================================================================================
SESSION 771 -- tau LXXXVI; ln(10^10 A_s) LXXXVII; t_0 LXXXVIII; CV-4 LXXXIX
================================================================================
  t_H = 9.778/h = 9.778/0.674 = 14.5074 Gyr

================================================================================
TRACK (a) -- Class LXXXVI: tau = 0.0544 (reionization optical depth)
================================================================================
  Target tau = 0.0544

  2-atom direct (tol 5%):
    [F_TRZ a*b 1/mpme] = 0.054462  err=+0.1134%
    [1/mpme a*b F_TRZ] = 0.054462  err=+0.1134%
    [1/mpme a/b SO5] = 0.054462  err=+0.1134%
    [F_TRZ a/b mpme] = 0.054462  err=+0.1134%
    [F_TRZ a*b 6/11] = 0.054545  err=+0.2674%
    [6/11 a*b F_TRZ] = 0.054545  err=+0.2674%
    [6/11 a/b SO5] = 0.054545  err=+0.2674%
    [F_TRZ a/b 11/6] = 0.054545  err=+0.2674%
    [5/108 a/b Phi_res] = 0.055556  err=+2.1242%
    [5/108 a/b 33/40] = 0.056117  err=+3.1557%
    [r a/b 137/200] = 0.052555  err=-3.3920%
    [63/200 a/b D_BSFG] = 0.052500  err=-3.4926%

  3-atom direct (tol 0.5%):
    [63/200 a/b/c D_BSFG n_s] = 0.054404  err=+0.0076%
    [63/200 a/b/c n_s D_BSFG] = 0.054404  err=+0.0076%
    [SSq a*b/c xi r] = 0.054427  err=+0.0498%
    [xi a*b/c SSq r] = 0.054427  err=+0.0498%
    [r a*b*c 33/40 11/6] = 0.054450  err=+0.0919%
    [r a*b*c 11/6 33/40] = 0.054450  err=+0.0919%
    [33/40 a*b*c r 11/6] = 0.054450  err=+0.0919%
    [33/40 a*b*c 11/6 r] = 0.054450  err=+0.0919%
    [11/6 a*b*c r 33/40] = 0.054450  err=+0.0919%
    [11/6 a*b*c 33/40 r] = 0.054450  err=+0.0919%
    [r a*b/c 33/40 6/11] = 0.054450  err=+0.0919%
    [33/40 a*b/c r 6/11] = 0.054450  err=+0.0919%
    [5/108 a/b/c 1-F_TRZ 307/325] = 0.054456  err=+0.1036%
    [5/108 a/b/c 307/325 1-F_TRZ] = 0.054456  err=+0.1036%
    [r a/b/c n_s 137/200] = 0.054461  err=+0.1119%

  4-atom direct (tol 0.05%):
    [Y_p a*b*c/d 5/108 1-n_s alpha] = 0.054402  err=+0.0037%
    [5/108 a*b*c/d Y_p 1-n_s alpha] = 0.054402  err=+0.0037%
    [1-n_s a*b*c/d Y_p 5/108 alpha] = 0.054402  err=+0.0037%
    [1-n_s a*b*c/d 5/108 Y_p alpha] = 0.054402  err=+0.0037%
    [Y_p a*b*c/d 1-n_s 5/108 alpha] = 0.054402  err=+0.0037%
    [5/108 a*b*c/d 1-n_s Y_p alpha] = 0.054402  err=+0.0037%
    [K_Mex a*b/(c*d) 307/325 beta_i A_5] = 0.054402  err=+0.0042%
    [K_Mex a*b/(c*d) 307/325 A_5 beta_i] = 0.054402  err=+0.0042%
    [307/325 a*b/(c*d) K_Mex beta_i A_5] = 0.054402  err=+0.0042%
    [307/325 a*b/(c*d) K_Mex A_5 beta_i] = 0.054402  err=+0.0042%
    [1-n_s a*b/(c*d) 11/6 n_s 11/9] = 0.054404  err=+0.0076%
    [1-n_s a*b/(c*d) 11/6 11/9 n_s] = 0.054404  err=+0.0076%
    [11/6 a*b/(c*d) 1-n_s n_s 11/9] = 0.054404  err=+0.0076%
    [11/6 a*b/(c*d) 1-n_s 11/9 n_s] = 0.054404  err=+0.0076%
    [SO5 a*b/(c*d) 63/200 A_5 n_s] = 0.054404  err=+0.0076%

  BEST tau: [5/108 a*b*c/d Y_p 1-n_s alpha] = 0.054402, err = +0.003718%
================================================================================
TRACK (b) -- Class LXXXVII: ln(10^10 A_s) = 3.044 (scalar amplitude)
================================================================================
  Target ln(10^10 A_s) = 3.044

