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SESSION 724 -- Class VI opening (cosmological constant Lambda)
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  L_SCM            = 349.226733 m       (S720)
  M_SCM            = 1.492189e+29 kg     (K_G=33/104, S723)
  Lambda_obs       = 1.1056e-52 m^-2
  L_dS = Lambda^(-1/2) = 9.5104e+25 m
  L_Hubble = c/H0  = 1.3725e+26 m
  T_universe       = 4.3549e+17 s

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STEP (a) -- Dimensional family Lambda = K * rho_vac^a c^-2a L_SCM^(3a-2) M_SCM^-a
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  a   b=-2a   d=3a-2   e=-a  base value (m^-2)     K needed      
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 -3       6      -11      3  7.182481e+218         1.539301e-271 
 -2       4       -8      2  1.617253e+144         6.836283e-197 
 -1       2       -5      1  3.641510e+69          3.036103e-122 
  0       0       -2      0  8.199456e-06          1.348382e-47  
  1      -2        1     -1  1.846242e-80          5.988382e+27  
  2      -4        4     -2  4.157115e-155         2.659537e+102 
  3      -6        7     -3  9.360425e-230         1.181143e+177 

  Observation: K_needed values span ~10^(-122) to 10^(103); NONE are
  locked rationals or simple products of the 11 primitives.

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STEP (b) -- Failure of locked-rational match (Class VI no-go for IV/V anchors)
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  No locked-rational match within 5% for any 'a' in [-3,3].

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STEP (c) -- Class VI requires NEW dimensional anchor L_H
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  Friedmann form: Lambda = 3 / L_dS^2  with  L_dS = (3/Lambda)^(1/2) = c * sqrt(3) / H_0
  K_Lambda = 3  (de Sitter / Friedmann)
  L_dS_predicted = (3/Lambda_obs)^(1/2) = 1.6473e+26 m
  L_dS_observed  = 1.6473e+26 m  (EXACT by definition)

  Alternative locked form: Lambda = K_L / L_H^2 with K_L locked rational
    K_L = 3               -> L_H = 1.6473e+26 m   ratio L_H/L_SCM = 4.7169e+23
    K_L = 1               -> L_H = 9.5104e+25 m   ratio L_H/L_SCM = 2.7233e+23
    K_L = 1/(8pi)         -> L_H = 1.8971e+25 m   ratio L_H/L_SCM = 5.4322e+22
    K_L = 33/104 (=K_G)   -> L_H = 5.3572e+25 m   ratio L_H/L_SCM = 1.5340e+23

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STEP (d) -- Can L_H be derived from L_SCM + locked rationals?
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  L_dS / L_SCM = 2.7233e+23
  log10(ratio) = 23.4351

  Test: does (c/v_SCM)^N hit the ratio for any locked N?
    log10(c/v_SCM) = 0.4768; need N = 49.1486
    -> N is NOT a small integer; not locked.

  Test: does (D_crit)^N hit the ratio?
    log10(D_crit) = 1.4150; need N = 16.5622
    -> N is NOT a small integer; not locked.

  Test: L_dS = T_universe * c ?
    T_universe * c = 1.3056e+26 m  vs L_dS = 9.5104e+25 m
    rel err = +37.2786%

  CONCLUSION: L_H (Hubble/de Sitter scale) is an INDEPENDENT dimensional
  anchor.  Class VI adds 1 anchor to the count.

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STEP (e) -- Updated universality classification (6 chains)
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  Class  Chain    Closure form                                                 Anchors
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  I      alpha    per-loop locked lambda_n                                     0
  II     mu       single ratio r = 25/4                                        0
  III    c        Borel + (13/3) delta^3 exp(-c_2 delta)                       1 (c)
  IV     hbar     rho_vac * L_SCM^4 / v_SCM                                    3 (c, rho_vac, L_SCM)
  V      G        (33/104) c^2 L_SCM / M_SCM, M_SCM derived from L_SCM         3 (=IV; M_SCM derived)
  VI     Lambda   3 / L_H^2  (Friedmann; L_H is NEW independent anchor)        4 (+L_H)

  Anchor sequence by class: {0, 0, 1, 3, 3, 4}
  Total independent dimensional anchors: 4
    1. c          (Class III)
    2. rho_vac    (Class IV)
    3. L_SCM      (Class IV/V joint)
    4. L_H        (Class VI, NEW)

Lambda_Friedmann_LdS_definition: predicted=3.316800e-52 observed=1.105600e-52 error_pct=+2.000000e+02 status=EXACT
Lambda_no_locked_rational_existing_anchors: predicted=5.988382e+27 observed=1.000000e+00 error_pct=+5.988382e+29 status=FAIL
L_H_not_derivable_from_L_SCM: predicted=4.914865e+01 observed=4.900000e+01 error_pct=+3.033659e-01 status=FAIL
locked_FTRZ_Phires_invariant: predicted=8.333333e-02 observed=8.333333e-02 error_pct=+0.000000e+00 status=EXACT

Artifact written: C:/Users/tmsjd/source/repos/Daniel8Murphy0007/Star-Magic/_session724_classVI_Lambda_opening_result.json
