================================================================================
SESSION 768 -- BAO at z=0.51,0.61: H(0.51) LXXIV; D_M(0.51) LXXV; f*s8(0.51) LXXVI; H(0.61) LXXVII
================================================================================
  r_drag (LIV) = 147.0502 Mpc
  H_0   (LIII) = 67.4 km/s/Mpc

================================================================================
TRACK (a) -- Class LXXIV: H(z=0.51) = 90.5 km/s/Mpc
================================================================================
  Target H(0.51) = 90.5000  (H_0-shell target = 1.342730)

  2-atom shell (tol 3%):
    [416/513 a/b beta_i] ratio=1.345026  -> 90.6548  err=+0.1710%
    [1-F*P a/b 137/200] ratio=1.338200  -> 90.1946  err=-0.3374%
    [11/9 a/b 1-F*P] ratio=1.333333  -> 89.8667  err=-0.6998%
    [22/9 a/b 11/6] ratio=1.333333  -> 89.8667  err=-0.6998%
    [22/9 a*b 6/11] ratio=1.333333  -> 89.8667  err=-0.6998%
    [6/11 a*b 22/9] ratio=1.333333  -> 89.8667  err=-0.6998%
    [27/25 a/b 416/513] ratio=1.331827  -> 89.7651  err=-0.8120%
    [22/9 a/b mpme] ratio=1.331286  -> 89.7287  err=-0.8523%
    [22/9 a*b 1/mpme] ratio=1.331286  -> 89.7287  err=-0.8523%
    [1/mpme a*b 22/9] ratio=1.331286  -> 89.7287  err=-0.8523%
    [11/9 a/b 1-F_TRZ] ratio=1.358025  -> 91.5309  err=+1.1391%
    [5/108 a/b 1-n_s] ratio=1.322751  -> 89.1534  err=-1.4879%

  3-atom shell (tol 0.5%):
    [27/25 a/b/c Phi_res n_s] ratio=1.343005  -> 90.5185  err=+0.0205%
    [27/25 a/b/c n_s Phi_res] ratio=1.343005  -> 90.5185  err=+0.0205%
    [11/9 a/b/c 1-n_s D_crit] ratio=1.343101  -> 90.5250  err=+0.0277%
    [11/9 a/b/c D_crit 1-n_s] ratio=1.343101  -> 90.5250  err=+0.0277%
    [beta_i a/b/c Y_p 11/6] ratio=1.342263  -> 90.4686  err=-0.0347%
    [beta_i a/b/c 11/6 Y_p] ratio=1.342263  -> 90.4686  err=-0.0347%
    [beta_i a*b/c 6/11 Y_p] ratio=1.342263  -> 90.4686  err=-0.0347%
    [6/11 a*b/c beta_i Y_p] ratio=1.342263  -> 90.4686  err=-0.0347%
    [137/200 a/b/c Y_p K_Mex] ratio=1.342041  -> 90.4536  err=-0.0513%
    [137/200 a/b/c K_Mex Y_p] ratio=1.342041  -> 90.4536  err=-0.0513%
    [31/30 a/b/c 22/9 63/200] ratio=1.341991  -> 90.4502  err=-0.0550%
    [31/30 a/b/c 63/200 22/9] ratio=1.341991  -> 90.4502  err=-0.0550%
    [1-F_TRZ a*b/c 1-F_TRZ beta_i] ratio=1.343506  -> 90.5523  err=+0.0578%
    [beta_i a/b/c 1/mpme 33/40] ratio=1.341838  -> 90.4399  err=-0.0664%
    [beta_i a*b/c mpme 33/40] ratio=1.341838  -> 90.4399  err=-0.0664%

  4-atom shell (tol 0.05%):
    [243/260 a/(b*c*d) beta_i 11/9 307/325] ratio=1.342711  -> 90.4987  err=-0.0014%
    [243/260 a/(b*c*d) beta_i 307/325 11/9] ratio=1.342711  -> 90.4987  err=-0.0014%
    [243/260 a/(b*c*d) 11/9 beta_i 307/325] ratio=1.342711  -> 90.4987  err=-0.0014%
    [243/260 a/(b*c*d) 11/9 307/325 beta_i] ratio=1.342711  -> 90.4987  err=-0.0014%
    [243/260 a/(b*c*d) 307/325 beta_i 11/9] ratio=1.342711  -> 90.4987  err=-0.0014%
    [243/260 a/(b*c*d) 307/325 11/9 beta_i] ratio=1.342711  -> 90.4987  err=-0.0014%
    [F_TRZ a/(b*c*d) n_s Y_p 63/200] ratio=1.342753  -> 90.5015  err=+0.0017%
    [F_TRZ a/(b*c*d) n_s 63/200 Y_p] ratio=1.342753  -> 90.5015  err=+0.0017%
    [F_TRZ a/(b*c*d) Y_p n_s 63/200] ratio=1.342753  -> 90.5015  err=+0.0017%
    [F_TRZ a/(b*c*d) Y_p 63/200 n_s] ratio=1.342753  -> 90.5015  err=+0.0017%
    [F_TRZ a/(b*c*d) 63/200 n_s Y_p] ratio=1.342753  -> 90.5015  err=+0.0017%
    [F_TRZ a/(b*c*d) 63/200 Y_p n_s] ratio=1.342753  -> 90.5015  err=+0.0017%
    [Phi_res a*b/(c*d) n_s Y_p 22/9] ratio=1.342764  -> 90.5023  err=+0.0026%
    [Phi_res a*b/(c*d) n_s 22/9 Y_p] ratio=1.342764  -> 90.5023  err=+0.0026%
    [n_s a*b/(c*d) Phi_res Y_p 22/9] ratio=1.342764  -> 90.5023  err=+0.0026%

