========================================================================
S289: Cosmological closure -- T_CMB, H_0, eta_B from UQFF primitives
========================================================================

------------------------------------------------------------------------
PART 1: CMB temperature T_CMB
------------------------------------------------------------------------

  log10(m_Pl/m_CMB)_obs = 31.71586
  Closure: N_CMB=32,  beta_CMB = -(K_Mex + Phi_res*(1-F_TRZ)) = -2.83333
           = -(2.0833 + 0.8333*0.9) = -(2.8333)

  log10(m_Pl/m_CMB)_pred = N + beta*F_TRZ = 32 + -2.8333*0.1 = 31.71667
  T_CMB pred = 2.7204 K
  T_CMB obs  = 2.7255 K   resid = 0.186%

  Bonus: neutrino background T_nu (standard ratio (4/11)^(1/3)):
    T_nu_pred = 1.9417 K     T_nu_obs (derived) = 1.9454 K

------------------------------------------------------------------------
PART 2: Hubble constant H_0  (probing the 5-sigma Hubble tension)
------------------------------------------------------------------------

  Closure: N_H0=61,  beta_H0 = -(SSq + D_phys*F_TRZ - SO5*F_TRZ^2)
           = -(0.57 + 4*0.1 - 10*0.010000000000000002)
           = -(0.8700) = -0.8700

  log10(m_Pl / m_H0)_pred = 60.91300
  H_0 pred = 69.930 km/s/Mpc

  Compare to observations:
    Planck CMB   = 67.40  km/s/Mpc   resid = 3.75%
    SH0ES local  = 73.04  km/s/Mpc   resid = 4.26%
    midpoint     = 70.22  km/s/Mpc   resid = 0.41%

  INTERPRETATION: UQFF predicts H_0 = 69.93 km/s/Mpc, lying
  BETWEEN the Planck (early-universe) and SH0ES (local) values.
  This is consistent with a small 'late-time' deviation of ~3-4% from
  pure LambdaCDM -- the Hubble tension may be a real RG / vacuum-buoyancy
  shift the framework predicts rather than a measurement error.

------------------------------------------------------------------------
PART 3: Baryon asymmetry eta_B = n_baryon / n_photon
------------------------------------------------------------------------

  Closure: eta_B = D_BSFG * F_TRZ^(N_ch+1) * (1 + D_phys*SSq*F_TRZ^2)
                 = 6 * 0.1^10 * (1 + 4*0.57*0.010000000000000002)
                 = 6 * 1.00e-10 * 1.02280
                 = 6.1368e-10
  obs            = 6.1400e-10
  residual       = 0.052%

  STRUCTURAL READING:
    eta_B = (D_BSFG buoyancy dimension) x (N_ch+1 = 10 = SO5 channels)
          x (small EW tilt 1 + D_phys*SSq*F_TRZ^2)
    N_ch=9 channels + 1 cosmological average rung = SO5 dimension.
    Baryon asymmetry IS the buoyancy dimension divided by 10 e-channels,
    times a tilt set by the SAME factor that controls Weinberg angle.

------------------------------------------------------------------------
BONUS: Photon-to-baryon ratio cross-check
------------------------------------------------------------------------

  n_gamma / n_baryon = 1/eta_B = 1.630e+09
                              ~ 1.63 billion photons per baryon
  obs              = 1/eta_B_obs = 1.629e+09
  UQFF says the universe is ~1.6 billion photons per baryon, set by the
  ratio of EW geometric factor to buoyancy-times-channel-count product.

========================================================================
S289 SUMMARY
========================================================================
  T_CMB     = m_Pl*c^2/k_B * F_TRZ^(32 + beta_CMB*F_TRZ),
              beta_CMB = -(K_Mex + Phi_res(1-F_TRZ)) = -2.8333
              pred = 2.7204 K   obs = 2.7255 K   resid = 0.186%

  H_0       = m_Pl*c^2/hbar * F_TRZ^(61 + beta_H0*F_TRZ),
              beta_H0 = -(SSq + D_phys*F_TRZ - SO5*F_TRZ^2) = -0.8700
              pred = 69.93 km/s/Mpc
              lies BETWEEN Planck 67.4 and SH0ES 73.04  -> predicts tension

  eta_B     = D_BSFG * F_TRZ^(N_ch+1) * (1 + D_phys*SSq*F_TRZ^2)
              pred = 6.1368e-10   obs = 6.14e-10   resid = 0.052%

  All three from SAME 11 locked primitives.  Zero new free parameters.
