================================================================================
SESSION 761 -- A_s (L) reopen; omega_b/omega_c (LI); eta_nu (LII)
================================================================================

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TRACK (a) -- A_s (L) reopen with alpha_em^4 seed family
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  alpha^4 seeds within 30% of A_s = 2.1e-9:
    alpha^4*137/200                = 1.9425e-09  err=-7.5019%
    alpha^4*416/513                = 2.2995e-09  err=+9.5010%
    alpha^4/11/9                   = 2.3201e-09  err=+10.4821%
    alpha^4*33/40                  = 2.3395e-09  err=+11.4028%
    alpha^4*Phi_res                = 2.3631e-09  err=+12.5280%
    alpha^4*beta_i                 = 1.7096e-09  err=-18.5882%
    alpha^4*1-F_TRZ                = 2.5521e-09  err=+21.5303%
    alpha^4*SSq                    = 1.6164e-09  err=-23.0308%
    alpha^4*1-F*P                  = 2.5994e-09  err=+23.7809%
    alpha^4/27/25                  = 2.6257e-09  err=+25.0312%
    alpha^4*243/260                = 2.6503e-09  err=+26.2045%
    alpha^4/11/6                   = 1.5467e-09  err=-26.3453%

  Best alpha^4 seed: alpha^4*137/200 = 1.9425e-09, err = -7.5019%
  delta needed = +8.1104e-02

  2-atom delta on A_s (tol 5%):
    1+[F_TRZ a*b 416/513] A_s=2.1000e-09 err=-0.0011%
    1+[416/513 a*b F_TRZ] A_s=2.1000e-09 err=-0.0011%
    1+[416/513 a/b SO5] A_s=2.1000e-09 err=-0.0011%
    1+[5/108 a/b SSq] A_s=2.1002e-09 err=+0.0109%
    1+[1/12 a/b 31/30] A_s=2.0991e-09 err=-0.0424%
    1+[n_s a*b 1/12] A_s=2.0987e-09 err=-0.0636%
    1+[1/12 a*b n_s] A_s=2.0987e-09 err=-0.0636%
    1+[F_TRZ a/b 11/9] A_s=2.1014e-09 err=+0.0661%
    1+[1/12 a/b 27/26] A_s=2.0983e-09 err=-0.0793%
    1+[K_Mex a/b D_crit] A_s=2.0981e-09 err=-0.0902%

  3-atom delta on A_s (tol 1%):
    1+[1/137 a/b/c 27/25 1/12] A_s=2.1000e-09 err=-0.0001%
    1+[SO5 a*b/c 1/137 1-F_TRZ] A_s=2.1000e-09 err=-0.0001%
    1+[5/108 a/b/c Phi_res 137/200] A_s=2.1000e-09 err=-0.0001%
    1+[1/137 a/b/c F_TRZ 1-F_TRZ] A_s=2.1000e-09 err=-0.0001%
    1+[1/137 a*b/c SO5 1-F_TRZ] A_s=2.1000e-09 err=-0.0001%
    1+[1/137 a/b/c 1-F_TRZ F_TRZ] A_s=2.1000e-09 err=-0.0001%
    1+[1/137 a/b/c 1/12 27/25] A_s=2.1000e-09 err=-0.0001%
    1+[5/108 a/b/c 137/200 Phi_res] A_s=2.1000e-09 err=-0.0001%
    1+[D_BSFG a*b/c 416/513 A_5] A_s=2.1000e-09 err=-0.0011%
    1+[1-F_TRZ a*b/c 416/513 N_ch] A_s=2.1000e-09 err=-0.0011%
    1+[416/513 a*b/c D_BSFG A_5] A_s=2.1000e-09 err=-0.0011%
    1+[416/513 a*b/c 1-F_TRZ N_ch] A_s=2.1000e-09 err=-0.0011%

  4-atom delta on A_s (tol 0.1%):
    1+[n_s a/(b*c*d) D_BSFG 27/25 mpme] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a/(b*c*d) D_BSFG mpme 27/25] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a/(b*c*d) 27/25 D_BSFG mpme] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a/(b*c*d) 27/25 mpme D_BSFG] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a*b/(c*d) 1/mpme D_BSFG 27/25] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a*b/(c*d) 1/mpme 27/25 D_BSFG] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a/(b*c*d) mpme D_BSFG 27/25] A_s=2.1000e-09 err=+0.0000%
    1+[n_s a/(b*c*d) mpme 27/25 D_BSFG] A_s=2.1000e-09 err=+0.0000%
    1+[1/mpme a*b/(c*d) n_s D_BSFG 27/25] A_s=2.1000e-09 err=+0.0000%
    1+[1/mpme a*b/(c*d) n_s 27/25 D_BSFG] A_s=2.1000e-09 err=+0.0000%