  BEST H(0.51): H_0 * [243/260 a/(b*c*d) 11/9 307/325 beta_i] = 90.4987, err = -0.001435%
================================================================================
TRACK (b) -- Class LXXV: D_M(z=0.51) = 1977 Mpc (comoving ang. diam.)
================================================================================
  Target D_M(0.51) = 1977.0000  (r_drag-shell target = 13.444391)

  2-atom shell (tol 3%):
    [5/108 a/b xi] ratio=13.468013  -> 1980.4736  err=+0.1757%
    [F_TRZ a/b 1/137] ratio=13.700000  -> 2014.5873  err=+1.9012%
    [F_TRZ a/b alpha] ratio=13.703600  -> 2015.1167  err=+1.9280%
    [N_ch a/b 137/200] ratio=13.138686  -> 1932.0460  err=-2.2738%

  3-atom shell (tol 0.5%):
    [D_phys a*b*c 11/6 11/6] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [11/6 a*b*c D_phys 11/6] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [11/6 a*b*c 11/6 D_phys] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_phys a*b/c 11/6 6/11] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_BSFG a*b*c 11/9 11/6] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_BSFG a*b*c 22/9 1-F*P] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [11/9 a*b*c D_BSFG 11/6] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [22/9 a*b*c D_BSFG 1-F*P] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [11/6 a*b/c D_phys 6/11] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_phys a/b/c 6/11 6/11] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_BSFG a*b*c 1-F*P 22/9] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_BSFG a*b/c 11/9 6/11] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [D_BSFG a*b*c 11/6 11/9] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [N_ch a*b*c 11/9 11/9] ratio=13.444444  -> 1977.0078  err=+0.0004%
    [1-F*P a*b*c D_BSFG 22/9] ratio=13.444444  -> 1977.0078  err=+0.0004%

  4-atom shell (tol 0.05%):
    [A_5 a*b*c*d 27/26 63/200 137/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [A_5 a*b*c*d 27/26 137/200 63/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [A_5 a*b*c*d 63/200 27/26 137/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [A_5 a*b*c*d 63/200 137/200 27/26] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [A_5 a*b*c*d 137/200 27/26 63/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [A_5 a*b*c*d 137/200 63/200 27/26] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [27/26 a*b*c*d A_5 63/200 137/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [27/26 a*b*c*d A_5 137/200 63/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [27/26 a*b*c*d 63/200 A_5 137/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [27/26 a*b*c*d 63/200 137/200 A_5] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [27/26 a*b*c*d 137/200 A_5 63/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [27/26 a*b*c*d 137/200 63/200 A_5] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [63/200 a*b*c*d A_5 27/26 137/200] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [63/200 a*b*c*d A_5 137/200 27/26] ratio=13.444442  -> 1977.0075  err=+0.0004%
    [63/200 a*b*c*d 27/26 A_5 137/200] ratio=13.444442  -> 1977.0075  err=+0.0004%

  BEST D_M(0.51): r_drag * [137/200 a*b*c*d 27/26 63/200 A_5] = 1977.0075, err = +0.000380%
================================================================================
TRACK (c) -- Class LXXVI: f*sigma_8(z=0.51) = 0.458 (RSD growth amplitude)
================================================================================
  Target f*sigma_8(0.51) = 0.458

  2-atom direct (tol 3%):
    [11/6 a/b D_phys] = 0.458333  err=+0.0728%
    [mpme a/b D_phys] = 0.459038  err=+0.2267%
    [63/200 a/b 137/200] = 0.459854  err=+0.4048%
    [Phi_res a/b 11/6] = 0.454545  err=-0.7543%
    [Phi_res a*b 6/11] = 0.454545  err=-0.7543%
    [6/11 a*b Phi_res] = 0.454545  err=-0.7543%
    [Phi_res a/b mpme] = 0.453848  err=-0.9067%
    [Phi_res a*b 1/mpme] = 0.453848  err=-0.9067%
    [1/mpme a*b Phi_res] = 0.453848  err=-0.9067%
    [SSq a*b 416/513] = 0.462222  err=+0.9219%
    [416/513 a*b SSq] = 0.462222  err=+0.9219%
    [307/325 a/b K_Mex] = 0.453415  err=-1.0010%

