================================================================================
SESSION 773 -- z_eq XCIV; r_drag/D_M(0.38) XCV; omega_nu*h^2 XCVI; CV-6 XCVII
================================================================================

================================================================================
TRACK (a) -- Class XCIV: z_eq = 3402 (matter-radiation equality)
================================================================================
  Target z_eq = 3402.0

  2-atom direct (tol 5%):
    [D_crit a/b 1/137] = 3.562000e+03  err=+4.7031%
    [D_crit a/b alpha] = 3.562936e+03  err=+4.7306%

  3-atom direct (tol 0.5%):
    [A_5 a*b*c A_5 307/325] = 3.400615e+03  err=-0.0407%
    [A_5 a*b*c 307/325 A_5] = 3.400615e+03  err=-0.0407%
    [307/325 a*b*c A_5 A_5] = 3.400615e+03  err=-0.0407%

  4-atom direct (tol 0.05%):
    [D_BSFG a/(b*c*d) SSq 1-F_TRZ xi] = 3.402446e+03  err=+0.0131%
    [D_BSFG a/(b*c*d) 1-F_TRZ SSq xi] = 3.402446e+03  err=+0.0131%
    [D_BSFG a/(b*c*d) 1-F_TRZ xi SSq] = 3.402446e+03  err=+0.0131%
    [D_BSFG a/(b*c*d) xi 1-F_TRZ SSq] = 3.402446e+03  err=+0.0131%
    [A_5 a/(b*c*d) SSq N_ch xi] = 3.402446e+03  err=+0.0131%
    [A_5 a/(b*c*d) N_ch SSq xi] = 3.402446e+03  err=+0.0131%
    [D_BSFG a/(b*c*d) SSq xi 1-F_TRZ] = 3.402446e+03  err=+0.0131%
    [D_BSFG a/(b*c*d) xi SSq 1-F_TRZ] = 3.402446e+03  err=+0.0131%
    [A_5 a/(b*c*d) SSq xi N_ch] = 3.402446e+03  err=+0.0131%
    [A_5 a/(b*c*d) N_ch xi SSq] = 3.402446e+03  err=+0.0131%
    [A_5 a/(b*c*d) xi SSq N_ch] = 3.402446e+03  err=+0.0131%
    [A_5 a/(b*c*d) xi N_ch SSq] = 3.402446e+03  err=+0.0131%
    [D_crit a*b/(c*d) D_crit Y_p 416/513] = 3.402551e+03  err=+0.0162%
    [D_crit a*b/(c*d) D_crit 416/513 Y_p] = 3.402551e+03  err=+0.0162%
    [D_crit a*b*c/d Y_p mpme xi] = 3.402558e+03  err=+0.0164%

  BEST z_eq: [A_5 a/(b*c*d) N_ch SSq xi] = 3.402446e+03, err = +0.013095%
================================================================================
TRACK (b) -- Class XCV: r_drag / D_M(0.38) = 0.0969 (BAO dimensionless)
================================================================================
  Target r_drag/D_M(0.38) = 0.0969

  2-atom direct (tol 5%):
    [F_TRZ a/b 31/30] = 9.677419e-02  err=-0.1298%
    [F_TRZ a*b n_s] = 9.650000e-02  err=-0.4128%
    [n_s a*b F_TRZ] = 9.650000e-02  err=-0.4128%
    [n_s a/b SO5] = 9.650000e-02  err=-0.4128%
    [K_Mex a*b 5/108] = 9.645062e-02  err=-0.4638%
    [5/108 a*b K_Mex] = 9.645062e-02  err=-0.4638%
    [F_TRZ a/b 27/26] = 9.629630e-02  err=-0.6230%
    [xi a/b 1-n_s] = 9.821429e-02  err=+1.3563%
    [xi a/b r] = 9.548611e-02  err=-1.4591%
    [SSq a/b D_BSFG] = 9.500000e-02  err=-1.9608%
    [63/200 a*b 63/200] = 9.922500e-02  err=+2.3994%
    [F_TRZ a*b 307/325] = 9.446154e-02  err=-2.5165%