  2-atom direct (tol 5%):
    [mpme a/b beta_i] = 3.045534  err=+0.0504%
    [K_Mex a/b 137/200] = 3.041363  err=-0.0866%
    [11/6 a/b beta_i] = 3.040858  err=-0.1032%
    [n_s a/b 63/200] = 3.063492  err=+0.6403%
    [22/9 a/b 416/513] = 3.014423  err=-0.9716%
    [307/325 a/b 63/200] = 2.998779  err=-1.4856%
    [11/9 a*b 22/9] = 2.987654  err=-1.8510%
    [22/9 a*b 11/9] = 2.987654  err=-1.8510%
    [243/260 a/b 63/200] = 2.967033  err=-2.5285%
    [22/9 a/b 33/40] = 2.962963  err=-2.6622%
    [Y_p a/b 1/12] = 2.940000  err=-3.4166%
    [SO5 a*b 63/200] = 3.150000  err=+3.4823%

  3-atom direct (tol 0.5%):
    [5/108 a/b/c K_Mex 1/137] = 3.044444  err=+0.0146%
    [5/108 a/b/c 1/137 K_Mex] = 3.044444  err=+0.0146%
    [D_phys a*b/c 137/200 1-F_TRZ] = 3.044444  err=+0.0146%
    [137/200 a*b/c D_phys 1-F_TRZ] = 3.044444  err=+0.0146%
    [307/325 a/b/c SSq 1/mpme] = 3.042909  err=-0.0358%
    [307/325 a/b/c 1/mpme SSq] = 3.042909  err=-0.0358%
    [307/325 a*b/c mpme SSq] = 3.042909  err=-0.0358%
    [mpme a*b/c 307/325 SSq] = 3.042909  err=-0.0358%
    [5/108 a/b/c K_Mex alpha] = 3.045244  err=+0.0409%
    [5/108 a/b/c alpha K_Mex] = 3.045244  err=+0.0409%
    [Phi_res a*b/c K_Mex SSq] = 3.045809  err=+0.0594%
    [K_Mex a*b/c Phi_res SSq] = 3.045809  err=+0.0594%
    [27/26 a*b/c 22/9 Phi_res] = 3.046154  err=+0.0708%
    [22/9 a*b/c 27/26 Phi_res] = 3.046154  err=+0.0708%
    [Y_p a/b/c n_s 1/12] = 3.046632  err=+0.0865%

  4-atom direct (tol 0.05%):
    [22/9 a/(b*c*d) 1-F_TRZ 307/325 307/325] = 3.043881  err=-0.0039%
    [22/9 a/(b*c*d) 307/325 1-F_TRZ 307/325] = 3.043881  err=-0.0039%
    [22/9 a/(b*c*d) 307/325 307/325 1-F_TRZ] = 3.043881  err=-0.0039%
    [n_s a*b/(c*d) 307/325 Y_p 11/9] = 3.044150  err=+0.0049%
    [n_s a*b/(c*d) 307/325 11/9 Y_p] = 3.044150  err=+0.0049%
    [307/325 a*b/(c*d) n_s Y_p 11/9] = 3.044150  err=+0.0049%
    [307/325 a*b/(c*d) n_s 11/9 Y_p] = 3.044150  err=+0.0049%
    [22/9 a*b/(c*d) 137/200 SSq n_s] = 3.044168  err=+0.0055%
    [22/9 a*b/(c*d) 137/200 n_s SSq] = 3.044168  err=+0.0055%
    [137/200 a*b/(c*d) 22/9 SSq n_s] = 3.044168  err=+0.0055%
    [137/200 a*b/(c*d) 22/9 n_s SSq] = 3.044168  err=+0.0055%
    [r a/(b*c*d) 416/513 63/200 5/108] = 3.044176  err=+0.0058%
    [r a/(b*c*d) 63/200 416/513 5/108] = 3.044176  err=+0.0058%
    [r a/(b*c*d) 416/513 5/108 63/200] = 3.044176  err=+0.0058%
    [r a/(b*c*d) 5/108 416/513 63/200] = 3.044176  err=+0.0058%

  BEST ln(10^10 A_s): [22/9 a/(b*c*d) 1-F_TRZ 307/325 307/325] = 3.043881, err = -0.003918%
================================================================================
TRACK (c) -- Class LXXXVIII: t_0 = 13.797 Gyr (age of universe)
================================================================================
  Target t_0 = 13.7970  (t_H-shell target = 0.951031)

  2-atom shell (tol 3%):
    [1-F*P a*b 27/26] ratio=0.951923  -> 13.8099  err=+0.0938%
    [27/26 a*b 1-F*P] ratio=0.951923  -> 13.8099  err=+0.0938%
    [1-F*P a/b n_s] ratio=0.949914  -> 13.7808  err=-0.1175%
    [1-F_TRZ a/b 307/325] ratio=0.952769  -> 13.8222  err=+0.1828%
    [1-F*P a*b 31/30] ratio=0.947222  -> 13.7417  err=-0.4005%
    [31/30 a*b 1-F*P] ratio=0.947222  -> 13.7417  err=-0.4005%
    [1/mpme a/b SSq] ratio=0.955468  -> 13.8614  err=+0.4666%
    [SSq a/b beta_i] ratio=0.945430  -> 13.7158  err=-0.5889%
    [31/30 a/b 27/25] ratio=0.956790  -> 13.8806  err=+0.6056%
    [6/11 a/b SSq] ratio=0.956938  -> 13.8827  err=+0.6211%
    [27/26 a/b 27/25] ratio=0.961538  -> 13.9494  err=+1.1049%
    [1-F_TRZ a/b 243/260] ratio=0.962963  -> 13.9701  err=+1.2547%

