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SESSION 759 -- tau/z_* unblock; Omega_c*h^2 (XLVII); k_pivot (XLVIII)
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TRACK (a) -- tau + z_* unblock retry with 11/6, 6/11, 1/12 atoms
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  tau base (S755): pred=5.440202e-02, err=+0.744487%
  delta needed = -7.3898e-03

  2-atom delta on tau (tol 1%):

  3-atom delta on tau (tol 0.5%):
    1-[r a/b/c D_BSFG 416/513] tau=5.4000e-02 err=-0.000926%
    1-[r a/b/c 416/513 D_BSFG] tau=5.4000e-02 err=-0.000926%
    1-[K_Mex a*b*c xi 31/30] tau=5.3999e-02 err=-0.001040%
    1-[K_Mex a*b*c 31/30 xi] tau=5.3999e-02 err=-0.001040%
    1-[xi a*b*c K_Mex 31/30] tau=5.3999e-02 err=-0.001040%
    1-[xi a*b*c 31/30 K_Mex] tau=5.3999e-02 err=-0.001040%
    1-[31/30 a*b*c K_Mex xi] tau=5.3999e-02 err=-0.001040%
    1-[31/30 a*b*c xi K_Mex] tau=5.3999e-02 err=-0.001040%
    1-[307/325 a*b/c 1/137 243/260] tau=5.4001e-02 err=+0.001257%
    1-[1/137 a*b/c 307/325 243/260] tau=5.4001e-02 err=+0.001257%
    1-[307/325 a*b/c alpha 243/260] tau=5.4001e-02 err=+0.001453%
    1-[alpha a*b/c 307/325 243/260] tau=5.4001e-02 err=+0.001453%

  4-atom delta on tau (tol 0.05%):
    1-[D_phys a*b*c*d Y_p 31/30 alpha] tau=5.4000e-02 err=+0.000006%
    1-[D_phys a*b*c*d 31/30 Y_p alpha] tau=5.4000e-02 err=+0.000006%
    1-[Y_p a*b*c*d D_phys 31/30 alpha] tau=5.4000e-02 err=+0.000006%
    1-[Y_p a*b*c*d 31/30 D_phys alpha] tau=5.4000e-02 err=+0.000006%
    1-[Y_p a*b*c*d 31/30 alpha D_phys] tau=5.4000e-02 err=+0.000006%
    1-[31/30 a*b*c*d D_phys Y_p alpha] tau=5.4000e-02 err=+0.000006%
    1-[31/30 a*b*c*d Y_p D_phys alpha] tau=5.4000e-02 err=+0.000006%
    1-[31/30 a*b*c*d Y_p alpha D_phys] tau=5.4000e-02 err=+0.000006%
    1-[D_phys a*b*c*d Y_p alpha 31/30] tau=5.4000e-02 err=+0.000006%
    1-[D_phys a*b*c*d 31/30 alpha Y_p] tau=5.4000e-02 err=+0.000006%

  BEST tau: base*[1-D_phys a*b*c*d Y_p 31/30 alpha] = 5.4000e-02, err = +0.000006%

  z_* base (S756): pred=1089.809927, err=+0.000911%
  delta needed = -9.1092e-06

  2-atom delta on z_* (tol 1%):

  3-atom delta on z_* (tol 0.1%):

  4-atom delta on z_* (tol 0.02%):
    1-[r a*b*c/d r 1/137 27/26] z=1089.8000 err=-0.000000%
    1-[r a*b*c/d 1/137 r 27/26] z=1089.8000 err=-0.000000%
    1-[1/137 a*b*c/d r r 27/26] z=1089.8000 err=-0.000000%

  BEST z_*: base*[1-r a*b*c/d r 1/137 27/26] = 1089.8000, err = -0.000000%

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TRACK (b) -- Class XLVII: Omega_c * h^2 = 0.1206
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  XLVI Omega_m*h^2 = 0.143000; XXXVII Omega_b*h^2 = 0.022370; diff = 0.120630, err=+0.024894%