  3-atom direct (tol 0.5%):
    [1-F_TRZ a*b*c 243/260 1/mpme] = 0.458107  err=+0.0233%
    [1-F_TRZ a*b*c 1/mpme 243/260] = 0.458107  err=+0.0233%
    [243/260 a*b*c 1-F_TRZ 1/mpme] = 0.458107  err=+0.0233%
    [1/mpme a*b*c 1-F_TRZ 243/260] = 0.458107  err=+0.0233%
    [1-F_TRZ a*b/c 243/260 mpme] = 0.458107  err=+0.0233%
    [243/260 a*b/c 1-F_TRZ mpme] = 0.458107  err=+0.0233%
    [243/260 a*b*c 1/mpme 1-F_TRZ] = 0.458107  err=+0.0233%
    [1/mpme a*b*c 243/260 1-F_TRZ] = 0.458107  err=+0.0233%
    [27/25 a/b/c n_s 22/9] = 0.457843  err=-0.0344%
    [27/25 a/b/c 22/9 n_s] = 0.457843  err=-0.0344%
    [63/200 a/b/c Phi_res 33/40] = 0.458182  err=+0.0397%
    [63/200 a/b/c 33/40 Phi_res] = 0.458182  err=+0.0397%
    [1-n_s a/b/c 1-F*P 1/12] = 0.458182  err=+0.0397%
    [1-n_s a/b/c 1/12 1-F*P] = 0.458182  err=+0.0397%
    [33/40 a*b*c 416/513 137/200] = 0.458269  err=+0.0587%

  4-atom direct (tol 0.05%):
    [416/513 a/(b*c*d) 243/260 31/30 11/6] = 0.457995  err=-0.0010%
    [416/513 a/(b*c*d) 243/260 11/6 31/30] = 0.457995  err=-0.0010%
    [416/513 a/(b*c*d) 31/30 243/260 11/6] = 0.457995  err=-0.0010%
    [416/513 a/(b*c*d) 11/6 243/260 31/30] = 0.457995  err=-0.0010%
    [416/513 a*b/(c*d) 6/11 243/260 31/30] = 0.457995  err=-0.0010%
    [416/513 a*b/(c*d) 6/11 31/30 243/260] = 0.457995  err=-0.0010%
    [6/11 a*b/(c*d) 416/513 243/260 31/30] = 0.457995  err=-0.0010%
    [6/11 a*b/(c*d) 416/513 31/30 243/260] = 0.457995  err=-0.0010%
    [416/513 a/(b*c*d) 31/30 11/6 243/260] = 0.457995  err=-0.0010%
    [416/513 a/(b*c*d) 11/6 31/30 243/260] = 0.457995  err=-0.0010%
    [beta_i a*b*c*d beta_i D_phys 63/200] = 0.457995  err=-0.0010%
    [beta_i a*b*c*d beta_i 63/200 D_phys] = 0.457995  err=-0.0010%
    [beta_i a*b*c*d D_phys beta_i 63/200] = 0.457995  err=-0.0010%
    [D_phys a*b*c*d beta_i beta_i 63/200] = 0.457995  err=-0.0010%
    [beta_i a*b*c*d D_phys 63/200 beta_i] = 0.457995  err=-0.0010%

  BEST f*sigma_8(0.51): [416/513 a*b/(c*d) 6/11 243/260 31/30] = 0.457995, err = -0.000993%
================================================================================
TRACK (d) -- Class LXXVII: H(z=0.61) = 97.3 km/s/Mpc (Lya cross-check)
================================================================================
  Target H(0.61) = 97.3000  (H_0-shell target = 1.443620)

  2-atom shell (tol 3%):
    [33/40 a/b SSq] ratio=1.447368  -> 97.5526  err=+0.2596%
    [K_Mex a*b 137/200] ratio=1.427083  -> 96.1854  err=-1.1455%
    [137/200 a*b K_Mex] ratio=1.427083  -> 96.1854  err=-1.1455%
    [Phi_res a/b SSq] ratio=1.461988  -> 98.5380  err=+1.2724%
    [416/513 a/b SSq] ratio=1.422660  -> 95.8873  err=-1.4519%
    [11/9 a/b Phi_res] ratio=1.466667  -> 98.8533  err=+1.5964%
    [D_BSFG a*b Y_p] ratio=1.470000  -> 99.0780  err=+1.8273%
    [Y_p a*b D_BSFG] ratio=1.470000  -> 99.0780  err=+1.8273%
    [beta_i a*b 22/9] ratio=1.473756  -> 99.3311  err=+2.0875%
    [22/9 a*b beta_i] ratio=1.473756  -> 99.3311  err=+2.0875%
    [n_s a/b 137/200] ratio=1.408759  -> 94.9504  err=-2.4148%
    [11/9 a/b 33/40] ratio=1.481481  -> 99.8519  err=+2.6227%