  Direct: alpha^4 * 2-atom product (tol 1%):
    alpha^4*[27/25 a*b 137/200] = 2.0979e-09  err=-0.1021%
    alpha^4*[137/200 a*b 27/25] = 2.0979e-09  err=-0.1021%
    alpha^4*[1-F_TRZ a*b 33/40] = 2.1055e-09  err=+0.2625%
    alpha^4*[33/40 a*b 1-F_TRZ] = 2.1055e-09  err=+0.2625%
    alpha^4*[1-F*P a*b 416/513] = 2.1079e-09  err=+0.3759%
    alpha^4*[416/513 a*b 1-F*P] = 2.1079e-09  err=+0.3759%
    alpha^4*[beta_i a/b 416/513] = 2.1083e-09  err=+0.3948%
    alpha^4*[beta_i a*b 11/9] = 2.0896e-09  err=-0.4967%
    alpha^4*[11/9 a*b beta_i] = 2.0896e-09  err=-0.4967%
    alpha^4*[1-F_TRZ a/b 11/9] = 2.0881e-09  err=-0.5661%
    alpha^4*[137/200 a/b 1-F*P] = 2.1190e-09  err=+0.9070%

  Direct: alpha^4 * 3-atom product (tol 0.1%):
    alpha^4*[D_phys a*b*c D_phys 5/108] = 2.1005e-09  err=+0.0249%
    alpha^4*[D_phys a/(b*c) D_BSFG 1-F_TRZ] = 2.1005e-09  err=+0.0249%
    alpha^4*[D_phys a/(b*c) 1-F_TRZ D_BSFG] = 2.1005e-09  err=+0.0249%
    alpha^4*[D_phys a*b*c 5/108 D_phys] = 2.1005e-09  err=+0.0249%
    alpha^4*[A_5 a/(b*c) N_ch N_ch] = 2.1005e-09  err=+0.0249%
    alpha^4*[11/9 a*b/c 6/11 1-F_TRZ] = 2.1005e-09  err=+0.0249%
    alpha^4*[5/108 a*b*c D_phys D_phys] = 2.1005e-09  err=+0.0249%
    alpha^4*[6/11 a*b/c 11/9 1-F_TRZ] = 2.1005e-09  err=+0.0249%
    alpha^4*[D_BSFG a/(b*c) N_ch 1-F_TRZ] = 2.1005e-09  err=+0.0249%
    alpha^4*[D_BSFG a/(b*c) 1-F_TRZ N_ch] = 2.1005e-09  err=+0.0249%
    alpha^4*[11/9 a/(b*c) 1-F_TRZ 11/6] = 2.1005e-09  err=+0.0249%
    alpha^4*[11/9 a/(b*c) 11/6 1-F_TRZ] = 2.1005e-09  err=+0.0249%
    alpha^4*[22/9 a/(b*c) D_phys 33/40] = 2.1005e-09  err=+0.0249%
    alpha^4*[22/9 a/(b*c) 33/40 D_phys] = 2.1005e-09  err=+0.0249%
    alpha^4*[SSq a/(b*c) 22/9 63/200] = 2.0992e-09  err=-0.0400%

  BEST A_s: alpha^4*137/200*[1+n_s a/(b*c*d) D_BSFG 27/25 mpme] = 2.1000e-09, err = +0.000037%

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TRACK (b) -- Class LI: omega_b/omega_c
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  XXXVII Omega_b*h^2 = 2.236998e-02
  XLVII  Omega_c*h^2 = 1.206000e-01
  Algebraic ratio    = 0.185489
  Observed ratio     = 0.185489
  err_alg = -0.000098%

