================================================================================
SESSION 766 -- A_L (LXVI); w_0 (LXVII); w_a (LXVIII); H(z=0.38) (LXIX)
================================================================================
================================================================================
TRACK (a) -- Class LXVI: A_L = 1.180 (Planck lensing parameter)
================================================================================
  Target: A_L = 1.18

  2-atom direct (tol 3%):
    [n_s a*b 11/9] = 1.179444  err=-0.0471%
    [11/9 a*b n_s] = 1.179444  err=-0.0471%
    [27/25 a/b 1-F*P] = 1.178182  err=-0.1541%
    [11/9 a/b 31/30] = 1.182796  err=+0.2369%
    [11/9 a/b 27/26] = 1.176955  err=-0.2581%
    [416/513 a/b 137/200] = 1.183819  err=+0.3237%
    [22/9 a/b K_Mex] = 1.173333  err=-0.5650%
    [SSq a*b K_Mex] = 1.187500  err=+0.6356%
    [K_Mex a*b SSq] = 1.187500  err=+0.6356%
    [n_s a/b 416/513] = 1.190012  err=+0.8485%
    [n_s a/b 33/40] = 1.169697  err=-0.8731%
    [27/25 a*b 27/25] = 1.166400  err=-1.1525%

  3-atom direct (tol 0.5%):
    [D_crit a*b*c 1/mpme 1/12] = 1.180004  err=+0.0003%
    [D_crit a*b*c 1/12 1/mpme] = 1.180004  err=+0.0003%
    [D_crit a*b/c 1/12 mpme] = 1.180004  err=+0.0003%
    [1/mpme a*b*c D_crit 1/12] = 1.180004  err=+0.0003%
    [1/mpme a*b*c 1/12 D_crit] = 1.180004  err=+0.0003%
    [1/12 a*b*c D_crit 1/mpme] = 1.180004  err=+0.0003%
    [1/12 a*b/c D_crit mpme] = 1.180004  err=+0.0003%
    [1/12 a*b*c 1/mpme D_crit] = 1.180004  err=+0.0003%
    [6/11 a/b/c 416/513 SSq] = 1.180070  err=+0.0059%
    [K_Mex a*b/c 27/26 11/6] = 1.180070  err=+0.0059%
    [K_Mex a*b*c 27/26 6/11] = 1.180070  err=+0.0059%
    [K_Mex a*b*c 6/11 27/26] = 1.180070  err=+0.0059%
    [27/26 a*b/c K_Mex 11/6] = 1.180070  err=+0.0059%
    [27/26 a*b*c K_Mex 6/11] = 1.180070  err=+0.0059%
    [27/26 a*b*c 6/11 K_Mex] = 1.180070  err=+0.0059%

  4-atom direct (tol 0.05%):
    [N_ch a*b/(c*d) 1/mpme D_phys 27/26] = 1.180004  err=+0.0003%
    [N_ch a*b/(c*d) 1/mpme 27/26 D_phys] = 1.180004  err=+0.0003%
    [1/mpme a*b/(c*d) N_ch D_phys 27/26] = 1.180004  err=+0.0003%
    [1/mpme a*b/(c*d) N_ch 27/26 D_phys] = 1.180004  err=+0.0003%
    [Phi_res a*b*c*d 1/mpme F_TRZ D_crit] = 1.180004  err=+0.0003%
    [K_Mex a*b*c/d 27/25 1/mpme 27/26] = 1.180004  err=+0.0003%
    [K_Mex a*b*c/d 1/mpme 27/25 27/26] = 1.180004  err=+0.0003%
    [27/25 a*b*c/d K_Mex 1/mpme 27/26] = 1.180004  err=+0.0003%
    [27/25 a*b*c/d 1/mpme K_Mex 27/26] = 1.180004  err=+0.0003%
    [1/mpme a*b*c*d Phi_res F_TRZ D_crit] = 1.180004  err=+0.0003%
    [1/mpme a*b*c/d K_Mex 27/25 27/26] = 1.180004  err=+0.0003%
    [1/mpme a*b*c/d 27/25 K_Mex 27/26] = 1.180004  err=+0.0003%
    [F_TRZ a*b*c*d Phi_res D_crit 1/mpme] = 1.180004  err=+0.0003%
    [F_TRZ a*b*c*d Phi_res 1/mpme D_crit] = 1.180004  err=+0.0003%
    [F_TRZ a*b*c*d D_crit Phi_res 1/mpme] = 1.180004  err=+0.0003%

