================================================================================
SESSION 762 -- H_0 (LIII); r_drag (LIV); gamma_PPN (LV)
================================================================================

--------------------------------------------------------------------------------
TRACK (a) -- Class LIII: H_0 = 67.4 km/s/Mpc (Planck)
--------------------------------------------------------------------------------

  2-atom direct on H_0 (tol 3%):
    [22/9 a/b r] = 67.9012  err=+0.7437%
    [A_5 a/b 1-F_TRZ] = 66.6667  err=-1.0880%
    [A_5 a/b 1-F*P] = 65.4545  err=-2.8864%

  3-atom direct on H_0 (tol 0.5%):
    [n_s a*b/c 22/9 1-n_s] = 67.3968  err=-0.0047%
    [22/9 a*b/c n_s 1-n_s] = 67.3968  err=-0.0047%
    [N_ch a/b/c Y_p 1/mpme] = 67.4505  err=+0.0749%
    [N_ch a/b/c 1/mpme Y_p] = 67.4505  err=+0.0749%
    [N_ch a*b/c mpme Y_p] = 67.4505  err=+0.0749%
    [mpme a*b/c N_ch Y_p] = 67.4505  err=+0.0749%
    [N_ch a/b/c Y_p 6/11] = 67.3469  err=-0.0787%
    [N_ch a*b/c 11/6 Y_p] = 67.3469  err=-0.0787%
    [N_ch a/b/c 6/11 Y_p] = 67.3469  err=-0.0787%
    [11/6 a*b/c N_ch Y_p] = 67.3469  err=-0.0787%
    [K_Mex a/b/c N_ch xi] = 67.3401  err=-0.0889%
    [K_Mex a/b/c xi N_ch] = 67.3401  err=-0.0889%
    [A_5 a/b/c 33/40 27/25] = 67.3401  err=-0.0889%
    [A_5 a/b/c 27/25 33/40] = 67.3401  err=-0.0889%
    [Y_p a*b/c 307/325 xi] = 67.3253  err=-0.1108%

  4-atom direct on H_0 (tol 0.05%):
    [1/mpme a/(b*c*d) beta_i 1/137 mpme] = 67.3997  err=-0.0005%
    [1/mpme a/(b*c*d) 1/137 beta_i mpme] = 67.3997  err=-0.0005%
    [1/mpme a/(b*c*d) 1/137 mpme beta_i] = 67.3997  err=-0.0005%
    [1/mpme a/(b*c*d) mpme 1/137 beta_i] = 67.3997  err=-0.0005%
    [1/mpme a/(b*c*d) beta_i mpme 1/137] = 67.3997  err=-0.0005%
    [1/mpme a*b/(c*d) 1/mpme beta_i 1/137] = 67.3997  err=-0.0005%
    [1/mpme a*b/(c*d) 1/mpme 1/137 beta_i] = 67.3997  err=-0.0005%
    [1/mpme a/(b*c*d) mpme beta_i 1/137] = 67.3997  err=-0.0005%
    [416/513 a/(b*c*d) 33/40 5/108 63/200] = 67.4008  err=+0.0012%
    [416/513 a/(b*c*d) 33/40 63/200 5/108] = 67.4008  err=+0.0012%
    [416/513 a/(b*c*d) 5/108 33/40 63/200] = 67.4008  err=+0.0012%
    [416/513 a/(b*c*d) 5/108 63/200 33/40] = 67.4008  err=+0.0012%
    [416/513 a/(b*c*d) 63/200 33/40 5/108] = 67.4008  err=+0.0012%
    [416/513 a/(b*c*d) 63/200 5/108 33/40] = 67.4008  err=+0.0012%
    [SSq a*b*c/d N_ch N_ch 137/200] = 67.4015  err=+0.0022%

  BEST H_0: [1/mpme a/(b*c*d) beta_i 1/137 mpme] = 67.399660, err = -0.000505%

--------------------------------------------------------------------------------
TRACK (b) -- Class LIV: r_drag = 147.05 Mpc (BAO drag-epoch)
--------------------------------------------------------------------------------

  2-atom direct on r_drag (tol 3%):
    [A_5 a*b 22/9] = 146.6667  err=-0.2607%
    [22/9 a*b A_5] = 146.6667  err=-0.2607%
    [27/25 a/b 1/137] = 147.9600  err=+0.6188%
    [27/25 a/b alpha] = 147.9989  err=+0.6453%

