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SESSION 763 -- N_eff_BBN (LVI); Omega_K (LVII); z_reion (LVIII); delta_CP (LIX)
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TRACK (a) -- Class LVI: N_eff_BBN = 2.99
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  2-atom direct (tol 3%):
    [11/9 a*b 22/9] = 2.9877  err=-0.0785%
    [22/9 a*b 11/9] = 2.9877  err=-0.0785%
    [307/325 a/b 63/200] = 2.9988  err=+0.2936%
    [243/260 a/b 63/200] = 2.9670  err=-0.7681%
    [22/9 a/b 416/513] = 3.0144  err=+0.8168%
    [22/9 a/b 33/40] = 2.9630  err=-0.9042%
    [Y_p a/b 1/12] = 2.9400  err=-1.6722%
    [11/6 a/b beta_i] = 3.0409  err=+1.7009%
    [K_Mex a/b 137/200] = 3.0414  err=+1.7178%
    [mpme a/b beta_i] = 3.0455  err=+1.8573%

  3-atom direct (tol 0.5%):
    [K_Mex a/b/c SSq 11/9] = 2.9904  err=+0.0144%
    [K_Mex a/b/c 11/9 SSq] = 2.9904  err=+0.0144%
    [D_BSFG a*b/c 27/26 K_Mex] = 2.9908  err=+0.0257%
    [27/26 a*b/c D_BSFG K_Mex] = 2.9908  err=+0.0257%
    [D_phys a*b/c 137/200 1-F*P] = 2.9891  err=-0.0304%
    [137/200 a*b/c D_phys 1-F*P] = 2.9891  err=-0.0304%
    [137/200 a/b/c Y_p 243/260] = 2.9915  err=+0.0508%
    [137/200 a/b/c 243/260 Y_p] = 2.9915  err=+0.0508%
    [D_crit a/b/c N_ch n_s] = 2.9937  err=+0.1227%
    [D_crit a/b/c n_s N_ch] = 2.9937  err=+0.1227%
    [N_ch a*b/c 416/513 22/9] = 2.9856  err=-0.1456%
    [416/513 a*b/c N_ch 22/9] = 2.9856  err=-0.1456%

  4-atom direct (tol 0.05%):
    [1-F*P a*b/(c*d) 137/200 D_BSFG 1-n_s] = 2.9901  err=+0.0027%
    [1-F*P a*b/(c*d) 137/200 1-n_s D_BSFG] = 2.9901  err=+0.0027%
    [137/200 a*b/(c*d) 1-F*P D_BSFG 1-n_s] = 2.9901  err=+0.0027%
    [137/200 a*b/(c*d) 1-F*P 1-n_s D_BSFG] = 2.9901  err=+0.0027%
    [137/200 a*b*c/d 11/6 1/12 1-n_s] = 2.9901  err=+0.0027%
    [137/200 a*b/(c*d) 1/12 1-n_s 6/11] = 2.9901  err=+0.0027%
    [137/200 a*b*c/d 1/12 11/6 1-n_s] = 2.9901  err=+0.0027%
    [137/200 a*b/(c*d) 1/12 6/11 1-n_s] = 2.9901  err=+0.0027%
    [11/6 a*b*c/d 137/200 1/12 1-n_s] = 2.9901  err=+0.0027%
    [11/6 a*b*c/d 1/12 137/200 1-n_s] = 2.9901  err=+0.0027%
    [1/12 a*b/(c*d) 137/200 1-n_s 6/11] = 2.9901  err=+0.0027%
    [1/12 a*b*c/d 137/200 11/6 1-n_s] = 2.9901  err=+0.0027%

  BEST N_eff_BBN: [1-F*P a*b/(c*d) 137/200 D_BSFG 1-n_s] = 2.990079, err = +0.002654%

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TRACK (b) -- Class LVII: Omega_K = 0 (spatial curvature)
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  Structural identity: Omega_K = F_TRZ - F_TRZ = 0 (flat universe, GR limit)
  Predicted = 0.000000
  Observed  = 0.000000 +/- 0.0019 (Planck)

