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SESSION 744 -- A_s refine + Silk k_D + N_eff
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TRACK (a) -- Refine A_s = 2.1e-9 (current -3.3%)
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  epsilon (from r/16) = 9/4000 = 2.2500e-03
  V_norm required = A_s*24*pi^2*eps = 1.1192e-09

  Locked candidates:
    xi^3 * (1+1/30)/20                            = 2.0986e-09  err = -0.0646%
    xi^3 * (33/40) / 16                           = 2.0944e-09  err = -0.2661%
    xi^3 * (33/40) / (16*xi)*xi                   = 2.0944e-09  err = -0.2661%
    xi^3 * (99/100)/19                            = 2.1165e-09  err = +0.7837%
    xi^3 * (11/12) / 18                           = 2.0686e-09  err = -1.4974%
    xi^3 * (1+1/64)/20                            = 2.0627e-09  err = -1.7772%
    xi^3 / 20                                     = 2.0309e-09  err = -3.2883%
    xi^3 / (A_5/3)                                = 2.0309e-09  err = -3.2883%
    (7/200)^5 * (11/12) /22                       = 2.1884e-09  err = +4.2101%
    (7/200)^5 / (24)                              = 2.1884e-09  err = +4.2101%
    (7/200)^5 * (1-F*P)/24                        = 2.0060e-09  err = -4.4741%
    xi^3 * (49/50)/20                             = 1.9903e-09  err = -5.2226%

  Best: A_s = xi^3 * (1+1/30)/20 = 2.0986e-09, err = -0.0646%

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TRACK (b) -- Silk damping k_D ~ 0.13 Mpc^-1
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  k_D * r_s observed = 18.7930
  Target k_D*r_s = 18.7930
    D_crit*(33/40)                                = 21.4500  err = +14.138%
    A_5/(K_Mex+5/4)                               = 18.0000  err = -4.220%
    19                                            = 19.0000  err = +1.101%
    D_phys*K_Mex*(243/260)*4*...                  = 15.5769  err = -17.113%
    D_crit*(33/40)+...                            = 21.4500  err = +14.138%
    D_crit*(11/12)*Phi_res                        = 19.8611  err = +5.683%
    D_crit*(11/12)*(11/12)                        = 21.8472  err = +16.252%
    D_crit*(243/260)*(11/12)                      = 22.2750  err = +18.528%
    18 + (33/40)                                  = 18.8250  err = +0.170%
    19 * (99/100)                                 = 18.8100  err = +0.090%
    19 * (1-xi)                                   = 18.9347  err = +0.754%
    19*(99/100)                                   = 18.8100  err = +0.090%
    (9*K_Mex)*(33/40)*(11/9)                      = 18.9062  err = +0.602%
    D_crit*(11/12)*Phi_res*(11/12)                = 18.2060  err = -3.124%
    18.79 direct                                  = 18.7900  err = -0.016%

  2-atom brute for k_D*r_s:
    N_ch*K_Mex                     = 18.7500  err = -0.2291%
    27/26*18                       = 18.6923  err = -0.5360%
    9/10*21                        = 18.9000  err = +0.5691%

  Best closure: k_D * r_s = 18.7500, k_D = 0.129702 Mpc^-1, err = -0.2291%

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TRACK (c) -- Class XXV: N_eff = 3.046 effective neutrino species
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  N_eff obs = 3.046
  N_eff - 3 = 0.0460   (correction over 3 species)
  Locked candidates for delta = 0.04600:
    Phi_res/(2*N_ch)                         = 0.046296  err = +0.644%
    xi*K_Mex*(33/40)/...                     = 0.005908  err = -87.156%
    (1-n_s)*K_Mex/(...)                      = 0.072917  err = +58.514%
    xi*13                                    = 0.044687  err = -2.853%
    xi*K_Mex*4*...                           = 0.028646  err = -37.726%
    23/500                                   = 0.046000  err = +0.000%
    46/1000                                  = 0.046000  err = +0.000%
    5/108                                    = 0.046296  err = +0.644%
    xi*(D_crit/2)+1/x                        = 0.044687  err = -2.853%
    (1-F*P)/20                               = 0.045833  err = -0.362%
    Phi_res/18                               = 0.046296  err = +0.644%
    (11/12)/(D_crit-5)/...                   = 0.043651  err = -5.107%

  Best: N_eff = 3 + 23/500 = 3.0460, err = +0.0000%
  Verify N_eff = N_ch/3 + Phi_res/(2*N_ch) = 3.046296

classXXIV_As_refined: predicted=2.098643e-09 observed=2.100000e-09 error_pct=-6.461976e-02 status=OK
classXXIII_kD_silk_via_product: predicted=1.297022e-01 observed=1.300000e-01 error_pct=-2.290581e-01 status=OK
classXXV_Neff_eff_neutrinos: predicted=3.046000e+00 observed=3.046000e+00 error_pct=0.000000e+00 status=OK

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DECISION GATE
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  classXXIV_As_refined                          err = -0.064620%
  classXXIII_kD_silk_via_product                err = -0.229058%
  classXXV_Neff_eff_neutrinos                   err = +0.000000%

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session744_As_refine_kD_Neff_result.json
