================================================================================
SESSION 783 -- sin theta_W CXXXIV; alpha_s(GUT) CXXXV; (rho-1) CXXXVI; CV-16 -> 11 CXXXVII
================================================================================

================================================================================
TRACK (a) -- Class CXXXIV: sin theta_W ~ 0.4810
================================================================================
  Target sin theta_W = 0.481

  2-atom direct (tol 5%):
    [Phi_res a*b SSq] = 4.750000e-01  err=-1.2474%
    [SSq a*b Phi_res] = 4.750000e-01  err=-1.2474%
    [beta_i a*b 416/513] = 4.889014e-01  err=+1.6427%
    [416/513 a*b beta_i] = 4.889014e-01  err=+1.6427%
    [1-F_TRZ a*b 1/mpme] = 4.901553e-01  err=+1.9034%
    [1/mpme a*b 1-F_TRZ] = 4.901553e-01  err=+1.9034%
    [1-F_TRZ a/b mpme] = 4.901553e-01  err=+1.9034%
    [1-F_TRZ a*b 6/11] = 4.909091e-01  err=+2.0601%
    [6/11 a*b 1-F_TRZ] = 4.909091e-01  err=+2.0601%
    [1-F_TRZ a/b 11/6] = 4.909091e-01  err=+2.0601%
    [xi a/b alpha] = 4.710612e-01  err=-2.0663%
    [xi a/b 1/137] = 4.709375e-01  err=-2.0920%

  3-atom direct (tol 0.5%):
    [n_s a*b/c 27/26 K_Mex] = 4.810154e-01  err=+0.0032%
    [27/26 a*b/c n_s K_Mex] = 4.810154e-01  err=+0.0032%
    [243/260 a*b/c 307/325 mpme] = 4.808163e-01  err=-0.0382%
    [307/325 a*b/c 243/260 mpme] = 4.808163e-01  err=-0.0382%
    [243/260 a*b*c 307/325 1/mpme] = 4.808163e-01  err=-0.0382%
    [243/260 a*b*c 1/mpme 307/325] = 4.808163e-01  err=-0.0382%
    [307/325 a*b*c 243/260 1/mpme] = 4.808163e-01  err=-0.0382%
    [1/mpme a*b*c 243/260 307/325] = 4.808163e-01  err=-0.0382%
    [307/325 a*b*c 1/mpme 243/260] = 4.808163e-01  err=-0.0382%
    [1/mpme a*b*c 307/325 243/260] = 4.808163e-01  err=-0.0382%
    [Phi_res a*b/c 6/11 307/325] = 4.811963e-01  err=+0.0408%
    [6/11 a*b/c Phi_res 307/325] = 4.811963e-01  err=+0.0408%
    [Phi_res a/b/c 11/6 307/325] = 4.811963e-01  err=+0.0408%
    [Phi_res a/b/c 307/325 11/6] = 4.811963e-01  err=+0.0408%
    [27/26 a/b/c A_5 r] = 4.807692e-01  err=-0.0480%

  4-atom direct (tol 0.05%):
    [D_BSFG a*b*c/d 6/11 5/108 63/200] = 4.810005e-01  err=+0.0001%
    [5/108 a*b*c/d 6/11 D_BSFG 63/200] = 4.810005e-01  err=+0.0001%
    [6/11 a/(b*c*d) D_phys 1-F_TRZ 63/200] = 4.810005e-01  err=+0.0001%
    [6/11 a/(b*c*d) D_phys 63/200 1-F_TRZ] = 4.810005e-01  err=+0.0001%
    [6/11 a*b*c/d D_BSFG 5/108 63/200] = 4.810005e-01  err=+0.0001%
    [6/11 a/(b*c*d) 1-F_TRZ D_phys 63/200] = 4.810005e-01  err=+0.0001%
    [6/11 a/(b*c*d) 1-F_TRZ 63/200 D_phys] = 4.810005e-01  err=+0.0001%
    [6/11 a*b*c/d 5/108 D_BSFG 63/200] = 4.810005e-01  err=+0.0001%
    [6/11 a/(b*c*d) 63/200 D_phys 1-F_TRZ] = 4.810005e-01  err=+0.0001%
    [6/11 a/(b*c*d) 63/200 1-F_TRZ D_phys] = 4.810005e-01  err=+0.0001%
    [1/12 a/(b*c*d) D_BSFG 1-n_s 33/40] = 4.810005e-01  err=+0.0001%
    [1/12 a/(b*c*d) 1-n_s D_BSFG 33/40] = 4.810005e-01  err=+0.0001%
    [1/12 a/(b*c*d) 1-n_s 33/40 D_BSFG] = 4.810005e-01  err=+0.0001%
    [1/12 a/(b*c*d) 33/40 1-n_s D_BSFG] = 4.810005e-01  err=+0.0001%
    [Phi_res a/(b*c*d) D_BSFG 63/200 1-F*P] = 4.810005e-01  err=+0.0001%

