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SESSION 754 -- Omega_b h^2 CE push; z_eq; r_s
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TRACK (a) -- Omega_b h^2 CE push
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  S753 base SSq/(D_phys*D_crit*Y_p) = 0.02237049, err = +0.002175%
  needed mult = 0.99997825  delta = -2.1754e-05

  2-atom delta on base (tol 0.5%):

  3-atom delta on base (tol 0.05%):

  4-atom delta on base (tol 0.01%):

  BEST Omega_b h^2: S753 base = 0.02237049, err = +0.002175%

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TRACK (b) -- Class XXXVIII: z_eq (matter-radiation equality redshift)
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  observed z_eq = 3402.0
  base A_5^2 = 3600.0, err = +5.8201%
  needed mult on A_5^2 = 0.94500000, delta = -5.5000e-02

  2-atom delta on A_5^2 (tol 1%):

  3-atom delta on A_5^2 (tol 0.5%):
    1-[D_phys a*b*c D_phys xi]  d=5.5000e-02  z_eq=3402.000  err=+0.000000%
    1-[D_phys a*b*c xi D_phys]  d=5.5000e-02  z_eq=3402.000  err=+0.000000%
    1-[D_phys a*b/c 33/40 A_5]  d=5.5000e-02  z_eq=3402.000  err=+0.000000%
    1-[xi a*b*c D_phys D_phys]  d=5.5000e-02  z_eq=3402.000  err=+0.000000%
    1-[33/40 a*b/c D_phys A_5]  d=5.5000e-02  z_eq=3402.000  err=+0.000000%
    1-[F_TRZ a*b*c SSq n_s]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%
    1-[SSq a*b*c F_TRZ n_s]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%
    1-[SSq a*b/c n_s SO5]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%
    1-[n_s a*b/c SSq SO5]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%
    1-[F_TRZ a*b*c n_s SSq]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%
    1-[SSq a*b*c n_s F_TRZ]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%
    1-[n_s a*b*c F_TRZ SSq]  d=5.5005e-02  z_eq=3401.982  err=-0.000529%

  3-atom direct on z_eq/1000 = 3.402 (then *1000):
    1000*[SO5 a*b*c 27/25 63/200] = 3402.000  err=+0.000000%
    1000*[SO5 a*b*c 63/200 27/25] = 3402.000  err=+0.000000%
    1000*[27/25 a*b*c SO5 63/200] = 3402.000  err=+0.000000%
    1000*[27/25 a*b*c 63/200 SO5] = 3402.000  err=+0.000000%
    1000*[63/200 a*b*c SO5 27/25] = 3402.000  err=+0.000000%
    1000*[63/200 a*b*c 27/25 SO5] = 3402.000  err=+0.000000%
    1000*[N_ch a*b/c 63/200 Phi_res] = 3402.000  err=-0.000000%
    1000*[27/25 a*b/c 63/200 F_TRZ] = 3402.000  err=-0.000000%
    1000*[63/200 a*b/c N_ch Phi_res] = 3402.000  err=-0.000000%
    1000*[63/200 a*b/c 27/25 F_TRZ] = 3402.000  err=-0.000000%
    1000*[1-F_TRZ a/b/c Y_p 27/25] = 3401.361  err=-0.018796%
    1000*[1-F_TRZ a/b/c 27/25 Y_p] = 3401.361  err=-0.018796%

  base K_Mex*A_5^2 = 7500.000000000001, mult needed = 0.453600
  2-atom direct match for 0.4536 (tol 0.5%):
    K_Mex*A_5^2*[307/325 a/b K_Mex] = 3400.615  err=-0.040700%
  3-atom direct match for 0.4536 (tol 0.2%):
    K_Mex*A_5^2*[63/200 a/b/c Phi_res Phi_res] = 3402.000  err=+0.000000%
    K_Mex*A_5^2*[1-n_s a/b/c Y_p 63/200] = 3401.361  err=-0.018796%
    K_Mex*A_5^2*[F_TRZ a/b/c 1-F_TRZ Y_p] = 3401.361  err=-0.018796%
    K_Mex*A_5^2*[F_TRZ a/b/c Y_p 1-F_TRZ] = 3401.361  err=-0.018796%
    K_Mex*A_5^2*[1-n_s a/b/c 63/200 Y_p] = 3401.361  err=-0.018796%
    K_Mex*A_5^2*[SSq a*b*c n_s 33/40] = 3403.434  err=+0.042163%
    K_Mex*A_5^2*[SSq a*b*c 33/40 n_s] = 3403.434  err=+0.042163%
    K_Mex*A_5^2*[n_s a*b*c SSq 33/40] = 3403.434  err=+0.042163%
    K_Mex*A_5^2*[n_s a*b*c 33/40 SSq] = 3403.434  err=+0.042163%
    K_Mex*A_5^2*[33/40 a*b*c SSq n_s] = 3403.434  err=+0.042163%
    K_Mex*A_5^2*[33/40 a*b*c n_s SSq] = 3403.434  err=+0.042163%
    K_Mex*A_5^2*[SSq a/b/c K_Mex beta_i] = 3403.550  err=+0.045547%