  3-atom direct (tol 0.5%):
    [F_TRZ a*b/c 243/260 n_s] = 9.685134e-02  err=-0.0502%
    [243/260 a*b/c F_TRZ n_s] = 9.685134e-02  err=-0.0502%
    [243/260 a/b/c SO5 n_s] = 9.685134e-02  err=-0.0502%
    [243/260 a/b/c n_s SO5] = 9.685134e-02  err=-0.0502%
    [beta_i a*b/c n_s D_BSFG] = 9.696642e-02  err=+0.0685%
    [n_s a*b/c beta_i D_BSFG] = 9.696642e-02  err=+0.0685%
    [Y_p a/b/c 22/9 31/30] = 9.699413e-02  err=+0.0971%
    [Y_p a/b/c 31/30 22/9] = 9.699413e-02  err=+0.0971%
    [11/6 a/b/c A_5 63/200] = 9.700176e-02  err=+0.1050%
    [11/6 a/b/c 63/200 A_5] = 9.700176e-02  err=+0.1050%
    [Y_p a*b/c 33/40 K_Mex] = 9.702000e-02  err=+0.1238%
    [33/40 a*b/c Y_p K_Mex] = 9.702000e-02  err=+0.1238%
    [D_BSFG a/b/c A_5 31/30] = 9.677419e-02  err=-0.1298%
    [1-F_TRZ a/b/c N_ch 31/30] = 9.677419e-02  err=-0.1298%
    [D_BSFG a/b/c 31/30 A_5] = 9.677419e-02  err=-0.1298%

  4-atom direct (tol 0.05%):
    [1-F*P a*b/(c*d) 5/108 A_5 1/137] = 9.690072e-02  err=+0.0007%
    [1-F*P a*b/(c*d) 5/108 1/137 A_5] = 9.690072e-02  err=+0.0007%
    [1-F*P a*b/(c*d) 137/200 D_BSFG 27/25] = 9.690072e-02  err=+0.0007%
    [1-F*P a*b/(c*d) 137/200 27/25 D_BSFG] = 9.690072e-02  err=+0.0007%
    [5/108 a*b/(c*d) 1-F*P A_5 1/137] = 9.690072e-02  err=+0.0007%
    [5/108 a*b/(c*d) 1-F*P 1/137 A_5] = 9.690072e-02  err=+0.0007%
    [137/200 a*b/(c*d) 1-F*P D_BSFG 27/25] = 9.690072e-02  err=+0.0007%
    [137/200 a*b/(c*d) 1-F*P 27/25 D_BSFG] = 9.690072e-02  err=+0.0007%
    [137/200 a*b*c/d 11/6 1/12 27/25] = 9.690072e-02  err=+0.0007%
    [137/200 a*b/(c*d) 1/12 27/25 6/11] = 9.690072e-02  err=+0.0007%
    [137/200 a*b*c/d 1/12 11/6 27/25] = 9.690072e-02  err=+0.0007%
    [137/200 a*b/(c*d) 1/12 6/11 27/25] = 9.690072e-02  err=+0.0007%
    [11/6 a*b*c/d 137/200 1/12 27/25] = 9.690072e-02  err=+0.0007%
    [11/6 a*b*c/d 1/12 137/200 27/25] = 9.690072e-02  err=+0.0007%
    [1/12 a*b/(c*d) 137/200 27/25 6/11] = 9.690072e-02  err=+0.0007%

  BEST r_drag/D_M(0.38): [1-F*P a*b/(c*d) 137/200 27/25 D_BSFG] = 9.690072e-02, err = +0.000743%
================================================================================
TRACK (c) -- Class XCVI: omega_nu * h^2 = 6.44e-4 (neutrino density)
================================================================================
  Target omega_nu*h^2 = 0.000644

  2-atom direct (tol 5%):

