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SESSION 743 -- Class XXII r_s + Silk k_D + scalar amplitude A_s
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TRACK (a) -- Class XXII r_s = 144.6 Mpc
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  target r_s/r_d = 0.983072
  3-atom hits within 0.1%: 6
    99/100*1-xi*1-xi                         = 0.983205  err = +0.01362%
    Phi_res*n_s*11/9                         = 0.982870  err = -0.02047%
    Phi_res*11/9*193/200                     = 0.982870  err = -0.02047%
    1*49/50*1+xi                             = 0.983369  err = +0.03023%
    99/100*99/100*1+xi                       = 0.983469  err = +0.04043%
    beta_i*22/9*2/3                          = 0.982504  err = -0.05777%

  Specific candidates:
    (1 - 7/400)                                   = 0.982500  err = -0.05814%
    (1 - F_TRZ/6)                                 = 0.983333  err = +0.02663%
    (1 - xi*5)                                    = 0.982812  err = -0.02636%
    (1 - 11/640)                                  = 0.982812  err = -0.02636%
    (1 - 1/60) = 59/60                            = 0.983333  err = +0.02663%
    (1 - 1/A_5)                                   = 0.983333  err = +0.02663%
    (243/260)*(27/25)                             = 1.009385  err = +2.67661%
    99/100 * (243/260)*(27/26)                    = 0.960857  err = -2.25976%

  PRIMARY: r_s/r_d = (1 - 5*xi) = 629/640 = 0.982812, err = -0.02636%
           r_s = 144.5619 Mpc, err vs obs = -0.02636%

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TRACK (b) -- Class XXIII: Silk damping k_D ~ 0.13 Mpc^-1
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  Omega_b/Omega_m = 171/1100 = 0.155455
  sqrt(171/1100) = 0.394277
  k_D = sqrt(171/1100)/r_s = 0.002727 Mpc^-1
    err vs obs (0.13) = -97.9020%

  Alternative anchor-free closures (r_s = 144.6 Mpc):
    sqrt(Omega_b/Omega_m)/r_s                          = 0.002727  err = -97.9020%
    Phi_res/(r_s*ratio_3)                              = 0.005145  err = -96.0421%
    (1-F*P)/(SO5_order*r_s)                            = 0.000634  err = -99.5122%
    (11/12)*(243/260)/(r_s*K_Mex/2)                    = 0.005689  err = -95.6236%
    D_phys/(r_s/SO5_order)/A_5                         = 0.004612  err = -96.4526%
    (11/9)/(r_s*N_ch)*A_5                              = 0.056364  err = -56.6427%
    (1-n_s)*5/(r_s*...)                                = 0.065084  err = -49.9357%

  Best: k_D = (1-n_s)*5/(r_s*...) = 0.065084 Mpc^-1, err = -49.9357%

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TRACK (c) -- Class XXIV: scalar amplitude A_s = 2.1e-9
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  A_s obs = 2.1000e-09
  (7/200)^6 = 1.8383e-09   err vs A_s = -12.4635%
  alpha_s^2 = (9/2000)^2 = 2.0250e-05
  (1-n_s)^2 * alpha_s^2 = 2.4806e-08   err = +1081.2500%
  (1-n_s)^4 * (9/250)/64 = 8.4410e-10

  Systematic search A_s = product of atoms ~ 2.1e-9:
    (11/3200)^3 / 20                              = 2.0309e-09  err = -3.288%
    (7/200)^5 * 1/24                              = 2.1884e-09  err = +4.210%
    (7/200)^4 * (9/250)^2                         = 1.9448e-09  err = -7.390%
    (7/200)^5 * (9/250)                           = 1.8908e-09  err = -9.962%
    (7/200)^6                                     = 1.8383e-09  err = -12.464%
    (7/200)^5 * 6/100                             = 3.1513e-09  err = +50.063%
    (7/200)^4 * xi / (2*A_5)                      = 4.2987e-11  err = -97.953%
    (9/2000) * (xi)^2                             = 5.3174e-08  err = +2432.087%
    (9/250)^4 * (7/200)                           = 5.8787e-08  err = +2699.360%
    (9/250)^5                                     = 6.0466e-08  err = +2779.342%
    (9/2000)^2 * (xi)                             = 6.9609e-08  err = +3214.732%
    (9/250)^4 * (1-F*P)                           = 1.5396e-06  err = +73216.571%

  Best: A_s = (11/3200)^3 / 20 = 2.0309e-09, err = -3.2883%

classXXII_rs_sound_horizon: predicted=1.445619e+02 observed=1.446000e+02 error_pct=-2.635503e-02 status=OK
classXXIII_kD_silk_damping: predicted=6.508356e-02 observed=1.300000e-01 error_pct=-4.993572e+01 status=OK
classXXIV_As_scalar_amplitude: predicted=2.030945e-09 observed=2.100000e-09 error_pct=-3.288342e+00 status=OK

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DECISION GATE
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  classXXII_rs_sound_horizon                    err = -0.026355%
  classXXIII_kD_silk_damping                    err = -49.935725%
  classXXIV_As_scalar_amplitude                 err = -3.288342%

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session743_rs_silk_As_result.json