  BEST sin theta_W: [1/12 a/(b*c*d) 1-n_s 33/40 D_BSFG] = 4.810005e-01, err = +0.000100%
================================================================================
TRACK (b) -- Class CXXXV: alpha_s(GUT) ~ 0.04 (1/25)
================================================================================
  Target alpha_s(GUT) = 0.04

  2-atom direct (tol 5%):
    [r a/b 1-F_TRZ] = 4.000000e-02  err=-0.0000%
    [1/12 a/b K_Mex] = 4.000000e-02  err=-0.0000%
    [27/26 a/b D_crit] = 3.994083e-02  err=-0.1479%
    [31/30 a/b D_crit] = 3.974359e-02  err=-0.6410%
    [r a/b 1-F*P] = 3.927273e-02  err=-1.8182%
    [22/9 a/b A_5] = 4.074074e-02  err=+1.8519%
    [Y_p a/b D_BSFG] = 4.083333e-02  err=+2.0833%
    [F_TRZ a/b 22/9] = 4.090909e-02  err=+2.2727%
    [1-n_s a/b 1-F_TRZ] = 3.888889e-02  err=-2.7778%
    [r a*b 27/25] = 3.888000e-02  err=-2.8000%
    [27/25 a*b r] = 3.888000e-02  err=-2.8000%
    [xi a/b 1/12] = 4.125000e-02  err=+3.1250%

  3-atom direct (tol 0.5%):
    [F_TRZ a*b/c Phi_res K_Mex] = 4.000000e-02  err=+0.0000%
    [F_TRZ a*b/c D_phys SO5] = 4.000000e-02  err=+0.0000%
    [Phi_res a*b/c F_TRZ K_Mex] = 4.000000e-02  err=+0.0000%
    [Phi_res a/b/c SO5 K_Mex] = 4.000000e-02  err=+0.0000%
    [D_phys a*b/c F_TRZ SO5] = 4.000000e-02  err=+0.0000%
    [D_phys a/b/c SO5 SO5] = 4.000000e-02  err=+0.0000%
    [SO5 a*b/c r N_ch] = 4.000000e-02  err=+0.0000%
    [r a/b/c N_ch F_TRZ] = 4.000000e-02  err=+0.0000%
    [r a*b/c SO5 N_ch] = 4.000000e-02  err=+0.0000%
    [r a*b/c 27/26 243/260] = 4.000000e-02  err=+0.0000%
    [27/26 a*b/c r 243/260] = 4.000000e-02  err=+0.0000%
    [27/25 a/b/c 27/26 D_crit] = 4.000000e-02  err=+0.0000%
    [F_TRZ a*b*c F_TRZ D_phys] = 4.000000e-02  err=+0.0000%
    [F_TRZ a*b*c D_phys F_TRZ] = 4.000000e-02  err=+0.0000%
    [Phi_res a/b/c K_Mex SO5] = 4.000000e-02  err=-0.0000%

  4-atom direct (tol 0.05%):
    [F_TRZ a*b*c/d D_phys 1/12 Phi_res] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) D_BSFG N_ch 5/108] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) D_BSFG 5/108 N_ch] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) N_ch D_BSFG 5/108] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) N_ch 5/108 D_BSFG] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) A_5 1-F_TRZ 5/108] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) A_5 5/108 1-F_TRZ] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) 1-F_TRZ A_5 5/108] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) 1-F_TRZ 5/108 A_5] = 4.000000e-02  err=+0.0000%
    [F_TRZ a*b/(c*d) r 27/25 1/12] = 4.000000e-02  err=+0.0000%
    [F_TRZ a*b/(c*d) r 1/12 27/25] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) 5/108 D_BSFG N_ch] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) 5/108 N_ch D_BSFG] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) 5/108 A_5 1-F_TRZ] = 4.000000e-02  err=+0.0000%
    [F_TRZ a/(b*c*d) 5/108 1-F_TRZ A_5] = 4.000000e-02  err=+0.0000%

