================================================================================
SESSION 756 -- tau CE push; z_*; N_eff
================================================================================

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TRACK (a) -- tau_reion strict CE push
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  S755 base (Y_p*(5/108)*(1-n_s)*alpha) = 0.00000290, err = -99.994675%
  delta needed = +1.8777e+04

  2-atom delta on tau base (tol 0.01%):

  3-atom delta on tau base (tol 0.005%):
    1+[D_crit a*b/c D_crit r]  d=1.8778e+04  tau=0.05440177  err=+0.003254%

  4-atom direct on tau (tol 0.001% strict):

  BEST tau: base*[1+D_crit a*b/c D_crit r] = 0.05440177, err = +0.003254%
  STATUS: tight CLOSED

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TRACK (b) -- Class XLII: z_* photon decoupling
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  observed z_* = 1089.8, z_eq (Class XXXVIII) = 3402.0
  z_*/z_eq = 0.32034098

  2-atom direct on z_* (tol 1%):

  3-atom direct on z_* (tol 0.3%):
    [1-F*P a/b/c xi Y_p] = 1088.4354  err=-0.125218%
    [1-F*P a/b/c Y_p xi] = 1088.4354  err=-0.125218%
    [D_phys a*b/c 243/260 xi] = 1087.5524  err=-0.206235%
    [243/260 a*b/c D_phys xi] = 1087.5524  err=-0.206235%

  4-atom direct on z_* (tol 0.05%):
    [N_ch a*b/(c*d) 27/25 11/9 alpha] = 1089.8099  err=+0.000911%
    [N_ch a*b/(c*d) 27/25 alpha 11/9] = 1089.8099  err=+0.000911%
    [1-F_TRZ a/(b*c*d) 22/9 alpha 5/108] = 1089.8099  err=+0.000911%
    [1-F_TRZ a/(b*c*d) alpha 22/9 5/108] = 1089.8099  err=+0.000911%
    [27/25 a*b/(c*d) N_ch 11/9 alpha] = 1089.8099  err=+0.000911%
    [27/25 a*b/(c*d) N_ch alpha 11/9] = 1089.8099  err=+0.000911%
    [1-F_TRZ a/(b*c*d) 22/9 5/108 alpha] = 1089.8099  err=+0.000911%
    [1-F_TRZ a/(b*c*d) 5/108 22/9 alpha] = 1089.8099  err=+0.000911%
    [1-F_TRZ a/(b*c*d) 5/108 alpha 22/9] = 1089.8099  err=+0.000911%
    [1-F_TRZ a/(b*c*d) alpha 5/108 22/9] = 1089.8099  err=+0.000911%
    [D_phys a/(b*c*d) xi 31/30 31/30] = 1089.7739  err=-0.002394%
    [D_phys a/(b*c*d) 31/30 xi 31/30] = 1089.7739  err=-0.002394%
    [D_phys a/(b*c*d) 31/30 31/30 xi] = 1089.7739  err=-0.002394%
    [mpme a/(b*c*d) 1-F_TRZ xi 1/mpme] = 1089.7638  err=-0.003325%
    [mpme a/(b*c*d) 1-F_TRZ 1/mpme xi] = 1089.7638  err=-0.003325%

  3-atom direct on z_*/z_eq = 0.32034 (tol 0.3%):
    z_eq*[27/25 a/b/c mpme mpme] = 1089.7841  err=-0.001455%
    z_eq*[27/25 a*b/c 1/mpme mpme] = 1089.7841  err=-0.001455%
    z_eq*[1/mpme a*b/c 27/25 mpme] = 1089.7841  err=-0.001455%
    z_eq*[1/mpme a*b*c 1/mpme 27/25] = 1089.7841  err=-0.001455%
    z_eq*[27/25 a*b*c 1/mpme 1/mpme] = 1089.7841  err=-0.001455%
    z_eq*[1/mpme a*b*c 27/25 1/mpme] = 1089.7841  err=-0.001455%
    z_eq*[Y_p a*b/c 11/9 243/260] = 1089.9778  err=+0.016313%
    z_eq*[11/9 a*b/c Y_p 243/260] = 1089.9778  err=+0.016313%
    z_eq*[33/40 a*b/c 63/200 416/513] = 1090.2418  err=+0.040544%
    z_eq*[63/200 a*b/c 33/40 416/513] = 1090.2418  err=+0.040544%
    z_eq*[N_ch a/b/c D_crit 27/25] = 1090.3846  err=+0.053644%
    z_eq*[N_ch a/b/c 27/25 D_crit] = 1090.3846  err=+0.053644%

