================================================================================
SESSION 784 -- log(M_GUT/M_Pl) CXXXVIII; log(Dm2_atm) CXXXIX; sin^2 th23 CXL; CV-17 CXLI
================================================================================

================================================================================
TRACK (a) -- Class CXXXVIII: log10(M_GUT/M_Pl) ~ -2.78 (search on |val|)
================================================================================
  Target |log10(M_GUT/M_Pl)| = 2.78

  2-atom direct (tol 5%):
    [F_TRZ a/b r] = 2.777778e+00  err=-0.0799%
    [A_5 a*b 5/108] = 2.777778e+00  err=-0.0799%
    [5/108 a*b A_5] = 2.777778e+00  err=-0.0799%
    [137/200 a/b Y_p] = 2.795918e+00  err=+0.5726%
    [D_phys a*b 137/200] = 2.740000e+00  err=-1.4388%
    [137/200 a*b D_phys] = 2.740000e+00  err=-1.4388%
    [N_ch a*b 63/200] = 2.835000e+00  err=+1.9784%
    [63/200 a*b N_ch] = 2.835000e+00  err=+1.9784%
    [22/9 a/b 1-F_TRZ] = 2.716049e+00  err=-2.3004%
    [F_TRZ a/b 1-n_s] = 2.857143e+00  err=+2.7749%
    [1-F_TRZ a/b 63/200] = 2.857143e+00  err=+2.7749%
    [mpme a/b 137/200] = 2.680515e+00  err=-3.5786%

  3-atom direct (tol 0.5%):
    [27/25 a*b/c 416/513 63/200] = 2.780284e+00  err=+0.0102%
    [416/513 a*b/c 27/25 63/200] = 2.780284e+00  err=+0.0102%
    [27/26 a/b/c 137/200 6/11] = 2.779337e+00  err=-0.0238%
    [27/26 a/b/c 6/11 137/200] = 2.779337e+00  err=-0.0238%
    [27/26 a*b/c 11/6 137/200] = 2.779337e+00  err=-0.0238%
    [11/6 a*b/c 27/26 137/200] = 2.779337e+00  err=-0.0238%
    [D_BSFG a*b/c n_s K_Mex] = 2.779200e+00  err=-0.0288%
    [n_s a*b/c D_BSFG K_Mex] = 2.779200e+00  err=-0.0288%
    [33/40 a*b*c mpme mpme] = 2.781452e+00  err=+0.0522%
    [mpme a*b*c 33/40 mpme] = 2.781452e+00  err=+0.0522%
    [mpme a*b*c mpme 33/40] = 2.781452e+00  err=+0.0522%
    [33/40 a*b/c mpme 1/mpme] = 2.781452e+00  err=+0.0522%
    [mpme a*b/c 33/40 1/mpme] = 2.781452e+00  err=+0.0522%
    [33/40 a/b/c 1/mpme 1/mpme] = 2.781452e+00  err=+0.0522%
    [D_crit a/b/c N_ch 27/26] = 2.781893e+00  err=+0.0681%

  4-atom direct (tol 0.05%):
    [alpha a/(b*c*d) F_TRZ 63/200 1/12] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) 63/200 F_TRZ 1/12] = 2.779944e+00  err=-0.0020%
    [SO5 a*b/(c*d) alpha 63/200 1/12] = 2.779944e+00  err=-0.0020%
    [SO5 a*b/(c*d) alpha 1/12 63/200] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) F_TRZ 1/12 63/200] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) K_Mex r 1-n_s] = 2.779944e+00  err=-0.0020%
    [alpha a*b/(c*d) SO5 63/200 1/12] = 2.779944e+00  err=-0.0020%
    [alpha a*b/(c*d) SO5 1/12 63/200] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) 1-F_TRZ 1/12 1-n_s] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) 1-n_s r K_Mex] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) 1-n_s 1/12 1-F_TRZ] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) r K_Mex 1-n_s] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) r 1-n_s K_Mex] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) 63/200 1/12 F_TRZ] = 2.779944e+00  err=-0.0020%
    [alpha a/(b*c*d) 1/12 F_TRZ 63/200] = 2.779944e+00  err=-0.0020%

  BEST |log10(M_GUT/M_Pl)|: [alpha a/(b*c*d) 63/200 F_TRZ 1/12] = 2.779944e+00, err = -0.002020%
================================================================================
TRACK (b) -- Class CXXXIX: log10(Dm2_atm/eV^2) ~ -2.602 (search on |val|)
================================================================================
  Target |log10(Dm2_atm)| = 2.602