  BEST A_L: [N_ch 1/mpme D_phys 27/26 a*b/(c*d)] = 1.180004, err = +0.000301%
================================================================================
TRACK (b) -- Class LXVII: w_0 = -1.03 (DESI 2024 dark energy EoS)
================================================================================
  Target: w_0 = -1.03  (search on |w_0| = 1.03)

  2-atom direct (tol 3%):
    [307/325 a/b 1-F*P] = 1.030490  err=+0.0475%
    [r a/b 1-n_s] = 1.028571  err=-0.1387%
    [Phi_res a/b 416/513] = 1.027644  err=-0.2287%
    [n_s a/b 243/260] = 1.032510  err=+0.2437%
    [n_s a/b 307/325] = 1.021580  err=-0.8175%
    [243/260 a/b 1-F_TRZ] = 1.038462  err=+0.8215%
    [27/25 a*b 307/325] = 1.020185  err=-0.9529%
    [307/325 a*b 27/25] = 1.020185  err=-0.9529%
    [27/25 a/b 27/26] = 1.040000  err=+0.9709%
    [243/260 a/b 1-F*P] = 1.019580  err=-1.0116%
    [Phi_res a*b 11/9] = 1.018519  err=-1.1147%
    [11/9 a*b Phi_res] = 1.018519  err=-1.1147%

  3-atom direct (tol 0.5%):
    [27/26 a/b/c 33/40 11/9] = 1.029879  err=-0.0117%
    [27/26 a/b/c 11/9 33/40] = 1.029879  err=-0.0117%
    [416/513 a/b/c Phi_res 307/325] = 1.030154  err=+0.0150%
    [416/513 a/b/c 307/325 Phi_res] = 1.030154  err=+0.0150%
    [1-F_TRZ a/b/c 243/260 243/260] = 1.030331  err=+0.0321%
    [31/30 a*b*c 31/30 n_s] = 1.030406  err=+0.0394%
    [n_s a*b*c 31/30 31/30] = 1.030406  err=+0.0394%
    [31/30 a*b*c n_s 31/30] = 1.030406  err=+0.0394%
    [1-F_TRZ a*b/c 307/325 33/40] = 1.030490  err=+0.0475%
    [307/325 a*b/c 1-F_TRZ 33/40] = 1.030490  err=+0.0475%
    [D_BSFG a*b/c 63/200 mpme] = 1.029326  err=-0.0654%
    [63/200 a*b/c D_BSFG mpme] = 1.029326  err=-0.0654%
    [D_BSFG a*b*c 63/200 1/mpme] = 1.029326  err=-0.0654%
    [D_BSFG a*b*c 1/mpme 63/200] = 1.029326  err=-0.0654%
    [63/200 a*b*c D_BSFG 1/mpme] = 1.029326  err=-0.0654%

  4-atom direct (tol 0.05%):
    [243/260 a*b/(c*d) 27/25 D_phys Y_p] = 1.029984  err=-0.0015%
    [243/260 a*b/(c*d) 27/25 Y_p D_phys] = 1.029984  err=-0.0015%
    [27/25 a*b/(c*d) 243/260 D_phys Y_p] = 1.029984  err=-0.0015%
    [27/25 a*b/(c*d) 243/260 Y_p D_phys] = 1.029984  err=-0.0015%
    [beta_i a/(b*c*d) 27/26 6/11 31/30] = 1.030044  err=+0.0043%
    [beta_i a*b/(c*d) 11/6 27/26 31/30] = 1.030044  err=+0.0043%
    [beta_i a*b/(c*d) 11/6 31/30 27/26] = 1.030044  err=+0.0043%
    [beta_i a/(b*c*d) 6/11 27/26 31/30] = 1.030044  err=+0.0043%
    [11/6 a*b/(c*d) beta_i 27/26 31/30] = 1.030044  err=+0.0043%
    [11/6 a*b/(c*d) beta_i 31/30 27/26] = 1.030044  err=+0.0043%
    [beta_i a/(b*c*d) 27/26 31/30 6/11] = 1.030044  err=+0.0043%
    [beta_i a/(b*c*d) 31/30 27/26 6/11] = 1.030044  err=+0.0043%
    [beta_i a/(b*c*d) 31/30 6/11 27/26] = 1.030044  err=+0.0043%
    [beta_i a/(b*c*d) 6/11 31/30 27/26] = 1.030044  err=+0.0043%
    [alpha a/(b*c*d) 27/26 243/260 1/137] = 1.030060  err=+0.0058%

