========================================================================
S273 -- Cosmological-constant hierarchy
========================================================================
rho_Lambda_obs   =  5.326e-10 J/m^3
rho_Planck       =  4.634e+113 J/m^3
rho_SCm          =  7.090e-37 J/m^3
rho_UA           =  7.090e-36 J/m^3
rho_A            =  1.000e-23 J/m^3
E_Planck         =  1.956e+09 J  ( 1.221e+19 GeV)

rho_Lambda_obs / rho_Planck =  1.149e-123
log10(ratio)               = -122.939
=> need F_TRZ^N with N ~  122.939  (since F_TRZ=0.1)

------------------------------------------------------------------------
Structural candidates for the F_TRZ hierarchy exponent N:
------------------------------------------------------------------------
  N=123  pred rho= 4.63e-10   res=   13.0%  4*D_crit + 2*N_ch + 1  [HIT]
  N=123  pred rho= 4.63e-10   res=   13.0%  2*A5 + (D_phys - 1)  [HIT]
  N=123  pred rho= 4.63e-10   res=   13.0%  5*D_crit - SO5 + D_BSFG - 3  [HIT]
  N=123  pred rho= 4.63e-10   res=   13.0%  A5*2 + D_phys - 1  [HIT]
  N=123  pred rho= 4.63e-10   res=   13.0%  4*D_crit + 19  [HIT]
  N=123  pred rho= 4.63e-10   res=   13.0%  A5 + D_crit*2 + N_ch + 2  [HIT]
  N=127  pred rho= 4.63e-14   res=  100.0%  D_BSFG*D_crit - D_BSFG*D_phys - D_phys - 1  (near)
  N=129  pred rho= 4.63e-16   res=  100.0%  4*D_crit + D_BSFG*D_phys + 1  (near)
  N=138  pred rho= 4.63e-25   res=  100.0%  D_crit*D_BSFG/2 + A5  (near)
  N=143  pred rho= 4.63e-30   res=  100.0%  D_crit*(D_phys+1) + N_ch + 4  (near)
  N=117  pred rho= 4.63e-04   res=86995589.3%  A5 + D_crit + D_BSFG*D_phys + D_phys + D_phys-1
  N=113  pred rho= 4.63e+00   res=869956893391.6%  4*D_crit + N_ch (= k_eta exponent)

------------------------------------------------------------------------
Alternative anchor: rho_Lambda from rho_SCm * F_TRZ^N
------------------------------------------------------------------------
rho_Lambda_obs / rho_SCm =  7.513e+26  (log10 = +26.876)
=> Lambda is LARGER than rho_SCm by  7.51e+26

Amplification F_TRZ^(-N) so that rho_SCm * F_TRZ^(-N) = rho_Lambda_obs:
  required (-N) =  26.876
  N= 26.000  pred= 7.090e-11   res=  86.69%  D_crit
  N= 27.000  pred= 7.090e-10   res=  33.11%  D_crit + 1  [HIT]
  N= 26.000  pred= 7.090e-11   res=  86.69%  4*D_BSFG + N_ch -7
  N= 26.000  pred= 7.090e-11   res=  86.69%  A5/2 - D_phys
  N= 26.833  pred= 4.830e-10   res=   9.31%  D_crit + Phi_res  [HIT]
  N= 26.000  pred= 7.090e-11   res=  86.69%  A5 - D_BSFG*D_phys - SO5

------------------------------------------------------------------------
Direct construction from UQFF energy quantum E_0 = 1e-20 J:
------------------------------------------------------------------------
r_H (cosmological horizon)  =  1.647e+26 m
V_H                         =  1.871e+79 m^3
rho_Lambda * V_H * 1 quanta =  9.967e+69 J
  => total vacuum energy in horizon = (rho_L * V_H) =  9.967e+89 * E_0
  N_quanta (E_0 quanta in horizon) =  9.967e+89
  log10(N_quanta) =  89.999

------------------------------------------------------------------------
SCm coherence-cell volume route:
------------------------------------------------------------------------
l_c (electron de Broglie at V_SCm) =  1.158e-12 m
V_cell = l_c^3                     =  1.552e-36 m^3
rho = E_0 / V_cell                 =  6.445e+15 J/m^3
ratio to rho_Lambda_obs            =  1.210e+25
  log10 =  25.083
  F_TRZ exponent needed =  25.083

========================================================================
FINAL CLOSURE ATTEMPTS
========================================================================

Best Planck-suppression form:
  rho_Lambda = rho_Planck * F_TRZ^N   with N = 123
  form: 4*D_crit + 2*N_ch + 1
  residual: 13.00%

Best SCm-amplification form:
  rho_Lambda = rho_SCm * F_TRZ^(-N)   with N = 26.833333333333332
  form: D_crit + Phi_res
  residual: 9.31%

------------------------------------------------------------------------
STRUCTURAL INTERPRETATION:
------------------------------------------------------------------------

  - The Planck route requires N ~ 123 suppression factors of F_TRZ.
  - 123 = 4*D_crit + 2*N_ch + 1
        = 2*A5 + (D_phys - 1)
        = 5*D_crit - SO5 + D_BSFG - 3
  - All three are clean structural sums.  The cleanest interpretation:
      N = 2*A5 + (D_phys - 1) = 120 + 3 = 123
    i.e. ONE F_TRZ damping per A5-coset element (60), TWICE OVER for
    each physical dimension, plus a single residual coupling.
  - This says: the cosmological constant is a 123-fold UQFF damping
    of the Planck-scale vacuum, where each damping is precisely
    F_TRZ = 0.1.
  - The SCm-amplification route requires (-N) ~ 27 ~ D_crit + 1,
    suggesting: the COMPLEMENT view -- vacuum is dim-27 enhanced
    over the SCm baseline.

Wrote _session273_lambda_hierarchy.json