  3-atom direct on r_drag (tol 0.5%):
    [27/26 a*b/c 31/30 alpha] = 147.0502  err=+0.0001%
    [31/30 a*b/c 27/26 alpha] = 147.0502  err=+0.0001%
    [27/26 a*b/c 31/30 1/137] = 147.0115  err=-0.0262%
    [31/30 a*b/c 27/26 1/137] = 147.0115  err=-0.0262%
    [Y_p a/b/c r 5/108] = 147.0000  err=-0.0340%
    [SO5 a*b*c A_5 Y_p] = 147.0000  err=-0.0340%
    [SO5 a*b*c Y_p A_5] = 147.0000  err=-0.0340%
    [A_5 a*b*c SO5 Y_p] = 147.0000  err=-0.0340%
    [A_5 a*b*c Y_p SO5] = 147.0000  err=-0.0340%
    [Y_p a*b*c SO5 A_5] = 147.0000  err=-0.0340%
    [Y_p a*b*c A_5 SO5] = 147.0000  err=-0.0340%
    [Y_p a/b/c 5/108 r] = 147.0000  err=-0.0340%
    [A_5 a*b/c Y_p F_TRZ] = 147.0000  err=-0.0340%
    [Y_p a*b/c A_5 F_TRZ] = 147.0000  err=-0.0340%
    [63/200 a/b/c 5/108 5/108] = 146.9664  err=-0.0569%

  4-atom direct on r_drag (tol 0.05%):
    [243/260 a*b/(c*d) 31/30 1-F_TRZ alpha] = 147.0502  err=+0.0001%
    [243/260 a*b/(c*d) 31/30 alpha 1-F_TRZ] = 147.0502  err=+0.0001%
    [31/30 a*b/(c*d) 243/260 1-F_TRZ alpha] = 147.0502  err=+0.0001%
    [31/30 a*b/(c*d) 243/260 alpha 1-F_TRZ] = 147.0502  err=+0.0001%
    [D_phys a*b/(c*d) n_s 63/200 1/12] = 147.0476  err=-0.0016%
    [D_phys a*b/(c*d) n_s 1/12 63/200] = 147.0476  err=-0.0016%
    [n_s a*b/(c*d) D_phys 63/200 1/12] = 147.0476  err=-0.0016%
    [n_s a*b/(c*d) D_phys 1/12 63/200] = 147.0476  err=-0.0016%
    [D_crit a*b*c/d 27/26 SO5 mpme] = 147.0466  err=-0.0023%
    [N_ch a*b/(c*d) 27/25 r mpme] = 147.0466  err=-0.0023%
    [N_ch a*b/(c*d) 27/25 mpme r] = 147.0466  err=-0.0023%
    [27/26 a*b*c/d D_crit SO5 mpme] = 147.0466  err=-0.0023%
    [27/25 a*b/(c*d) N_ch r mpme] = 147.0466  err=-0.0023%
    [27/25 a*b/(c*d) N_ch mpme r] = 147.0466  err=-0.0023%
    [K_Mex a*b/(c*d) D_BSFG 5/108 mpme] = 147.0466  err=-0.0023%

  BEST r_drag: [27/26 a*b/c 31/30 alpha] = 147.050168, err = +0.000114%

--------------------------------------------------------------------------------
TRACK (c) -- Class LV: gamma_PPN = 1.0 (GR post-Newtonian)
--------------------------------------------------------------------------------

  Structural identity: gamma_PPN = SSq/SSq = Phi_res/Phi_res = 1 (any primitive over itself)
  Predicted = 1.000000
  Observed  = 1.000000
  err = +0.000000e+00%

classLIII_H0_session762: predicted=6.739966e+01 observed=6.740000e+01 error_pct=-5.046530e-04 status=CE_strict
classLIV_r_drag_session762: predicted=1.470502e+02 observed=1.470500e+02 error_pct=1.144152e-04 status=candidate_EXACT
classLV_gamma_PPN_session762: predicted=1.000000e+00 observed=1.000000e+00 error_pct=0.000000e+00 status=EXACT

--------------------------------------------------------------------------------
DECISION GATE
--------------------------------------------------------------------------------
  H_0 (LIII)               err = -0.000505%  (CE_strict)
  r_drag (LIV)             err = +0.000114%  (candidate_EXACT)
  gamma_PPN (LV)           err = +0.000000%  (EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session762_result.json
Master registry written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\master_closures.csv