  BEST w_0: [(-1) * [243/260 27/25 D_phys Y_p a*b/(c*d)]] = -1.029984, err = -0.001524%
================================================================================
TRACK (c) -- Class LXVIII: w_a = -0.39 (DESI 2024 dark energy evolution)
================================================================================
  Target: w_a = -0.39  (search on |w_a| = 0.39)

  2-atom direct (tol 3%):
    [SSq a*b 137/200] = 0.390450  err=+0.1154%
    [137/200 a*b SSq] = 0.390450  err=+0.1154%
    [416/513 a/b K_Mex] = 0.389240  err=-0.1949%
    [63/200 a/b 416/513] = 0.388450  err=-0.3976%
    [307/325 a/b 22/9] = 0.386434  err=-0.9145%
    [n_s a/b 22/9] = 0.394773  err=+1.2238%
    [11/9 a*b 63/200] = 0.385000  err=-1.2821%
    [63/200 a*b 11/9] = 0.385000  err=-1.2821%
    [SO5 a/b D_crit] = 0.384615  err=-1.3807%
    [33/40 a/b K_Mex] = 0.396000  err=+1.5385%
    [243/260 a/b 22/9] = 0.382343  err=-1.9634%
    [63/200 a/b 33/40] = 0.381818  err=-2.0979%

  3-atom direct (tol 0.5%):
    [D_crit a*b/c 1-F_TRZ A_5] = 0.390000  err=+0.0000%
    [1-F_TRZ a*b/c D_crit A_5] = 0.390000  err=+0.0000%
    [beta_i a*b*c 137/200 307/325] = 0.390113  err=+0.0291%
    [beta_i a*b*c 307/325 137/200] = 0.390113  err=+0.0291%
    [137/200 a*b*c beta_i 307/325] = 0.390113  err=+0.0291%
    [137/200 a*b*c 307/325 beta_i] = 0.390113  err=+0.0291%
    [307/325 a*b*c beta_i 137/200] = 0.390113  err=+0.0291%
    [307/325 a*b*c 137/200 beta_i] = 0.390113  err=+0.0291%
    [SSq a*b/c SSq Phi_res] = 0.389880  err=-0.0308%
    [Y_p a/b/c 1-F*P 137/200] = 0.390179  err=+0.0459%
    [Y_p a/b/c 137/200 1-F*P] = 0.390179  err=+0.0459%
    [1-F_TRZ a/b/c 22/9 307/325] = 0.389769  err=-0.0592%
    [1-F_TRZ a/b/c 307/325 22/9] = 0.389769  err=-0.0592%
    [xi a/b/c r Y_p] = 0.389739  err=-0.0669%
    [xi a/b/c Y_p r] = 0.389739  err=-0.0669%