  2-atom direct (tol 5%):
    [F_TRZ a*b D_crit] = 2.600000e+00  err=-0.0769%
    [D_crit a*b F_TRZ] = 2.600000e+00  err=-0.0769%
    [D_crit a/b SO5] = 2.600000e+00  err=-0.0769%
    [22/9 a/b 243/260] = 2.615455e+00  err=+0.5171%
    [22/9 a/b 307/325] = 2.587767e+00  err=-0.5470%
    [33/40 a/b 63/200] = 2.619048e+00  err=+0.6552%
    [416/513 a/b 63/200] = 2.574337e+00  err=-1.0631%
    [K_Mex a/b 416/513] = 2.569111e+00  err=-1.2640%
    [22/9 a*b 27/25] = 2.640000e+00  err=+1.4604%
    [27/25 a*b 22/9] = 2.640000e+00  err=+1.4604%
    [Phi_res a/b 63/200] = 2.645503e+00  err=+1.6719%
    [K_Mex a*b 11/9] = 2.546296e+00  err=-2.1408%

  3-atom direct (tol 0.5%):
    [D_BSFG a*b/c D_crit A_5] = 2.600000e+00  err=-0.0769%
    [D_crit a*b/c D_BSFG A_5] = 2.600000e+00  err=-0.0769%
    [D_crit a*b/c 1-F_TRZ N_ch] = 2.600000e+00  err=-0.0769%
    [1-F_TRZ a*b/c D_crit N_ch] = 2.600000e+00  err=-0.0769%
    [D_crit a*b/c 1/12 Phi_res] = 2.600000e+00  err=-0.0769%
    [1/12 a*b/c D_crit Phi_res] = 2.600000e+00  err=-0.0769%
    [beta_i a*b/c N_ch K_Mex] = 2.604528e+00  err=+0.0972%
    [N_ch a*b/c beta_i K_Mex] = 2.604528e+00  err=+0.0972%
    [beta_i a*b*c D_phys 27/25] = 2.604528e+00  err=+0.0972%
    [beta_i a*b*c 27/25 D_phys] = 2.604528e+00  err=+0.0972%
    [D_phys a*b*c beta_i 27/25] = 2.604528e+00  err=+0.0972%
    [D_phys a*b*c 27/25 beta_i] = 2.604528e+00  err=+0.0972%
    [27/25 a*b*c beta_i D_phys] = 2.604528e+00  err=+0.0972%
    [27/25 a*b*c D_phys beta_i] = 2.604528e+00  err=+0.0972%
    [11/9 a/b/c 137/200 137/200] = 2.604768e+00  err=+0.1064%

  4-atom direct (tol 0.05%):
    [D_BSFG a*b*c/d 1/mpme 6/11 137/200] = 2.602019e+00  err=+0.0007%
    [1/mpme a*b*c/d D_BSFG 6/11 137/200] = 2.602019e+00  err=+0.0007%
    [D_phys a/(b*c*d) 11/9 137/200 mpme] = 2.602019e+00  err=+0.0007%
    [D_phys a/(b*c*d) 11/9 mpme 137/200] = 2.602019e+00  err=+0.0007%
    [D_phys a/(b*c*d) 137/200 11/9 mpme] = 2.602019e+00  err=+0.0007%
    [D_phys a/(b*c*d) 137/200 mpme 11/9] = 2.602019e+00  err=+0.0007%
    [D_phys a*b/(c*d) 1/mpme 11/9 137/200] = 2.602019e+00  err=+0.0007%
    [D_phys a*b/(c*d) 1/mpme 137/200 11/9] = 2.602019e+00  err=+0.0007%
    [D_phys a/(b*c*d) mpme 11/9 137/200] = 2.602019e+00  err=+0.0007%
    [D_phys a/(b*c*d) mpme 137/200 11/9] = 2.602019e+00  err=+0.0007%
    [D_BSFG a*b/(c*d) 1/mpme 137/200 11/6] = 2.602019e+00  err=+0.0007%
    [D_BSFG a*b/(c*d) 1/mpme 11/6 137/200] = 2.602019e+00  err=+0.0007%
    [D_BSFG a*b*c/d 6/11 1/mpme 137/200] = 2.602019e+00  err=+0.0007%
    [1/mpme a*b/(c*d) D_phys 11/9 137/200] = 2.602019e+00  err=+0.0007%
    [1/mpme a*b/(c*d) D_phys 137/200 11/9] = 2.602019e+00  err=+0.0007%

  BEST |log10(Dm2_atm)|: [1/mpme a*b*c/d D_BSFG 6/11 137/200] = 2.602019e+00, err = +0.000728%
================================================================================
TRACK (c) -- Class CXL: sin^2 theta_23 (PMNS atm angle) ~ 0.55
================================================================================
  Target sin^2 theta_23 = 0.55

