO5 11/6] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b*c*d 416/513 SO5 6/11] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b/(c*d) 416/513 11/6 F_TRZ] = 9.214957e+00  err=-0.0005%
    [K_Mex a*b*c*d 6/11 SO5 416/513] = 9.214957e+00  err=-0.0005%
    [D_crit a/(b*c*d) SSq D_BSFG 33/40] = 9.214957e+00  err=-0.0005%
    [D_crit a/(b*c*d) D_BSFG SSq 33/40] = 9.214957e+00  err=-0.0005%
    [N_ch a/(b*c*d) SSq 243/260 11/6] = 9.214957e+00  err=-0.0005%
    [N_ch a/(b*c*d) SSq 11/6 243/260] = 9.214957e+00  err=-0.0005%

  BEST |log10(eta_B)|: [D_crit a/(b*c*d) 33/40 D_BSFG SSq] = 9.214957e+00, err = -0.000471%
================================================================================
TRACK (d) -- Class CXXXIII: CV-15 -> 1/alpha_em = 137 from dim algebra
================================================================================
  2*D_crit       = 2*26 = 52
  N_ch^2         = 9^2  = 81
  D_phys         = 4    = 4
  Sum            = 137  =  137.0000000000
  1/alpha_em ref = 137  =  137.0000000000
  Identity check: LHS == RHS ?  True
  Equivalent in {D_phys, D_BSFG}: 8*D_BSFG+4+D_BSFG^4/D_phys^2+D_phys
    = 8*6+4+6^4/4^2+4 = 137 (matches: True)
  err = +0.000000%  ->  EXACT atom-factorization identity

classCXXX_lambdaH_session782: predicted=1.290006e-01 observed=1.290000e-01 error_pct=4.793411e-04 status=candidate_EXACT
classCXXXI_yt_session782: predicted=9.929756e-01 observed=9.930000e-01 error_pct=-2.460218e-03 status=CE_strict
classCXXXII_log_etaB_session782: predicted=-9.214957e+00 observed=-9.215000e+00 error_pct=-4.711516e-04 status=candidate_EXACT
classCXXXIII_CV15_alpha137_dimalgebra_session782: predicted=1.370000e+02 observed=1.370000e+02 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  CXXX   lambda_H        pred=0.12900   err=+0.0005%  (candidate_EXACT)
  CXXXI  y_t             pred=0.99298   err=-0.0025%  (CE_strict)
  CXXXII log10(eta_B)    pred=-9.21496   err=-0.0005%  (candidate_EXACT)
  CXXXIII CV-15 -> 137   pred=137     err=+0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session782_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
