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SESSION 741 -- t_0 refinement + Class XX (z_eq) + ell_1 prediction
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TRACK (a) -- Refine Class XIX t_0 (target sub-0.05%)
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  t_0/t_H observed = 0.954697
  Candidates within 0.10% (3-atom):
    1-F*P*27/26*1+xi                              = 0.955195   err = +0.0522%
    27/26*11/12*1+xi                              = 0.955195   err = +0.0522%
    1-F*P*27/25*n_s                               = 0.955350   err = +0.0684%
    27/25*n_s*11/12                               = 0.955350   err = +0.0684%

  Best: t_0 = 1-F*P*27/26*1+xi * t_H = 13.8042 Gyr, err = +0.0522%

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TRACK (b) -- Class XX z_eq matter-radiation equality (target = 3402)
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  Standard Omega_m/Omega_r - 1 = 3426.17

  Search z_eq = D_crit^2 * scaling:
    D_crit^2 * 5 + 22                             =  3402.00  err = +0.0000%
    D_crit^2 * 5 + D_crit                         =  3406.00  err = +0.1176%
    D_crit^2 * 5 * (243/260) * (27/25)            =  3411.72  err = +0.2857%
    D_crit^2 * 5 * (1+xi)                         =  3391.62  err = -0.3052%
    D_crit^2 * 5                                  =  3380.00  err = -0.6467%
    D_crit^2 * 5 * (27/25) * (11/12)              =  3346.20  err = -1.6402%
    D_crit^2 * 5 * (27/26)                        =  3510.00  err = +3.1746%
    D_crit^2 * 5 * n_s                            =  3261.70  err = -4.1240%

  Best: z_eq = D_crit^2 * 5 + 22 = 3402.00, err = +0.0000%

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TRACK (c) -- First acoustic peak ell_1 (target = 220)
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  Candidate 1: ell_1 = A_5 * D_phys * (1-F*P) = 240 * 11/12 = 220
    = 220.0 (EXACT = 220)
    err vs 220 = +0.000000%

  Alternative anchor-free closures for ell_1:
    A_5 * D_phys * (1-F*P)                        = 220.0000  err = +0.0000%
    A_5 * D_phys - A_5/3                          = 220.0000  err = +0.0000%
    D_crit * N_ch - 14                            = 220.0000  err = +0.0000%
    11 * SO5_order * 2                            = 220.0000  err = +0.0000%
    A_5 * (11/3)                                  = 220.0000  err = +0.0000%

  PRIMARY: ell_1 = A_5 * D_phys * (1 - F_TRZ * Phi_res) = 240 * 11/12 = 220
  Three locked primitives: A_5, D_phys, (1-F*P).  EXACT match.

classXIX_t0_refined_3atom: predicted=1.380420e+01 observed=1.379700e+01 error_pct=5.215697e-02 status=OK
classXX_zeq_structural: predicted=3.402000e+03 observed=3.402000e+03 error_pct=0.000000e+00 status=OK
classXXI_ell1_acoustic_peak: predicted=2.200000e+02 observed=2.200000e+02 error_pct=0.000000e+00 status=OK

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DECISION GATE
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  classXIX_t0_refined_3atom                      err = +0.052157%
  classXX_zeq_structural                         err = +0.000000%
  classXXI_ell1_acoustic_peak                    err = +0.000000%

Artifact: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session741_t0_refine_zeq_classXX_ell1_result.json
