================================================================================
SESSION 776 -- z_drag CVI; 100*theta_* CVII; Omega_DE CVIII; CV-9 CIX
================================================================================

================================================================================
TRACK (a) -- Class CVI: z_drag = 1059.94 (baryon drag redshift)
================================================================================
  Target z_drag = 1059.94

  2-atom direct (tol 5%):

  3-atom direct (tol 0.5%):
    [A_5 a/b/c 11/9 5/108] = 1.060364e+03  err=+0.0400%
    [A_5 a/b/c 5/108 11/9] = 1.060364e+03  err=+0.0400%
    [D_crit a/b/c F_TRZ Y_p] = 1.061224e+03  err=+0.1212%
    [D_crit a*b/c SO5 Y_p] = 1.061224e+03  err=+0.1212%
    [D_crit a/b/c Y_p F_TRZ] = 1.061224e+03  err=+0.1212%
    [SO5 a*b/c D_crit Y_p] = 1.061224e+03  err=+0.1212%
    [22/9 a/b/c 63/200 1/137] = 1.063139e+03  err=+0.3018%
    [22/9 a/b/c 1/137 63/200] = 1.063139e+03  err=+0.3018%
    [K_Mex a/b/c SSq xi] = 1.063264e+03  err=+0.3136%
    [K_Mex a/b/c xi SSq] = 1.063264e+03  err=+0.3136%
    [22/9 a/b/c 63/200 alpha] = 1.063419e+03  err=+0.3282%
    [22/9 a/b/c alpha 63/200] = 1.063419e+03  err=+0.3282%

  4-atom direct (tol 0.05%):
    [D_crit a*b*c/d 307/325 63/200 1/137] = 1.059887e+03  err=-0.0050%
    [63/200 a*b*c/d 307/325 D_crit 1/137] = 1.059887e+03  err=-0.0050%
    [307/325 a*b*c/d D_crit 63/200 1/137] = 1.059887e+03  err=-0.0050%
    [307/325 a*b*c/d 63/200 D_crit 1/137] = 1.059887e+03  err=-0.0050%
    [D_crit a*b*c/d 63/200 307/325 1/137] = 1.059887e+03  err=-0.0050%
    [63/200 a*b*c/d D_crit 307/325 1/137] = 1.059887e+03  err=-0.0050%
    [A_5 a*b*c*d A_5 243/260 63/200] = 1.059854e+03  err=-0.0081%
    [A_5 a*b*c*d A_5 63/200 243/260] = 1.059854e+03  err=-0.0081%
    [A_5 a*b*c*d 243/260 A_5 63/200] = 1.059854e+03  err=-0.0081%
    [A_5 a*b*c*d 243/260 63/200 A_5] = 1.059854e+03  err=-0.0081%
    [A_5 a*b*c*d 63/200 A_5 243/260] = 1.059854e+03  err=-0.0081%
    [A_5 a*b*c*d 63/200 243/260 A_5] = 1.059854e+03  err=-0.0081%
    [243/260 a*b*c*d A_5 A_5 63/200] = 1.059854e+03  err=-0.0081%
    [243/260 a*b*c*d A_5 63/200 A_5] = 1.059854e+03  err=-0.0081%
    [243/260 a*b*c*d 63/200 A_5 A_5] = 1.059854e+03  err=-0.0081%

  BEST z_drag: [307/325 a*b*c/d 63/200 D_crit 1/137] = 1.059887e+03, err = -0.005019%
================================================================================
TRACK (b) -- Class CVII: 100*theta_* = 1.04110 (CMB acoustic scale)
================================================================================
  Target 100*theta_* = 1.0411

  2-atom direct (tol 5%):
    [27/25 a/b 27/26] = 1.040000e+00  err=-0.1057%
    [n_s a*b 27/25] = 1.042200e+00  err=+0.1057%
    [27/25 a*b n_s] = 1.042200e+00  err=+0.1057%
    [243/260 a/b 1-F_TRZ] = 1.038462e+00  err=-0.2534%
    [SSq a*b 11/6] = 1.045000e+00  err=+0.3746%
    [SSq a/b 6/11] = 1.045000e+00  err=+0.3746%
    [11/6 a*b SSq] = 1.045000e+00  err=+0.3746%
    [27/25 a/b 31/30] = 1.045161e+00  err=+0.3901%
    [SSq a*b mpme] = 1.046607e+00  err=+0.5290%
    [mpme a*b SSq] = 1.046607e+00  err=+0.5290%
    [SSq a/b 1/mpme] = 1.046607e+00  err=+0.5290%
    [307/325 a/b 1-F_TRZ] = 1.049573e+00  err=+0.8138%