  2-atom direct (tol 5%):
    [SSq a*b n_s] = 5.500500e-01  err=+0.0091%
    [n_s a*b SSq] = 5.500500e-01  err=+0.0091%
    [SSq a/b 27/26] = 5.488889e-01  err=-0.2020%
    [SSq a/b 31/30] = 5.516129e-01  err=+0.2933%
    [63/200 a/b SSq] = 5.526316e-01  err=+0.4785%
    [beta_i a*b 1-F*P] = 5.526583e-01  err=+0.4833%
    [1-F*P a*b beta_i] = 5.526583e-01  err=+0.4833%
    [416/513 a*b 137/200] = 5.554776e-01  err=+0.9959%
    [137/200 a*b 416/513] = 5.554776e-01  err=+0.9959%
    [5/108 a/b 1/12] = 5.555556e-01  err=+1.0101%
    [beta_i a*b 1-F_TRZ] = 5.426100e-01  err=-1.3436%
    [1-F_TRZ a*b beta_i] = 5.426100e-01  err=-1.3436%

  3-atom direct (tol 0.5%):
    [F_TRZ a*b*c D_BSFG 1-F*P] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c 1-F*P D_BSFG] = 5.500000e-01  err=+0.0000%
    [D_BSFG a*b*c F_TRZ 1-F*P] = 5.500000e-01  err=+0.0000%
    [D_BSFG a*b*c 1-F*P F_TRZ] = 5.500000e-01  err=+0.0000%
    [D_BSFG a*b/c 1-F*P SO5] = 5.500000e-01  err=+0.0000%
    [1-F_TRZ a*b/c 22/9 D_phys] = 5.500000e-01  err=+0.0000%
    [1-F*P a*b*c F_TRZ D_BSFG] = 5.500000e-01  err=+0.0000%
    [1-F*P a*b*c D_BSFG F_TRZ] = 5.500000e-01  err=+0.0000%
    [1-F*P a*b/c D_BSFG SO5] = 5.500000e-01  err=+0.0000%
    [33/40 a*b/c 11/9 11/6] = 5.500000e-01  err=+0.0000%
    [33/40 a*b*c 6/11 11/9] = 5.500000e-01  err=+0.0000%
    [11/9 a*b/c 33/40 11/6] = 5.500000e-01  err=+0.0000%
    [22/9 a*b/c 1-F_TRZ D_phys] = 5.500000e-01  err=+0.0000%
    [6/11 a*b*c 33/40 11/9] = 5.500000e-01  err=+0.0000%
    [D_phys a*b/c 33/40 D_BSFG] = 5.500000e-01  err=-0.0000%

  4-atom direct (tol 0.05%):
    [F_TRZ a*b*c*d F_TRZ A_5 1-F*P] = 5.500000e-01  err=+0.0000%
    [F_TRZ a/(b*c*d) D_phys 6/11 1/12] = 5.500000e-01  err=+0.0000%
    [F_TRZ a/(b*c*d) D_phys 1/12 6/11] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c/d D_BSFG 33/40 1-F_TRZ] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c/d N_ch 22/9 D_phys] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c*d A_5 F_TRZ 1-F*P] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c*d A_5 1-F*P F_TRZ] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c/d A_5 1-F*P SO5] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c*d 1-F*P A_5 F_TRZ] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c/d 1-F*P A_5 SO5] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c/d 33/40 A_5 N_ch] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c*d 22/9 K_Mex 27/25] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c/d 22/9 N_ch D_phys] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b*c*d 22/9 27/25 K_Mex] = 5.500000e-01  err=+0.0000%
    [F_TRZ a*b/(c*d) 11/6 D_phys 1/12] = 5.500000e-01  err=+0.0000%

  BEST sin^2 theta_23: [1-F*P a*b*c D_BSFG F_TRZ] = 5.500000e-01, err = +0.000000%
================================================================================
TRACK (d) -- Class CXLI: CV-17 -> 3 = N_ch - D_BSFG
================================================================================
  N_ch         = 9  = 9.0000
  D_BSFG       = 6  = 6.0000
  N_ch - D_BSFG = 3  =  3.0000000000
  '3' reference = 3  =  3.0000000000
  Identity check: LHS == RHS ?  True
  In {D_phys, D_BSFG}: D_BSFG^2/D_phys - D_BSFG = 36/4 - 6 = 3
  err = +0.000000%  ->  EXACT atom-factorization identity

classCXXXVIII_log_MGUT_MPl_session784: predicted=-2.779944e+00 observed=-2.780000e+00 error_pct=-2.020291e-03 status=CE_strict
classCXXXIX_log_Dm2atm_session784: predicted=-2.602019e+00 observed=-2.602000e+00 error_pct=7.282344e-04 status=CE_strict
classCXL_sin2_theta23_session784: predicted=5.500000e-01 observed=5.500000e-01 error_pct=0.000000e+00 status=EXACT
classCXLI_CV17_Nch_minus_DBSFG_eq3_session784: predicted=3.000000e+00 observed=3.000000e+00 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  CXXXVIII log10(M_GUT/M_Pl) pred=-2.77994   err=-0.0020%  (CE_strict)
  CXXXIX   log10(Dm2_atm)    pred=-2.60202   err=+0.0007%  (CE_strict)
  CXL      sin^2 theta_23    pred=0.55000   err=+0.0000%  (EXACT)
  CXLI     CV-17 -> 3        pred=3      err=+0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session784_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