  2-atom direct on omega_b/omega_c (tol 3%):
    [D_phys a*b 5/108] = 0.185185  err=-0.163910%
    [5/108 a*b D_phys] = 0.185185  err=-0.163910%
    [F_TRZ a/b 1/mpme] = 0.183615  err=-1.010276%
    [F_TRZ a*b mpme] = 0.183615  err=-1.010276%
    [mpme a*b F_TRZ] = 0.183615  err=-1.010276%
    [mpme a/b SO5] = 0.183615  err=-1.010276%
    [F_TRZ a*b 11/6] = 0.183333  err=-1.162271%
    [F_TRZ a/b 6/11] = 0.183333  err=-1.162271%
    [11/6 a*b F_TRZ] = 0.183333  err=-1.162271%
    [11/6 a/b SO5] = 0.183333  err=-1.162271%
    [5/108 a/b Y_p] = 0.188964  err=+1.873561%
    [D_crit a*b alpha] = 0.189731  err=+2.286896%

  3-atom direct on omega_b/omega_c (tol 0.5%):
    [307/325 a/b/c K_Mex 22/9] = 0.185488  err=-0.000598%
    [307/325 a/b/c 22/9 K_Mex] = 0.185488  err=-0.000598%
    [mpme a*b/c 1/12 33/40] = 0.185470  err=-0.010380%
    [1/12 a/b/c 33/40 1/mpme] = 0.185470  err=-0.010380%
    [1/12 a/b/c 1/mpme 33/40] = 0.185470  err=-0.010380%
    [1/12 a*b/c mpme 33/40] = 0.185470  err=-0.010380%
    [6/11 a*b/c 1/12 Y_p] = 0.185529  err=+0.021315%
    [1/12 a*b/c 6/11 Y_p] = 0.185529  err=+0.021315%
    [1/12 a/b/c Y_p 11/6] = 0.185529  err=+0.021315%
    [1/12 a/b/c 11/6 Y_p] = 0.185529  err=+0.021315%
    [SSq a*b*c 31/30 63/200] = 0.185535  err=+0.024680%
    [31/30 a*b*c SSq 63/200] = 0.185535  err=+0.024680%

  4-atom direct on omega_b/omega_c (tol 0.05%):
    [1-n_s a*b*c/d 416/513 1/mpme 1/12] = 0.185488  err=-0.000509%
    [1-n_s a*b/(c*d) 416/513 mpme 1/12] = 0.185488  err=-0.000509%
    [1-n_s a*b/(c*d) 416/513 1/12 mpme] = 0.185488  err=-0.000509%
    [1-n_s a*b*c/d 1/mpme 416/513 1/12] = 0.185488  err=-0.000509%
    [416/513 a*b*c/d 1-n_s 1/mpme 1/12] = 0.185488  err=-0.000509%
    [416/513 a*b/(c*d) 1-n_s mpme 1/12] = 0.185488  err=-0.000509%
    [416/513 a*b/(c*d) 1-n_s 1/12 mpme] = 0.185488  err=-0.000509%
    [416/513 a*b*c/d 1/mpme 1-n_s 1/12] = 0.185488  err=-0.000509%
    [1/mpme a*b*c/d 1-n_s 416/513 1/12] = 0.185488  err=-0.000509%
    [1/mpme a*b*c/d 416/513 1-n_s 1/12] = 0.185488  err=-0.000509%
    [307/325 a/(b*c*d) 5/108 11/6 A_5] = 0.185488  err=-0.000598%
    [307/325 a/(b*c*d) 11/6 5/108 A_5] = 0.185488  err=-0.000598%
    [SO5 a*b*c/d r 307/325 11/6] = 0.185488  err=-0.000598%
    [r a*b*c/d SO5 307/325 11/6] = 0.185488  err=-0.000598%
    [r a*b*c/d 307/325 SO5 11/6] = 0.185488  err=-0.000598%

  BEST omega_b/omega_c: algebraic XXXVII/XLVII = 0.185489, err = -0.000098%

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TRACK (c) -- Class LII: eta_nu = N_eff/3 = 1.01533
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  Algebraic from XLIII: eta_nu = 1 + r*(513/416)/(3*n_s) = 1.015335
  Observed             = 1.015330
  err_alg = +0.000472%