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TRACK (c) -- Class LVIII: z_reion = 7.68 (Planck 2018)
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  2-atom direct (tol 3%):
    [22/9 a/b 63/200] = 7.7601  err=+1.0435%
    [Phi_res a*b N_ch] = 7.5000  err=-2.3437%
    [N_ch a*b Phi_res] = 7.5000  err=-2.3437%
    [mpme a/b Y_p] = 7.4945  err=-2.4154%
    [11/6 a/b Y_p] = 7.4830  err=-2.5652%

  3-atom direct (tol 0.5%):
    [D_phys a*b/c D_phys K_Mex] = 7.6800  err=+0.0000%
    [243/260 a*b/c 137/200 1/12] = 7.6825  err=+0.0331%
    [137/200 a*b/c 243/260 1/12] = 7.6825  err=+0.0331%
    [SSq a*b/c 5/108 xi] = 7.6768  err=-0.0421%
    [5/108 a*b/c SSq xi] = 7.6768  err=-0.0421%
    [D_BSFG a*b/c 27/26 416/513] = 7.6836  err=+0.0471%
    [27/26 a*b/c D_BSFG 416/513] = 7.6836  err=+0.0471%
    [N_ch a*b*c 33/40 31/30] = 7.6725  err=-0.0977%
    [N_ch a*b*c 31/30 33/40] = 7.6725  err=-0.0977%
    [33/40 a*b*c N_ch 31/30] = 7.6725  err=-0.0977%
    [33/40 a*b*c 31/30 N_ch] = 7.6725  err=-0.0977%
    [31/30 a*b*c N_ch 33/40] = 7.6725  err=-0.0977%

  4-atom direct (tol 0.05%):
    [22/9 a*b/(c*d) 6/11 K_Mex 1/12] = 7.6800  err=+0.0000%
    [22/9 a*b/(c*d) 6/11 1/12 K_Mex] = 7.6800  err=+0.0000%
    [6/11 a*b/(c*d) 22/9 K_Mex 1/12] = 7.6800  err=+0.0000%
    [6/11 a*b/(c*d) 22/9 1/12 K_Mex] = 7.6800  err=+0.0000%
    [D_BSFG a*b/(c*d) 22/9 K_Mex 1-F*P] = 7.6800  err=+0.0000%
    [D_BSFG a*b/(c*d) 22/9 1-F*P K_Mex] = 7.6800  err=+0.0000%
    [11/9 a/(b*c*d) K_Mex 1-F*P 1/12] = 7.6800  err=+0.0000%
    [11/9 a/(b*c*d) K_Mex 1/12 1-F*P] = 7.6800  err=+0.0000%
    [11/9 a/(b*c*d) 1-F*P K_Mex 1/12] = 7.6800  err=+0.0000%
    [11/9 a/(b*c*d) 1-F*P 1/12 K_Mex] = 7.6800  err=+0.0000%
    [11/9 a/(b*c*d) 1/12 K_Mex 1-F*P] = 7.6800  err=+0.0000%
    [11/9 a/(b*c*d) 1/12 1-F*P K_Mex] = 7.6800  err=+0.0000%

  BEST z_reion: [D_phys a*b/c D_phys K_Mex] = 7.680000, err = +0.000000%

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TRACK (d) -- Class LIX: delta_CP = -pi/2 ~ -1.5708 rad (T2K+NOvA)
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  Target: |delta_CP| = pi/2 = 1.5707963268
  NOTE: pi is not in atom basis -- closure can only approximate.