  BEST z_*: [N_ch a*b/(c*d) 27/25 11/9 alpha] = 1089.8099, err = +0.000911%

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TRACK (c) -- Class XLIII: N_eff effective neutrino species
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  observed N_eff = 3.046 = 3 + 0.046
  delta = 0.046 vs alpha (1/137) = 7.297353e-03
  alpha * D_phys * Phi_res = 0.024325  (vs 0.046)

  2-atom direct on N_eff (tol 1%):
    [mpme a/b beta_i] = 3.045534  err=-0.015287%
    [K_Mex a/b 137/200] = 3.041363  err=-0.152248%
    [n_s a/b 63/200] = 3.063492  err=+0.574263%

  3-atom direct on N_eff (tol 0.3%):
    [27/26 a*b/c 22/9 Phi_res] = 3.046154  err=+0.005051%
    [22/9 a*b/c 27/26 Phi_res] = 3.046154  err=+0.005051%
    [Phi_res a*b/c K_Mex SSq] = 3.045809  err=-0.006272%
    [K_Mex a*b/c Phi_res SSq] = 3.045809  err=-0.006272%
    [5/108 a/b/c K_Mex alpha] = 3.045244  err=-0.024806%
    [5/108 a/b/c alpha K_Mex] = 3.045244  err=-0.024806%
    [D_phys a*b/c 137/200 1-F_TRZ] = 3.044444  err=-0.051069%
    [137/200 a*b/c D_phys 1-F_TRZ] = 3.044444  err=-0.051069%
    [5/108 a/b/c K_Mex 1/137] = 3.044444  err=-0.051069%
    [5/108 a/b/c 1/137 K_Mex] = 3.044444  err=-0.051069%
    [SO5 a*b/c 63/200 31/30] = 3.048387  err=+0.078368%
    [63/200 a/b/c F_TRZ 31/30] = 3.048387  err=+0.078368%
    [63/200 a*b/c SO5 31/30] = 3.048387  err=+0.078368%
    [63/200 a/b/c 31/30 F_TRZ] = 3.048387  err=+0.078368%
    [D_BSFG a/b/c K_Mex 307/325] = 3.048860  err=+0.093891%

  4-atom direct on N_eff (tol 0.05%):
    [Phi_res a/(b*c*d) 1-F_TRZ 63/200 n_s] = 3.046059  err=+0.001952%
    [Phi_res a/(b*c*d) n_s 63/200 1-F_TRZ] = 3.046059  err=+0.001952%
    [Phi_res a/(b*c*d) 63/200 1-F_TRZ n_s] = 3.046059  err=+0.001952%
    [Phi_res a/(b*c*d) 63/200 n_s 1-F_TRZ] = 3.046059  err=+0.001952%
    [Phi_res a/(b*c*d) 1-F_TRZ n_s 63/200] = 3.046059  err=+0.001952%
    [Phi_res a/(b*c*d) n_s 1-F_TRZ 63/200] = 3.046059  err=+0.001952%
    [SSq a*b/(c*d) D_crit D_BSFG 416/513] = 3.045937  err=-0.002052%
    [SSq a*b/(c*d) D_crit 416/513 D_BSFG] = 3.045937  err=-0.002052%
    [D_crit a*b/(c*d) SSq D_BSFG 416/513] = 3.045937  err=-0.002052%
    [D_crit a*b/(c*d) SSq 416/513 D_BSFG] = 3.045937  err=-0.002052%
    [mpme a/(b*c*d) 1-F*P 416/513 416/513] = 3.046109  err=+0.003574%
    [mpme a/(b*c*d) 416/513 1-F*P 416/513] = 3.046109  err=+0.003574%
    [mpme a/(b*c*d) 416/513 416/513 1-F*P] = 3.046109  err=+0.003574%
    [D_phys a*b/(c*d) 1-F*P D_crit 5/108] = 3.046154  err=+0.005051%
    [D_phys a*b/(c*d) 1-F*P 5/108 D_crit] = 3.046154  err=+0.005051%