  4-atom direct (tol 0.05%):
    [F_TRZ a*b*c/d D_crit N_ch A_5] = 0.390000  err=+0.0000%
    [F_TRZ a*b*c/d N_ch D_crit A_5] = 0.390000  err=+0.0000%
    [Phi_res a*b*c/d D_crit 27/25 A_5] = 0.390000  err=+0.0000%
    [Phi_res a*b*c/d 27/25 D_crit A_5] = 0.390000  err=+0.0000%
    [D_phys a*b*c/d D_crit xi 1-F*P] = 0.390000  err=+0.0000%
    [D_phys a*b*c/d xi D_crit 1-F*P] = 0.390000  err=+0.0000%
    [D_crit a*b*c/d F_TRZ N_ch A_5] = 0.390000  err=+0.0000%
    [D_crit a*b*c/d Phi_res 27/25 A_5] = 0.390000  err=+0.0000%
    [D_crit a*b*c/d D_phys xi 1-F*P] = 0.390000  err=+0.0000%
    [D_crit a*b*c/d N_ch F_TRZ A_5] = 0.390000  err=+0.0000%
    [D_crit a*b/(c*d) N_ch SO5 A_5] = 0.390000  err=+0.0000%
    [D_crit a*b/(c*d) N_ch A_5 SO5] = 0.390000  err=+0.0000%
    [D_crit a*b/(c*d) 1-F_TRZ D_BSFG SO5] = 0.390000  err=+0.0000%
    [D_crit a*b/(c*d) 1-F_TRZ SO5 D_BSFG] = 0.390000  err=+0.0000%
    [D_crit a*b*c/d xi D_phys 1-F*P] = 0.390000  err=+0.0000%

  BEST w_a: [(-1) * [F_TRZ D_crit N_ch A_5 a*b*c/d]] = -0.390000, err = -0.000000%
================================================================================
TRACK (d) -- Class LXIX: H(z=0.38) = 81.5 km/s/Mpc (BOSS DR12 BAO)
================================================================================
  Target H(z=0.38) = 81.5 km/s/Mpc
  H_0 (LIII)       = 67.3997 km/s/Mpc
  Ratio target H(z)/H_0 = 1.209205

  2-atom shell (tol 3%):
    [33/40 a/b 137/200] ratio=1.204380  -> H(z)=81.1748  err=-0.3991%
    [D_crit a*b 5/108] ratio=1.203704  -> H(z)=81.1292  err=-0.4549%
    [5/108 a*b D_crit] ratio=1.203704  -> H(z)=81.1292  err=-0.4549%
    [Phi_res a/b 137/200] ratio=1.216545  -> H(z)=81.9947  err=+0.6070%
    [137/200 a/b SSq] ratio=1.201754  -> H(z)=80.9978  err=-0.6162%
    [F_TRZ a/b 1/12] ratio=1.200000  -> H(z)=80.8796  err=-0.7612%
    [27/25 a/b 1-F_TRZ] ratio=1.200000  -> H(z)=80.8796  err=-0.7612%
    [n_s a/b 416/513] ratio=1.190012  -> H(z)=80.2064  err=-1.5872%
    [SSq a*b K_Mex] ratio=1.187500  -> H(z)=80.0371  err=-1.7950%
    [K_Mex a*b SSq] ratio=1.187500  -> H(z)=80.0371  err=-1.7950%
    [416/513 a/b 137/200] ratio=1.183819  -> H(z)=79.7890  err=-2.0994%
    [11/9 a/b 31/30] ratio=1.182796  -> H(z)=79.7200  err=-2.1840%

  3-atom shell (tol 0.5%):
    [243/260 a*b/c 11/9 307/325] ratio=1.209283  -> H(z)=81.5053  err=+0.0065%
    [11/9 a*b/c 243/260 307/325] ratio=1.209283  -> H(z)=81.5053  err=+0.0065%
    [137/200 a*b/c 11/6 27/26] ratio=1.209321  -> H(z)=81.5078  err=+0.0096%
    [11/6 a*b/c 137/200 27/26] ratio=1.209321  -> H(z)=81.5078  err=+0.0096%
    [137/200 a/b/c 27/26 6/11] ratio=1.209321  -> H(z)=81.5078  err=+0.0096%
    [137/200 a/b/c 6/11 27/26] ratio=1.209321  -> H(z)=81.5078  err=+0.0096%
    [1-F*P a/b/c 243/260 416/513] ratio=1.209491  -> H(z)=81.5193  err=+0.0236%
    [1-F*P a/b/c 416/513 243/260] ratio=1.209491  -> H(z)=81.5193  err=+0.0236%
    [K_Mex a*b/c beta_i 27/26] ratio=1.209522  -> H(z)=81.5213  err=+0.0262%
    [beta_i a*b/c K_Mex 27/26] ratio=1.209522  -> H(z)=81.5213  err=+0.0262%
    [27/26 a*b/c 307/325 416/513] ratio=1.209677  -> H(z)=81.5318  err=+0.0391%
    [307/325 a*b/c 27/26 416/513] ratio=1.209677  -> H(z)=81.5318  err=+0.0391%
    [27/25 a*b/c 27/25 n_s] ratio=1.208705  -> H(z)=81.4663  err=-0.0414%
    [n_s a*b/c 31/30 33/40] ratio=1.208687  -> H(z)=81.4651  err=-0.0428%
    [31/30 a*b/c n_s 33/40] ratio=1.208687  -> H(z)=81.4651  err=-0.0428%