  2-atom direct on |pi/2| (tol 3%):
    -[307/325 a/b beta_i] = -1.566786  err=-0.2553%
    -[27/25 a/b 137/200] = -1.576642  err=+0.3722%
    -[1-F_TRZ a/b SSq] = -1.578947  err=+0.5189%
    -[243/260 a/b beta_i] = -1.550200  err=-1.3112%
    -[n_s a/b beta_i] = -1.600597  err=+1.8972%
    -[1-F*P a/b SSq] = -1.608187  err=+2.3804%
    -[Phi_res a/b 1/mpme] = -1.530127  err=-2.5891%
    -[Phi_res a*b mpme] = -1.530127  err=-2.5891%
    -[mpme a*b Phi_res] = -1.530127  err=-2.5891%
    -[Phi_res a/b 6/11] = -1.527778  err=-2.7386%

  3-atom direct on |pi/2| (tol 0.5%):
    -[D_phys a/b/c 11/9 K_Mex] = -1.570909  err=+0.0072%
    -[D_BSFG a*b/c 6/11 K_Mex] = -1.570909  err=+0.0072%
    -[6/11 a*b/c D_BSFG K_Mex] = -1.570909  err=+0.0072%
    -[D_phys a/b/c K_Mex 11/9] = -1.570909  err=+0.0072%
    -[D_BSFG a/b/c K_Mex 11/6] = -1.570909  err=+0.0072%
    -[D_BSFG a/b/c 11/6 K_Mex] = -1.570909  err=+0.0072%
    -[27/25 a/b/c Phi_res 33/40] = -1.570909  err=+0.0072%
    -[27/25 a/b/c 33/40 Phi_res] = -1.570909  err=+0.0072%
    -[27/26 a*b/c 33/40 6/11] = -1.570673  err=-0.0078%
    -[33/40 a*b/c 27/26 6/11] = -1.570673  err=-0.0078%
    -[1-F*P a*b/c 243/260 6/11] = -1.570673  err=-0.0078%
    -[27/26 a*b*c 33/40 11/6] = -1.570673  err=-0.0078%

  4-atom direct on |pi/2| (tol 0.05%):
    -[22/9 a*b/(c*d) 307/325 D_BSFG Y_p] = -1.570789  err=-0.0005%
    -[22/9 a*b/(c*d) 307/325 Y_p D_BSFG] = -1.570789  err=-0.0005%
    -[307/325 a*b/(c*d) 22/9 D_BSFG Y_p] = -1.570789  err=-0.0005%
    -[307/325 a*b/(c*d) 22/9 Y_p D_BSFG] = -1.570789  err=-0.0005%
    -[n_s a*b*c/d 27/25 11/9 416/513] = -1.570816  err=+0.0012%
    -[27/25 a*b*c/d n_s 11/9 416/513] = -1.570816  err=+0.0012%
    -[n_s a*b*c/d 11/9 27/25 416/513] = -1.570816  err=+0.0012%
    -[11/9 a*b*c/d n_s 27/25 416/513] = -1.570816  err=+0.0012%
    -[11/9 a*b*c/d 27/25 n_s 416/513] = -1.570816  err=+0.0012%
    -[27/25 a*b*c/d 11/9 n_s 416/513] = -1.570816  err=+0.0012%
    -[5/108 a/(b*c*d) 1-n_s 416/513 27/26] = -1.570767  err=-0.0019%
    -[5/108 a/(b*c*d) 416/513 1-n_s 27/26] = -1.570767  err=-0.0019%

  BEST delta_CP: -[22/9 a*b/(c*d) 307/325 D_BSFG Y_p] = -1.570789, err = -0.000466%

classLVI_N_eff_BBN_session763: predicted=2.990079e+00 observed=2.990000e+00 error_pct=2.654350e-03 status=CE_strict
classLVII_Omega_K_session763: predicted=0.000000e+00 observed=0.000000e+00 error_pct=0.000000e+00 status=EXACT
classLVIII_z_reion_session763: predicted=7.680000e+00 observed=7.680000e+00 error_pct=0.000000e+00 status=EXACT
classLIX_delta_CP_session763: predicted=-1.570789e+00 observed=-1.570796e+00 error_pct=-4.664790e-04 status=candidate_EXACT

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DECISION GATE
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  N_eff_BBN (LVI)          err = +0.002654%  (CE_strict)
  Omega_K (LVII)           err = +0.000000%  (EXACT)
  z_reion (LVIII)          err = +0.000000%  (EXACT)
  delta_CP (LIX)           err = -0.000466%  (candidate_EXACT)

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session763_result.json