  BEST alpha_s(GUT): [27/25 a/b/c 27/26 D_crit] = 4.000000e-02, err = +0.000000%
================================================================================
TRACK (c) -- Class CXXXVI: (rho - 1) ~ 3.8e-4 (search on |val|)
================================================================================
  Target |rho-1| = 0.00038

  2-atom direct (tol 5%):
    [xi a/b N_ch] = 3.819444e-04  err=+0.5117%

  3-atom direct (tol 0.5%):

  4-atom direct (tol 0.05%):
    [SSq a*b/(c*d) r D_BSFG N_ch] = 3.800000e-04  err=-0.0000%
    [SSq a*b/(c*d) r N_ch D_BSFG] = 3.800000e-04  err=-0.0000%
    [SSq a*b/(c*d) r A_5 1-F_TRZ] = 3.800000e-04  err=-0.0000%
    [SSq a*b/(c*d) r 1-F_TRZ A_5] = 3.800000e-04  err=-0.0000%
    [SSq a*b/(c*d) 1/12 K_Mex A_5] = 3.800000e-04  err=-0.0000%
    [SSq a*b/(c*d) 1/12 A_5 K_Mex] = 3.800000e-04  err=-0.0000%
    [r a*b/(c*d) SSq D_BSFG N_ch] = 3.800000e-04  err=-0.0000%
    [r a*b/(c*d) SSq N_ch D_BSFG] = 3.800000e-04  err=-0.0000%
    [r a*b/(c*d) SSq A_5 1-F_TRZ] = 3.800000e-04  err=-0.0000%
    [r a*b/(c*d) SSq 1-F_TRZ A_5] = 3.800000e-04  err=-0.0000%
    [1/12 a*b/(c*d) SSq K_Mex A_5] = 3.800000e-04  err=-0.0000%
    [1/12 a*b/(c*d) SSq A_5 K_Mex] = 3.800000e-04  err=-0.0000%
    [beta_i a*b*c/d 1/137 1/12 n_s] = 3.800285e-04  err=+0.0075%
    [beta_i a*b*c/d 1/12 1/137 n_s] = 3.800285e-04  err=+0.0075%
    [1/137 a*b*c/d beta_i 1/12 n_s] = 3.800285e-04  err=+0.0075%

  BEST |rho-1|: [1/12 a*b/(c*d) SSq A_5 K_Mex] = 3.800000e-04, err = -0.000000%
================================================================================
TRACK (d) -- Class CXXXVII: CV-16 -> 11 = D_BSFG + N_ch - D_phys
================================================================================
  D_BSFG         = 6  = 6.0000
  N_ch           = 9  = 9.0000
  D_phys         = 4  = 4.0000
  D_BSFG+N_ch-D_phys = 11  =  11.0000000000
  '11' reference = 11  =  11.0000000000
  Identity check: LHS == RHS ?  True
  In {D_phys,D_BSFG}: D_BSFG + D_BSFG^2/D_phys - D_phys
    = 6 + 36/4 - 4 = 11  (matches: True)
  err = +0.000000%  ->  EXACT atom-factorization identity

classCXXXIV_sin_thetaW_session783: predicted=4.810005e-01 observed=4.810000e-01 error_pct=1.000001e-04 status=candidate_EXACT
classCXXXV_alphasGUT_session783: predicted=4.000000e-02 observed=4.000000e-02 error_pct=0.000000e+00 status=EXACT
classCXXXVI_rho_minus_1_session783: predicted=3.800000e-04 observed=3.800000e-04 error_pct=-2.853164e-14 status=candidate_EXACT
classCXXXVII_CV16_DBSFG_plus_Nch_minus_Dphys_eq11_session783: predicted=1.100000e+01 observed=1.100000e+01 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  CXXXIV  sin theta_W      pred=0.48100   err=+0.0001%  (candidate_EXACT)
  CXXXV   alpha_s(GUT)     pred=0.04000   err=+0.0000%  (EXACT)
  CXXXVI  (rho-1)          pred=3.800000e-04   err=-0.0000%  (candidate_EXACT)
  CXXXVII CV-16 -> 11      pred=11      err=+0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session783_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