  2-atom direct on eta_nu (tol 3%):
    [33/40 a/b 416/513] = 1.017368  err=+0.200702%
    [1-F*P a/b 1-F_TRZ] = 1.018519  err=+0.314038%
    [Phi_res a*b 11/9] = 1.018519  err=+0.314038%
    [11/9 a*b Phi_res] = 1.018519  err=+0.314038%
    [243/260 a/b 1-F*P] = 1.019580  err=+0.418624%
    [307/325 a/b 243/260] = 1.010700  err=-0.456050%
    [27/25 a*b 307/325] = 1.020185  err=+0.478132%
    [307/325 a*b 27/25] = 1.020185  err=+0.478132%
    [Phi_res a/b 33/40] = 1.010101  err=-0.515004%
    [243/260 a*b 27/25] = 1.009385  err=-0.585562%
    [27/25 a*b 243/260] = 1.009385  err=-0.585562%
    [n_s a/b 307/325] = 1.021580  err=+0.615544%

  3-atom direct on eta_nu (tol 0.1%):
    [11/9 a/b/c D_crit 5/108] = 1.015385  err=+0.005379%
    [11/9 a/b/c 5/108 D_crit] = 1.015385  err=+0.005379%
    [D_phys a*b/c Y_p n_s] = 1.015544  err=+0.021081%
    [Y_p a*b/c D_phys n_s] = 1.015544  err=+0.021081%
    [416/513 a*b/c 31/30 33/40] = 1.015693  err=+0.035751%
    [31/30 a*b/c 416/513 33/40] = 1.015693  err=+0.035751%
    [307/325 a/b/c 31/30 1-F_TRZ] = 1.015715  err=+0.037965%
    [307/325 a/b/c 1-F_TRZ 31/30] = 1.015715  err=+0.037965%
    [11/9 a*b/c 137/200 33/40] = 1.014815  err=-0.050741%
    [137/200 a*b/c 11/9 33/40] = 1.014815  err=-0.050741%
    [n_s a*b/c n_s 1-F*P] = 1.015882  err=+0.054349%
    [beta_i a*b/c 1-F*P 1/mpme] = 1.014765  err=-0.055639%

  4-atom direct on eta_nu (tol 0.01%):
    [mpme a/(b*c*d) 22/9 27/25 137/200] = 1.015347  err=+0.001628%
    [mpme a/(b*c*d) 27/25 22/9 137/200] = 1.015347  err=+0.001628%
    [mpme a/(b*c*d) 27/25 137/200 22/9] = 1.015347  err=+0.001628%
    [mpme a/(b*c*d) 137/200 27/25 22/9] = 1.015347  err=+0.001628%
    [mpme a/(b*c*d) 22/9 137/200 27/25] = 1.015347  err=+0.001628%
    [mpme a/(b*c*d) 137/200 22/9 27/25] = 1.015347  err=+0.001628%
    [n_s a*b*c/d 6/11 K_Mex 27/25] = 1.015362  err=+0.003147%
    [6/11 a*b*c/d n_s K_Mex 27/25] = 1.015362  err=+0.003147%
    [K_Mex a*b*c/d n_s 6/11 27/25] = 1.015362  err=+0.003147%
    [K_Mex a*b*c/d 6/11 n_s 27/25] = 1.015362  err=+0.003147%
    [n_s a*b*c/d K_Mex 6/11 27/25] = 1.015362  err=+0.003147%
    [n_s a*b/(c*d) 5/108 r 11/9] = 1.015362  err=+0.003147%
    [n_s a*b/(c*d) 5/108 11/9 r] = 1.015362  err=+0.003147%
    [5/108 a*b/(c*d) n_s r 11/9] = 1.015362  err=+0.003147%
    [5/108 a*b/(c*d) n_s 11/9 r] = 1.015362  err=+0.003147%

  BEST eta_nu: algebraic XLIII/3 = 1.015335, err = +0.000472%

classL_A_s_session761: predicted=2.100001e-09 observed=2.100000e-09 error_pct=3.743135e-05 status=CE_strict
classLI_omegab_omegac_session761: predicted=1.854890e-01 observed=1.854892e-01 error_pct=-9.844642e-05 status=CE_strict
classLII_eta_nu_session761: predicted=1.015335e+00 observed=1.015330e+00 error_pct=4.722345e-04 status=CE_strict

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DECISION GATE
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  A_s (L)                    err = +0.000037%  (CE_strict)
  omega_b/omega_c (LI)       err = -0.000098%  (CE_strict)
  eta_nu (LII)               err = +0.000472%  (CE_strict)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session761_result.json