  2-atom direct on Omega_c*h^2 (tol 5%):
    [27/25 a/b N_ch] = 0.120000  err=-0.497512%
    [F_TRZ a/b Phi_res] = 0.120000  err=-0.497512%
    [F_TRZ a/b 33/40] = 0.121212  err=+0.507563%
    [1/12 a/b 137/200] = 0.121655  err=+0.874379%
    [F_TRZ a*b 11/9] = 0.122222  err=+1.345126%
    [11/9 a*b F_TRZ] = 0.122222  err=+1.345126%
    [11/9 a/b SO5] = 0.122222  err=+1.345126%
    [F_TRZ a/b 416/513] = 0.123317  err=+2.253157%
    [Y_p a/b K_Mex] = 0.117600  err=-2.487562%
    [27/26 a/b N_ch] = 0.115385  err=-4.324531%

  3-atom direct on Omega_c*h^2 (tol 1%):
    [N_ch a*b/c alpha 1/mpme] = 0.120591  err=-0.007064%
    [N_ch a*b*c mpme alpha] = 0.120591  err=-0.007064%
    [alpha a*b/c N_ch 1/mpme] = 0.120591  err=-0.007064%
    [mpme a*b*c N_ch alpha] = 0.120591  err=-0.007064%
    [N_ch a*b*c alpha mpme] = 0.120591  err=-0.007064%
    [alpha a*b*c N_ch mpme] = 0.120591  err=-0.007064%
    [alpha a*b*c mpme N_ch] = 0.120591  err=-0.007064%
    [mpme a*b*c alpha N_ch] = 0.120591  err=-0.007064%
    [33/40 a*b/c 1/12 SSq] = 0.120614  err=+0.011638%
    [1/12 a*b/c 33/40 SSq] = 0.120614  err=+0.011638%
    [beta_i a/b/c Phi_res D_BSFG] = 0.120580  err=-0.016584%
    [beta_i a/b/c D_BSFG Phi_res] = 0.120580  err=-0.016584%

  4-atom direct on Omega_c*h^2 (tol 0.1%):
    [beta_i a/(b*c*d) N_ch 416/513 137/200] = 0.120597  err=-0.002549%
    [beta_i a/(b*c*d) N_ch 137/200 416/513] = 0.120597  err=-0.002549%
    [beta_i a/(b*c*d) 416/513 N_ch 137/200] = 0.120597  err=-0.002549%
    [beta_i a/(b*c*d) 416/513 137/200 N_ch] = 0.120597  err=-0.002549%
    [beta_i a/(b*c*d) 137/200 N_ch 416/513] = 0.120597  err=-0.002549%
    [beta_i a/(b*c*d) 137/200 416/513 N_ch] = 0.120597  err=-0.002549%
    [416/513 a*b*c/d 307/325 307/325 D_BSFG] = 0.120597  err=-0.002893%
    [307/325 a*b*c/d 416/513 307/325 D_BSFG] = 0.120597  err=-0.002893%
    [307/325 a*b*c/d 307/325 416/513 D_BSFG] = 0.120597  err=-0.002893%
    [SSq a*b*c/d Y_p Phi_res n_s] = 0.120596  err=-0.003437%
    [Y_p a*b*c/d SSq Phi_res n_s] = 0.120596  err=-0.003437%
    [Phi_res a*b*c/d SSq Y_p n_s] = 0.120596  err=-0.003437%
    [Phi_res a*b*c/d Y_p SSq n_s] = 0.120596  err=-0.003437%
    [SSq a*b*c/d Phi_res Y_p n_s] = 0.120596  err=-0.003437%
    [Y_p a*b*c/d Phi_res SSq n_s] = 0.120596  err=-0.003437%

  BEST Omega_c*h^2: [beta_i a/(b*c*d) N_ch 416/513 137/200] = 0.120597, err = -0.002549%

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TRACK (c) -- Class XLVIII: k_pivot = 0.05 Mpc^-1
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  Seed candidates:
    F_TRZ/2 = 0.050000  err=+0.000000%
    5/108   = 0.046296  err=-7.407407%