  3-atom direct (tol 0.5%):
    [1/137 a*b/c 1/12 307/325] = 6.439367e-04  err=-0.0098%
    [1/12 a*b/c 1/137 307/325] = 6.439367e-04  err=-0.0098%
    [alpha a*b/c 1/12 307/325] = 6.437675e-04  err=-0.0361%
    [1/12 a*b/c alpha 307/325] = 6.437675e-04  err=-0.0361%
    [Phi_res a*b/c 5/108 A_5] = 6.430041e-04  err=-0.1546%
    [5/108 a*b/c Phi_res A_5] = 6.430041e-04  err=-0.1546%
    [5/108 a*b/c 1/12 D_BSFG] = 6.430041e-04  err=-0.1546%
    [1/12 a*b/c 5/108 D_BSFG] = 6.430041e-04  err=-0.1546%
    [r a*b*c 1/137 22/9] = 6.423358e-04  err=-0.2584%
    [22/9 a*b*c 1/137 r] = 6.423358e-04  err=-0.2584%
    [1/137 a*b*c r 22/9] = 6.423358e-04  err=-0.2584%
    [1/137 a*b*c 22/9 r] = 6.423358e-04  err=-0.2584%
    [r a*b*c 22/9 1/137] = 6.423358e-04  err=-0.2584%
    [22/9 a*b*c r 1/137] = 6.423358e-04  err=-0.2584%
    [r a*b*c 22/9 alpha] = 6.421670e-04  err=-0.2846%

  4-atom direct (tol 0.05%):
    [xi a*b*c/d Y_p 243/260 11/9] = 6.440084e-04  err=+0.0013%
    [xi a*b*c/d 243/260 Y_p 11/9] = 6.440084e-04  err=+0.0013%
    [Y_p a*b*c/d xi 243/260 11/9] = 6.440084e-04  err=+0.0013%
    [Y_p a*b*c/d 243/260 xi 11/9] = 6.440084e-04  err=+0.0013%
    [243/260 a*b*c/d xi Y_p 11/9] = 6.440084e-04  err=+0.0013%
    [243/260 a*b*c/d Y_p xi 11/9] = 6.440084e-04  err=+0.0013%
    [r a*b*c/d 5/108 307/325 22/9] = 6.440559e-04  err=+0.0087%
    [r a*b*c/d 307/325 5/108 22/9] = 6.440559e-04  err=+0.0087%
    [5/108 a*b*c/d r 307/325 22/9] = 6.440559e-04  err=+0.0087%
    [5/108 a*b*c/d 307/325 r 22/9] = 6.440559e-04  err=+0.0087%
    [307/325 a/(b*c*d) A_5 22/9 SO5] = 6.440559e-04  err=+0.0087%
    [307/325 a*b*c/d r 5/108 22/9] = 6.440559e-04  err=+0.0087%
    [307/325 a/(b*c*d) 22/9 A_5 SO5] = 6.440559e-04  err=+0.0087%
    [307/325 a*b*c/d 5/108 r 22/9] = 6.440559e-04  err=+0.0087%
    [F_TRZ a*b/(c*d) 307/325 A_5 22/9] = 6.440559e-04  err=+0.0087%

  BEST omega_nu*h^2: [243/260 a*b*c/d Y_p xi 11/9] = 6.440084e-04, err = +0.001306%
================================================================================
TRACK (d) -- Class XCVII: CV-6 architectural identity
================================================================================
  alpha_s (XC pure) = -9/2000 = -0.004500
  r                 =  9/250  = 0.036000
  alpha_s / r       = -1/8  =  -0.1250000000
  -1/8              =  -0.1250000000
  Identity check: LHS == RHS ?  True
  err = -0.000000%  ->  EXACT architectural identity

classXCIV_z_eq_session773: predicted=3.402446e+03 observed=3.402000e+03 error_pct=1.309546e-02 status=CE_strict
classXCV_rdrag_over_DM38_session773: predicted=9.690072e-02 observed=9.690000e-02 error_pct=7.432039e-04 status=CE_strict
classXCVI_omega_nu_h2_session773: predicted=6.440084e-04 observed=6.440000e-04 error_pct=1.306438e-03 status=CE_strict
classXCVII_CV6_alphas_over_r_session773: predicted=-1.250000e-01 observed=-1.250000e-01 error_pct=-0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  XCIV   z_eq               pred=3402.446    err=+0.0131%  (CE_strict)
  XCV    r_drag/D_M(0.38)   pred=0.096901  err=+0.0007%  (CE_strict)
  XCVI   omega_nu*h^2       pred=6.4401e-04  err=+0.0013%  (CE_strict)
  XCVII  CV-6 alpha_s/r     pred=-0.125000  err=-0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session773_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