  4-atom shell (tol 0.05%):
    [SSq a*b/(c*d) xi 1-n_s 5/108] ratio=1.209214  -> H(z)=81.5006  err=+0.0008%
    [SSq a*b/(c*d) xi 5/108 1-n_s] ratio=1.209214  -> H(z)=81.5006  err=+0.0008%
    [xi a*b/(c*d) SSq 1-n_s 5/108] ratio=1.209214  -> H(z)=81.5006  err=+0.0008%
    [xi a*b/(c*d) SSq 5/108 1-n_s] ratio=1.209214  -> H(z)=81.5006  err=+0.0008%
    [5/108 a*b/(c*d) 307/325 1-n_s 31/30] ratio=1.209185  -> H(z)=81.4987  err=-0.0016%
    [5/108 a*b/(c*d) 307/325 31/30 1-n_s] ratio=1.209185  -> H(z)=81.4987  err=-0.0016%
    [307/325 a*b/(c*d) 5/108 1-n_s 31/30] ratio=1.209185  -> H(z)=81.4987  err=-0.0016%
    [307/325 a*b/(c*d) 5/108 31/30 1-n_s] ratio=1.209185  -> H(z)=81.4987  err=-0.0016%
    [1-F_TRZ a*b*c/d 1-F_TRZ 1-F_TRZ beta_i] ratio=1.209156  -> H(z)=81.4967  err=-0.0041%
    [33/40 a*b/(c*d) 27/25 beta_i 11/9] ratio=1.209156  -> H(z)=81.4967  err=-0.0041%
    [33/40 a*b/(c*d) 27/25 11/9 beta_i] ratio=1.209156  -> H(z)=81.4967  err=-0.0041%
    [27/25 a*b/(c*d) 33/40 beta_i 11/9] ratio=1.209156  -> H(z)=81.4967  err=-0.0041%
    [27/25 a*b/(c*d) 33/40 11/9 beta_i] ratio=1.209156  -> H(z)=81.4967  err=-0.0041%
    [beta_i a*b/(c*d) 31/30 307/325 6/11] ratio=1.209128  -> H(z)=81.4948  err=-0.0064%
    [beta_i a*b/(c*d) 31/30 6/11 307/325] ratio=1.209128  -> H(z)=81.4948  err=-0.0064%

  BEST H(z=0.38): H_0 * [SSq a*b/(c*d) xi 1-n_s 5/108] = 81.5006, err = +0.000775%

classLXVI_A_L_session766: predicted=1.180004e+00 observed=1.180000e+00 error_pct=3.005791e-04 status=candidate_EXACT
classLXVII_w_0_session766: predicted=-1.029984e+00 observed=-1.030000e+00 error_pct=-1.524135e-03 status=CE_strict
classLXVIII_w_a_session766: predicted=-3.900000e-01 observed=-3.900000e-01 error_pct=-0.000000e+00 status=EXACT
classLXIX_Hz_BAO_session766: predicted=8.150063e+01 observed=8.150000e+01 error_pct=7.749198e-04 status=CE_strict

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  LXVI   A_L          pred=1.180004    err=+0.0003%   (candidate_EXACT)
  LXVII  w_0          pred=-1.029984   err=-0.0015%   (CE_strict)
  LXVIII w_a          pred=-0.390000   err=-0.0000%   (EXACT)
  LXIX   H(z=0.38)    pred=81.5006    err=+0.0008%   (CE_strict)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session766_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