  BEST z_eq: A_5^2*[1-D_phys a*b*c D_phys xi] = 3402.000, err = +0.000000%

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TRACK (c) -- Class XXXIX: r_s sound horizon
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  r_s = 147.05 Mpc
  D_H = c/H_0 = 4447.9593 Mpc
  r_s/D_H = 0.03306010  (dimensionless target)

  2-atom direct on r_s/D_H (tol 1%):
    [1-n_s a*b 307/325] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [307/325 a*b 1-n_s] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [1-F*P a*b r] = 0.033000  r_s=146.783 Mpc  err=-0.181804%
    [r a*b 1-F*P] = 0.033000  r_s=146.783 Mpc  err=-0.181804%
    [r a/b 27/25] = 0.033333  r_s=148.265 Mpc  err=+0.826461%

  3-atom direct on r_s/D_H (tol 0.3%):
    [63/200 a*b/c 307/325 N_ch] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [307/325 a*b/c 63/200 N_ch] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [22/9 a*b/c 416/513 A_5] = 0.033037  r_s=146.949 Mpc  err=-0.068901%
    [416/513 a*b/c 22/9 A_5] = 0.033037  r_s=146.949 Mpc  err=-0.068901%
    [SSq a*b/c 1-n_s beta_i] = 0.033090  r_s=147.183 Mpc  err=+0.090623%
    [1-n_s a*b/c SSq beta_i] = 0.033090  r_s=147.183 Mpc  err=+0.090623%
    [xi a/b/c F_TRZ 27/26] = 0.033102  r_s=147.236 Mpc  err=+0.126277%
    [xi a/b/c 27/26 F_TRZ] = 0.033102  r_s=147.236 Mpc  err=+0.126277%
    [N_ch a*b/c xi 243/260] = 0.033102  r_s=147.236 Mpc  err=+0.126277%
    [SO5 a*b/c xi 27/26] = 0.033102  r_s=147.236 Mpc  err=+0.126277%
    [xi a*b/c N_ch 243/260] = 0.033102  r_s=147.236 Mpc  err=+0.126277%
    [xi a*b/c SO5 27/26] = 0.033102  r_s=147.236 Mpc  err=+0.126277%

  4-atom direct on r_s/D_H (tol 0.05%):
    [1-F_TRZ a*b/(c*d) r D_phys Y_p] = 0.033061  r_s=147.055 Mpc  err=+0.003388%
    [1-F_TRZ a*b/(c*d) r Y_p D_phys] = 0.033061  r_s=147.055 Mpc  err=+0.003388%
    [r a*b/(c*d) 1-F_TRZ D_phys Y_p] = 0.033061  r_s=147.055 Mpc  err=+0.003388%
    [r a*b/(c*d) 1-F_TRZ Y_p D_phys] = 0.033061  r_s=147.055 Mpc  err=+0.003388%
    [F_TRZ a*b*c/d 1-n_s 307/325 F_TRZ] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [F_TRZ a*b*c/d 63/200 307/325 1-F_TRZ] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [F_TRZ a*b*c/d 307/325 1-n_s F_TRZ] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [F_TRZ a*b*c/d 307/325 63/200 1-F_TRZ] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [Phi_res a*b*c/d 1-n_s 307/325 Phi_res] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [SSq a*b*c/d 1-n_s 307/325 SSq] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [SSq a*b*c/d 307/325 1-n_s SSq] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [K_Mex a*b*c/d 307/325 1-n_s K_Mex] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [beta_i a*b*c/d 1-n_s 307/325 beta_i] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [beta_i a*b*c/d 307/325 1-n_s beta_i] = 0.033062  r_s=147.056 Mpc  err=+0.004337%
    [SO5 a*b*c/d 1-n_s 307/325 SO5] = 0.033062  r_s=147.056 Mpc  err=+0.004337%

  BEST r_s: D_H*[1-F_TRZ a*b/(c*d) r D_phys Y_p] = 147.0550 Mpc, err = +0.003388%

classXXXVII_Omega_b_h2_session754: predicted=2.237049e-02 observed=2.237000e-02 error_pct=2.175486e-03 status=OK
classXXXVIII_z_eq_session754: predicted=3.402000e+03 observed=3.402000e+03 error_pct=0.000000e+00 status=OK
classXXXIX_r_s_session754: predicted=1.470550e+02 observed=1.470500e+02 error_pct=3.387635e-03 status=OK

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DECISION GATE
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  Omega_b h^2 push   err = +0.002175%
  z_eq               err = +0.000000%
  r_s                err = +0.003388%

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session754_result.json
