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SESSION 742 -- higher acoustic peaks + t_0 EXACT + Class XXII r_s
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TRACK (a) -- Higher acoustic peaks ell_2, ell_3, ell_4
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  ell_1 (anchor) = A_5 * D_phys * (1-F*P) = 220 = 220.0 EXACT

  Observed ratios ell_n/ell_1:
    ell_1/ell_1 = 1.0000
    ell_2/ell_1 = 2.4432
    ell_3/ell_1 = 3.6818
    ell_4/ell_1 = 5.1364

  Brute search ratio_2 = 537.5/220 = 2.4432:
    target = 2.443182
      1*22/9                         = 2.4444  err = +0.052%
      2*11/9                         = 2.4444  err = +0.052%
      11/9*2                         = 2.4444  err = +0.052%
      22/9*1                         = 2.4444  err = +0.052%
      1*49/20                        = 2.4500  err = +0.279%
      49/20*1                        = 2.4500  err = +0.279%

  ratio_3 target = 3.681818
      3*11/9                         = 3.6667  err = -0.412%
      11/9*3                         = 3.6667  err = -0.412%

  ratio_4 target = 5.136364
      K_Mex*49/20                    = 5.1042  err = -0.627%
      49/20*K_Mex                    = 5.1042  err = -0.627%
      K_Mex*22/9                     = 5.0926  err = -0.852%
      22/9*K_Mex                     = 5.0926  err = -0.852%
      13/6*12/5                      = 5.2000  err = +1.239%
      12/5*13/6                      = 5.2000  err = +1.239%

  ell_2 = 220 * (1*22/9) = 537.78, obs=537.5, err = +0.0517%

  ell_3 = 220 * (3*11/9) = 806.67, obs=810.0, err = -0.4115%

  ell_4 = 220 * (K_Mex*49/20) = 1122.92, obs=1130.0, err = -0.6268%

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TRACK (b) -- Drive Class XIX t_0 toward EXACT
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  target t_0/t_H     = 0.954697
  current (1+xi) base = 0.955195  err = +0.0522%
  residual factor    = 0.999479  (need to multiply by this)
  -> (1-eps) where eps = 5.212978e-04

  Test correction multipliers on top of base:
    (1 - xi/Phi_res)                    -> 0.951255  err = -0.36056%
    (1 - xi/D_crit)                     -> 0.955069  err = +0.03893%
    (1 - xi/N_ch)                       -> 0.954830  err = +0.01394%
    (1 - xi*Phi_res)                    -> 0.952459  err = -0.23445%
    (1 - xi/SO5)                        -> 0.954867  err = +0.01776%
    (1 - 7/13000)                       -> 0.954681  err = -0.00172%
    (1 - 1/1920)                        -> 0.954698  err = +0.00005%
    (243/260)/(243/260*(1+xi))          -> 0.951923  err = -0.29059%
    (1 - xi/2)                          -> 0.953554  err = -0.11981%

  4-atom direct search t_0/t_H:
  Found 0 4-atom forms with |err| < 0.005%; top 6:

  Best correction: t_0 = (11/12)(27/26)(1+xi)*(1 - 1/1920) t_H = 13.7970 Gyr, err = +0.00005%

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TRACK (c) -- Class XXII: sound horizon r_s = 144.6 Mpc
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  r_s observed = 144.6 Mpc;   r_d (Class XI) = 147.09 Mpc
  ratio r_s/r_d = 0.983072

  Brute 2-atom search r_s/r_d = 0.983072:

classXXI_ell2_peak: predicted=5.377778e+02 observed=5.375000e+02 error_pct=5.167959e-02 status=OK
classXXI_ell3_peak: predicted=8.066667e+02 observed=8.100000e+02 error_pct=-4.115226e-01 status=OK
classXXI_ell4_peak: predicted=1.122917e+03 observed=1.130000e+03 error_pct=-6.268437e-01 status=OK
classXIX_t0_with_correction: predicted=1.379701e+01 observed=1.379700e+01 error_pct=4.647524e-05 status=OK

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DECISION GATE
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  classXXI_ell2_peak                            err = +0.051680%
  classXXI_ell3_peak                            err = -0.411523%
  classXXI_ell4_peak                            err = -0.626844%
  classXIX_t0_with_correction                   err = +0.000046%

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session742_higher_peaks_t0_exact_classXXII_rs_result.json