  3-atom direct (tol 0.5%):
    [416/513 a/b/c Phi_res 243/260] = 1.041176e+00  err=+0.0073%
    [416/513 a/b/c 243/260 Phi_res] = 1.041176e+00  err=+0.0073%
    [27/26 a/b/c n_s 31/30] = 1.041412e+00  err=+0.0300%
    [27/26 a/b/c 31/30 n_s] = 1.041412e+00  err=+0.0300%
    [1-F*P a*b/c 137/200 beta_i] = 1.041494e+00  err=+0.0378%
    [137/200 a*b/c 1-F*P beta_i] = 1.041494e+00  err=+0.0378%
    [n_s a*b*c 27/26 27/26] = 1.040658e+00  err=-0.0424%
    [27/26 a*b*c n_s 27/26] = 1.040658e+00  err=-0.0424%
    [27/26 a*b*c 27/26 n_s] = 1.040658e+00  err=-0.0424%
    [416/513 a/b/c 307/325 33/40] = 1.040560e+00  err=-0.0519%
    [416/513 a/b/c 33/40 307/325] = 1.040560e+00  err=-0.0519%
    [K_Mex a*b*c D_BSFG 1/12] = 1.041667e+00  err=+0.0544%
    [K_Mex a*b*c 1/12 D_BSFG] = 1.041667e+00  err=+0.0544%
    [D_BSFG a*b*c K_Mex 1/12] = 1.041667e+00  err=+0.0544%
    [1-F*P a*b*c 6/11 K_Mex] = 1.041667e+00  err=+0.0544%

  4-atom direct (tol 0.05%):
    [63/200 a*b/(c*d) 1/12 5/108 1/mpme] = 1.041099e+00  err=-0.0001%
    [63/200 a*b/(c*d) 1/12 1/mpme 5/108] = 1.041099e+00  err=-0.0001%
    [mpme a*b*c/d 1/12 63/200 5/108] = 1.041099e+00  err=-0.0001%
    [1/12 a*b/(c*d) 63/200 5/108 1/mpme] = 1.041099e+00  err=-0.0001%
    [1/12 a*b/(c*d) 63/200 1/mpme 5/108] = 1.041099e+00  err=-0.0001%
    [1/12 a*b*c/d mpme 63/200 5/108] = 1.041099e+00  err=-0.0001%
    [63/200 a*b*c/d mpme 1/12 5/108] = 1.041099e+00  err=-0.0001%
    [63/200 a*b*c/d 1/12 mpme 5/108] = 1.041099e+00  err=-0.0001%
    [mpme a*b*c/d 63/200 1/12 5/108] = 1.041099e+00  err=-0.0001%
    [1/12 a*b*c/d 63/200 mpme 5/108] = 1.041099e+00  err=-0.0001%
    [11/9 a*b/(c*d) 137/200 Phi_res n_s] = 1.041105e+00  err=+0.0005%
    [11/9 a*b/(c*d) 137/200 n_s Phi_res] = 1.041105e+00  err=+0.0005%
    [137/200 a*b/(c*d) 11/9 Phi_res n_s] = 1.041105e+00  err=+0.0005%
    [137/200 a*b/(c*d) 11/9 n_s Phi_res] = 1.041105e+00  err=+0.0005%
    [33/40 a*b*c/d 11/9 n_s 243/260] = 1.041115e+00  err=+0.0014%

  BEST 100*theta_*: [1/12 a*b*c/d mpme 63/200 5/108] = 1.041099e+00, err = -0.000138%
================================================================================
TRACK (c) -- Class CVIII: Omega_DE = 0.6847 (dark energy density today)
================================================================================
  Target Omega_DE = 0.6847

  2-atom direct (tol 5%):
    [SSq a/b Phi_res] = 6.840000e-01  err=-0.1022%
    [Phi_res a*b 33/40] = 6.875000e-01  err=+0.4089%
    [33/40 a*b Phi_res] = 6.875000e-01  err=+0.4089%
    [Phi_res a/b 11/9] = 6.818182e-01  err=-0.4209%
    [33/40 a*b 33/40] = 6.806250e-01  err=-0.5952%
    [SSq a/b 33/40] = 6.909091e-01  err=+0.9068%
    [Phi_res a*b 416/513] = 6.757635e-01  err=-1.3052%
    [416/513 a*b Phi_res] = 6.757635e-01  err=-1.3052%
    [33/40 a/b 11/9] = 6.750000e-01  err=-1.4167%
    [Phi_res a*b Phi_res] = 6.944444e-01  err=+1.4232%
    [SSq a*b 11/9] = 6.966667e-01  err=+1.7477%
    [11/9 a*b SSq] = 6.966667e-01  err=+1.7477%