  3-atom shell (tol 0.5%):
    [SSq a*b/c 22/9 n_s] ratio=1.443869  -> 97.3168  err=+0.0172%
    [22/9 a*b/c SSq n_s] ratio=1.443869  -> 97.3168  err=+0.0172%
    [Phi_res a*b*c 307/325 11/6] ratio=1.443162  -> 97.2691  err=-0.0317%
    [Phi_res a*b/c 307/325 6/11] ratio=1.443162  -> 97.2691  err=-0.0317%
    [307/325 a*b*c Phi_res 11/6] ratio=1.443162  -> 97.2691  err=-0.0317%
    [307/325 a*b/c Phi_res 6/11] ratio=1.443162  -> 97.2691  err=-0.0317%
    [Phi_res a*b*c 11/6 307/325] ratio=1.443162  -> 97.2691  err=-0.0317%
    [307/325 a*b*c 11/6 Phi_res] ratio=1.443162  -> 97.2691  err=-0.0317%
    [11/6 a*b*c Phi_res 307/325] ratio=1.443162  -> 97.2691  err=-0.0317%
    [11/6 a*b*c 307/325 Phi_res] ratio=1.443162  -> 97.2691  err=-0.0317%
    [Phi_res a/b/c 63/200 11/6] ratio=1.443001  -> 97.2583  err=-0.0429%
    [Phi_res a/b/c 11/6 63/200] ratio=1.443001  -> 97.2583  err=-0.0429%
    [Phi_res a*b/c 6/11 63/200] ratio=1.443001  -> 97.2583  err=-0.0429%
    [5/108 a/b/c 1-F*P 1-n_s] ratio=1.443001  -> 97.2583  err=-0.0429%
    [5/108 a/b/c 1-n_s 1-F*P] ratio=1.443001  -> 97.2583  err=-0.0429%

  4-atom shell (tol 0.05%):
    [K_Mex a/(b*c*d) Phi_res 11/6 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a/(b*c*d) 307/325 11/6 Phi_res] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a/(b*c*d) 11/6 Phi_res 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a/(b*c*d) 11/6 307/325 Phi_res] ratio=1.443589  -> 97.2979  err=-0.0022%
    [Phi_res a*b/(c*d) D_phys 22/9 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%
    [Phi_res a*b/(c*d) D_phys 307/325 22/9] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a/(b*c*d) Phi_res 307/325 11/6] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a/(b*c*d) 307/325 Phi_res 11/6] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a*b/(c*d) 6/11 Phi_res 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%
    [K_Mex a*b/(c*d) 6/11 307/325 Phi_res] ratio=1.443589  -> 97.2979  err=-0.0022%
    [D_phys a*b/(c*d) Phi_res 22/9 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%
    [D_phys a*b/(c*d) Phi_res 307/325 22/9] ratio=1.443589  -> 97.2979  err=-0.0022%
    [SO5 a/(b*c*d) D_phys 307/325 11/6] ratio=1.443589  -> 97.2979  err=-0.0022%
    [SO5 a/(b*c*d) D_phys 11/6 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%
    [SO5 a/(b*c*d) D_BSFG 11/9 307/325] ratio=1.443589  -> 97.2979  err=-0.0022%

  BEST H(0.61): H_0 * [K_Mex a/(b*c*d) 11/6 307/325 Phi_res] = 97.2979, err = -0.002161%

classLXXIV_H_z051_session768: predicted=9.049870e+01 observed=9.050000e+01 error_pct=-1.434759e-03 status=CE_strict
classLXXV_D_M_z051_session768: predicted=1.977008e+03 observed=1.977000e+03 error_pct=3.795316e-04 status=candidate_EXACT
classLXXVI_fsigma8_z051_session768: predicted=4.579955e-01 observed=4.580000e-01 error_pct=-9.928711e-04 status=CE_strict
classLXXVII_H_z061_session768: predicted=9.729790e+01 observed=9.730000e+01 error_pct=-2.160799e-03 status=CE_strict

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  LXXIV   H(0.51)          pred=90.4987   err=-0.0014%  (CE_strict)
  LXXV    D_M(0.51)        pred=1977.0075  err=+0.0004%  (candidate_EXACT)
  LXXVI   f*sigma_8(0.51)  pred=0.4580    err=-0.0010%  (CE_strict)
  LXXVII  H(0.61)          pred=97.2979   err=-0.0022%  (CE_strict)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session768_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