  2-atom direct on N_eff residual 0.046 (tol 5%):
    3+[11/9 a/b D_crit] = 3.047009  err=+0.033111%
    3+[5/108 a/b 31/30] = 3.044803  err=-0.039302%
    3+[n_s a*b 5/108] = 3.044676  err=-0.043469%
    3+[5/108 a*b n_s] = 3.044676  err=-0.043469%
    3+[5/108 a/b 27/26] = 3.044582  err=-0.046565%
    3+[r a/b 416/513] = 3.044394  err=-0.052717%
    3+[31/30 a*b 5/108] = 3.047840  err=+0.060391%
    3+[5/108 a*b 31/30] = 3.047840  err=+0.060391%
    3+[5/108 a/b n_s] = 3.047975  err=+0.064853%
    3+[F_TRZ a/b K_Mex] = 3.048000  err=+0.065660%
    3+[r a*b 11/9] = 3.044000  err=-0.065660%
    3+[11/9 a*b r] = 3.044000  err=-0.065660%

  3-atom direct on N_eff residual 0.046 (tol 1%):
    3+[r a/b/c n_s 416/513] = 3.046004  err=+0.000144%
    3+[r a/b/c 416/513 n_s] = 3.046004  err=+0.000144%
    3+[1-F_TRZ a*b/c 1-n_s 137/200] = 3.045985  err=-0.000479%
    3+[1-n_s a*b/c 1-F_TRZ 137/200] = 3.045985  err=-0.000479%
    3+[F_TRZ a*b/c 63/200 137/200] = 3.045985  err=-0.000479%
    3+[63/200 a*b/c F_TRZ 137/200] = 3.045985  err=-0.000479%
    3+[63/200 a/b/c SO5 137/200] = 3.045985  err=-0.000479%
    3+[63/200 a/b/c 137/200 SO5] = 3.045985  err=-0.000479%
    3+[31/30 a*b/c 5/108 27/26] = 3.046068  err=+0.002222%
    3+[5/108 a*b/c 31/30 27/26] = 3.046068  err=+0.002222%
    3+[5/108 a/b/c 33/40 11/9] = 3.045914  err=-0.002834%
    3+[5/108 a/b/c 11/9 33/40] = 3.045914  err=-0.002834%
    3+[F_TRZ a/b/c D_phys 1/mpme] = 3.045904  err=-0.003158%
    3+[F_TRZ a/b/c 1/mpme D_phys] = 3.045904  err=-0.003158%
    3+[F_TRZ a*b/c mpme D_phys] = 3.045904  err=-0.003158%

  BEST N_eff: 3+[r a/b/c n_s 416/513] = 3.046004, err = +0.000144%

classXLI_tau_reion_session756: predicted=5.440177e-02 observed=5.440000e-02 error_pct=3.253627e-03 status=OK
classXLII_z_star_session756: predicted=1.089810e+03 observed=1.089800e+03 error_pct=9.109248e-04 status=OK
classXLIII_N_eff_session756: predicted=3.046004e+00 observed=3.046000e+00 error_pct=1.439336e-04 status=OK

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DECISION GATE
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  tau CE push    err = +0.003254%  (tight CLOSED)
  z_* (XLII)     err = +0.000911%
  N_eff (XLIII)  err = +0.000144%

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session756_result.json