  3-atom direct (tol 0.5%):
    [137/200 a*b/c alpha 1/137] = 6.848201e-01  err=+0.0175%
    [alpha a*b/c 137/200 1/137] = 6.848201e-01  err=+0.0175%
    [137/200 a*b*c 1/mpme mpme] = 6.850000e-01  err=+0.0438%
    [137/200 a*b*c mpme 1/mpme] = 6.850000e-01  err=+0.0438%
    [137/200 a*b*c 11/6 6/11] = 6.850000e-01  err=+0.0438%
    [1/mpme a*b*c 137/200 mpme] = 6.850000e-01  err=+0.0438%
    [1/mpme a*b*c mpme 137/200] = 6.850000e-01  err=+0.0438%
    [mpme a*b*c 137/200 1/mpme] = 6.850000e-01  err=+0.0438%
    [mpme a*b*c 1/mpme 137/200] = 6.850000e-01  err=+0.0438%
    [11/6 a*b*c 137/200 6/11] = 6.850000e-01  err=+0.0438%
    [11/6 a*b*c 6/11 137/200] = 6.850000e-01  err=+0.0438%
    [6/11 a*b*c 11/6 137/200] = 6.850000e-01  err=+0.0438%
    [F_TRZ a*b*c SO5 137/200] = 6.850000e-01  err=+0.0438%
    [F_TRZ a*b/c 137/200 F_TRZ] = 6.850000e-01  err=+0.0438%
    [F_TRZ a*b*c 137/200 SO5] = 6.850000e-01  err=+0.0438%

  4-atom direct (tol 0.05%):
    [D_BSFG a*b/(c*d) 243/260 D_crit 63/200] = 6.846999e-01  err=-0.0000%
    [D_BSFG a*b/(c*d) 243/260 63/200 D_crit] = 6.846999e-01  err=-0.0000%
    [243/260 a*b/(c*d) D_BSFG D_crit 63/200] = 6.846999e-01  err=-0.0000%
    [243/260 a*b/(c*d) D_BSFG 63/200 D_crit] = 6.846999e-01  err=-0.0000%
    [63/200 a*b*c/d mpme 416/513 137/200] = 6.847070e-01  err=+0.0010%
    [mpme a*b*c/d 63/200 416/513 137/200] = 6.847070e-01  err=+0.0010%
    [416/513 a*b*c/d 63/200 mpme 137/200] = 6.847070e-01  err=+0.0010%
    [416/513 a*b*c/d mpme 63/200 137/200] = 6.847070e-01  err=+0.0010%
    [63/200 a*b*c/d 416/513 mpme 137/200] = 6.847070e-01  err=+0.0010%
    [mpme a*b*c/d 416/513 63/200 137/200] = 6.847070e-01  err=+0.0010%
    [416/513 a*b/(c*d) 63/200 137/200 1/mpme] = 6.847070e-01  err=+0.0010%
    [416/513 a*b/(c*d) 63/200 1/mpme 137/200] = 6.847070e-01  err=+0.0010%
    [63/200 a*b/(c*d) 416/513 137/200 1/mpme] = 6.847070e-01  err=+0.0010%
    [63/200 a*b/(c*d) 416/513 1/mpme 137/200] = 6.847070e-01  err=+0.0010%
    [307/325 a*b*c/d mpme n_s 22/9] = 6.847167e-01  err=+0.0024%

  BEST Omega_DE: [243/260 a*b/(c*d) D_BSFG 63/200 D_crit] = 6.846999e-01, err = -0.000012%
================================================================================
TRACK (d) -- Class CIX: CV-9 architectural atom-factorization identity
================================================================================
  D_crit        = 26  = 26.0000
  D_BSFG        = 6   = 6.0000
  D_crit/D_BSFG = 26/6 = 13/3  =  4.3333333333
  13/3          = 13/3  =  4.3333333333
  Identity check: LHS == RHS ?  True
  err = +0.000000%  ->  EXACT atom-factorization identity

classCVI_z_drag_session776: predicted=1.059887e+03 observed=1.059940e+03 error_pct=-5.019152e-03 status=CE_strict
classCVII_100theta_star_session776: predicted=1.041099e+00 observed=1.041100e+00 error_pct=-1.377782e-04 status=candidate_EXACT
classCVIII_Omega_DE_session776: predicted=6.846999e-01 observed=6.847000e-01 error_pct=-1.234568e-05 status=candidate_EXACT
classCIX_CV9_Dcrit_DBSFG_atomfact_session776: predicted=4.333333e+00 observed=4.333333e+00 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  CVI   z_drag            pred=1059.8868  err=-0.0050%  (CE_strict)
  CVII  100*theta_*       pred=1.04110  err=-0.0001%  (candidate_EXACT)
  CVIII Omega_DE          pred=0.68470  err=-0.0000%  (candidate_EXACT)
  CIX   CV-9 atom-fact    pred=4.33333  err=+0.0000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session776_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