  3-atom shell (tol 0.5%):
    [243/260 a*b/c 33/40 416/513] ratio=0.950848  -> 13.7943  err=-0.0193%
    [33/40 a*b/c 243/260 416/513] ratio=0.950848  -> 13.7943  err=-0.0193%
    [416/513 a/b/c 33/40 31/30] ratio=0.951221  -> 13.7998  err=+0.0200%
    [416/513 a/b/c 31/30 33/40] ratio=0.951221  -> 13.7998  err=+0.0200%
    [1/12 a*b/c 1/12 1/137] ratio=0.951389  -> 13.8022  err=+0.0377%
    [Y_p a*b/c 11/9 63/200] ratio=0.950617  -> 13.7910  err=-0.0435%
    [11/9 a*b/c Y_p 63/200] ratio=0.950617  -> 13.7910  err=-0.0435%
    [22/9 a*b/c 416/513 K_Mex] ratio=0.951475  -> 13.8034  err=+0.0467%
    [416/513 a*b/c 22/9 K_Mex] ratio=0.951475  -> 13.8034  err=+0.0467%
    [beta_i a*b/c 27/25 137/200] ratio=0.950558  -> 13.7901  err=-0.0497%
    [27/25 a*b/c beta_i 137/200] ratio=0.950558  -> 13.7901  err=-0.0497%
    [Phi_res a/b/c 27/25 416/513] ratio=0.951522  -> 13.8041  err=+0.0517%
    [Phi_res a/b/c 416/513 27/25] ratio=0.951522  -> 13.8041  err=+0.0517%
    [1/12 a*b/c 1/12 alpha] ratio=0.951639  -> 13.8058  err=+0.0640%
    [r a*b/c 11/9 5/108] ratio=0.950400  -> 13.7879  err=-0.0663%

  4-atom shell (tol 0.05%):
    [SSq a*b/(c*d) n_s 63/200 mpme] ratio=0.951005  -> 13.7966  err=-0.0027%
    [SSq a*b/(c*d) n_s mpme 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [n_s a*b/(c*d) SSq 63/200 mpme] ratio=0.951005  -> 13.7966  err=-0.0027%
    [n_s a*b/(c*d) SSq mpme 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [SSq a*b*c/d n_s 1/mpme 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [SSq a*b*c/d 1/mpme n_s 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [n_s a*b*c/d SSq 1/mpme 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [n_s a*b*c/d 1/mpme SSq 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [1/mpme a*b*c/d SSq n_s 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [1/mpme a*b*c/d n_s SSq 63/200] ratio=0.951005  -> 13.7966  err=-0.0027%
    [D_phys a*b*c/d 1-F*P Y_p 307/325] ratio=0.951004  -> 13.7966  err=-0.0028%
    [D_phys a*b*c/d Y_p 1-F*P 307/325] ratio=0.951004  -> 13.7966  err=-0.0028%
    [1-F*P a*b*c/d D_phys Y_p 307/325] ratio=0.951004  -> 13.7966  err=-0.0028%
    [1-F*P a*b*c/d Y_p D_phys 307/325] ratio=0.951004  -> 13.7966  err=-0.0028%
    [Y_p a*b*c/d D_phys 1-F*P 307/325] ratio=0.951004  -> 13.7966  err=-0.0028%

  BEST t_0: t_H * [SSq a*b/(c*d) n_s 63/200 mpme] = 13.7966, err = -0.002694%
================================================================================
TRACK (d) -- Class LXXXIX: CV-4 architectural identity
================================================================================
  LXXXII prediction:    omega_b*h^2 = 23/1000 = 0.02300
  LXXXIII EXACT:        omega_c*h^2 = 3/25    = 0.12000
  Sum (LHS):                              = 0.14300
  LXXXI EXACT:          Omega_m*h^2 = 143/1000 = 0.14300
  Identity check: LHS == RHS ?  True
  err = +0.000000%  ->  EXACT architectural identity

classLXXXVI_tau_reion_session771: predicted=5.440202e-02 observed=5.440000e-02 error_pct=3.718354e-03 status=CE_strict
classLXXXVII_lnAs_session771: predicted=3.043881e+00 observed=3.044000e+00 error_pct=-3.917807e-03 status=CE_strict
classLXXXVIII_t0_session771: predicted=1.379663e+01 observed=1.379700e+01 error_pct=-2.694425e-03 status=CE_strict
classLXXXIX_CV4_matter_sum_session771: predicted=1.430000e-01 observed=1.430000e-01 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  LXXXVI    tau              pred=0.05440  err=+0.0037%  (CE_strict)
  LXXXVII   ln(10^10 A_s)    pred=3.0439   err=-0.0039%  (CE_strict)
  LXXXVIII  t_0 (Gyr)        pred=13.7966  err=-0.0027%  (CE_strict)
  LXXXIX    CV-4 sum-rule    pred=0.14300  err=+0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session771_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