  2-atom direct on k_pivot (tol 5%):
    [27/25 a*b 5/108] = 0.050000  err=+0.000000%
    [5/108 a*b 27/25] = 0.050000  err=+0.000000%
    [beta_i a*b 1/12] = 0.050242  err=+0.483333%
    [1/12 a*b beta_i] = 0.050242  err=+0.483333%
    [5/108 a/b 243/260] = 0.049535  err=-0.929736%
    [5/108 a/b 1-F*P] = 0.050505  err=+1.010101%
    [5/108 a/b 307/325] = 0.049011  err=-1.978526%
    [1-n_s a/b 137/200] = 0.051095  err=+2.189781%
    [5/108 a/b 1-F_TRZ] = 0.051440  err=+2.880658%
    [27/26 a*b 5/108] = 0.048077  err=-3.846154%
    [5/108 a*b 27/26] = 0.048077  err=-3.846154%
    [F_TRZ a/b K_Mex] = 0.048000  err=-4.000000%

  3-atom direct on k_pivot (tol 0.5%):
    [F_TRZ a*b*c D_BSFG 1/12] = 0.050000  err=+0.000000%
    [F_TRZ a*b/c 1-F*P 11/6] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c 1-F*P 6/11] = 0.050000  err=+0.000000%
    [F_TRZ a*b/c 11/9 22/9] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c 1/12 D_BSFG] = 0.050000  err=+0.000000%
    [D_BSFG a*b*c F_TRZ 1/12] = 0.050000  err=+0.000000%
    [D_BSFG a*b*c 1/12 F_TRZ] = 0.050000  err=+0.000000%
    [D_BSFG a*b/c 1/12 SO5] = 0.050000  err=+0.000000%
    [SO5 a*b*c 137/200 1/137] = 0.050000  err=+0.000000%
    [SO5 a*b*c 1/137 137/200] = 0.050000  err=+0.000000%
    [1-F*P a*b/c F_TRZ 11/6] = 0.050000  err=+0.000000%
    [1-F*P a*b*c F_TRZ 6/11] = 0.050000  err=+0.000000%

  4-atom direct on k_pivot (tol 0.05%):
    [F_TRZ a*b*c*d F_TRZ A_5 1/12] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c*d Phi_res D_BSFG F_TRZ] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c/d Phi_res D_BSFG SO5] = 0.050000  err=+0.000000%
    [F_TRZ a/(b*c*d) D_phys D_BSFG 1/12] = 0.050000  err=+0.000000%
    [F_TRZ a/(b*c*d) D_phys 1/12 D_BSFG] = 0.050000  err=+0.000000%
    [F_TRZ a/(b*c*d) D_BSFG D_phys 1/12] = 0.050000  err=+0.000000%
    [F_TRZ a/(b*c*d) D_BSFG 1/12 D_phys] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c*d SO5 27/25 5/108] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c*d SO5 5/108 27/25] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c*d A_5 F_TRZ 1/12] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c*d A_5 1/12 F_TRZ] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c/d A_5 1/12 SO5] = 0.050000  err=+0.000000%
    [F_TRZ a*b*c/d 1-F_TRZ 5/108 1/12] = 0.050000  err=+0.000000%
    [F_TRZ a*b/(c*d) 33/40 1-F_TRZ 11/6] = 0.050000  err=+0.000000%
    [F_TRZ a*b/(c*d) 33/40 11/6 1-F_TRZ] = 0.050000  err=+0.000000%

  BEST k_pivot: [27/25 a*b 5/108] = 0.050000, err = +0.000000%

classXLI_tau_session759: predicted=5.400000e-02 observed=5.400000e-02 error_pct=6.470853e-06 status=CE_strict
classXLII_zstar_session759: predicted=1.089800e+03 observed=1.089800e+03 error_pct=-3.241542e-08 status=CE_strict
classXLVII_Omega_c_h2_session759: predicted=1.205969e-01 observed=1.206000e-01 error_pct=-2.549018e-03 status=tight CLOSED
classXLVIII_k_pivot_session759: predicted=5.000000e-02 observed=5.000000e-02 error_pct=0.000000e+00 status=EXACT

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DECISION GATE
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  tau (XLI retry)     err = +0.000006%  (CE_strict)
  z_* (XLII retry)    err = -0.000000%  (CE_strict)
  Omega_c*h^2 (XLVII) err = -0.002549%  (tight CLOSED)
  k_pivot (XLVIII)    err = +0.000000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session759_result.json
