================================================================================
SESSION 727 -- derive exponent 42 + close Lambda ratio
================================================================================
  L_H_obs            = 1.647258e+26 m
  L_H/L_SCM target   = 4.716872e+23
  (c/v_SCM)          = 2.997925

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TRACK (a) -- structural derivation hunt for exponent 42
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  Integer combinations evaluating to 42:
    D_crit + 2 D_BSFG + 2 D_phys             =  46.0000
    D_crit + D_BSFG + 2 D_phys               =  40.0000
    D_crit + D_BSFG + N_ch + 1               =  42.0000 <-- MATCH 42
    D_crit + 2 SO5 - D_phys                  =  42.0000 <-- MATCH 42
    D_crit + D_phys + 3 D_phys               =  42.0000 <-- MATCH 42
    D_crit + 4 D_phys                        =  42.0000 <-- MATCH 42
    D_crit + SO5 + D_BSFG                    =  42.0000 <-- MATCH 42
    (D_crit-1) + N_ch + SO5 - 3              =  41.0000
    7 D_phys + D_crit - 12                   =  42.0000 <-- MATCH 42
    A_5 - 3 D_phys - D_BSFG                  =  42.0000 <-- MATCH 42
    A_5 - D_crit - D_phys + 12               =  42.0000 <-- MATCH 42
    D_crit + SO5 + N_ch - 3                  =  42.0000 <-- MATCH 42
    N_ch + D_BSFG + D_crit + 1               =  42.0000 <-- MATCH 42
    K_Mex * SO5 * D_phys + 2                 =  85.3333
    D_crit * Phi_res + ...                   =   0.0000

  Found 10 integer expressions = 42.
  Most parsimonious: 'D_crit + 4*D_phys' (26 + 16)
  String-theory reading: D_crit (26 bosonic) + 4 copies of D_phys (4D spacetime)
                        = 'critical dim + four space-time slots'
  Alternative parsimony: 'D_crit + SO5 + D_BSFG' (26 + 10 + 6)
                        = critical + Lie-group order + BSFG fiber dim

  Sub-0.1% L_H hit density per p-value (window p in [0,59]):
     p   #hits
    28       2
    42       3 <-- 42
    55       3
    56       1
  Total hits: 9; avg hits per active p: 2.25
  Hits at p=42: 3
  p=42 is NOT distinguished from neighbors.

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TRACK (b) -- full (p,q,K) search for rho_Lambda / rho_vac_SCm
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  rho_Lambda           = 5.923711e-27 J/m^3
  rho_vac_SCm          = 7.090000e-37 J/m^3
  ratio (target)       = 8.355022e+09  (log10 = 8.3550e+09 ...)
  log10(ratio)         = 9.921948
  Top sub-1% (p,q,K) hits:
  rank    p    q  K name                               K val       predicted     rel err
  1       9    4  1-F_TRZ*27/26                     0.934615      8.3543e+09    -0.0081% <-- SUB-0.1%
  2       9    4  27/26*1-F_TRZ                     0.934615      8.3543e+09    -0.0081% <-- SUB-0.1%
  3      28   -3  D_BSFG/1-F*P                      6.545455      8.3560e+09    +0.0119% <-- SUB-0.1%
  4      17    0  A_5/1-F*P                        65.454545      8.3539e+09    -0.0129% <-- SUB-0.1%
  5      18    1  1-F*P*1-F*P                       0.840278      8.3593e+09    +0.0510% <-- SUB-0.1%
  6      21    0  1-F_TRZ*1-F_TRZ                   0.810000      8.3506e+09    -0.0524% <-- SUB-0.1%
  7       1    7  K_Mex/D_BSFG                      0.347222      8.3607e+09    +0.0677% <-- SUB-0.1%
  8      10    3  N_ch*1-F_TRZ                      8.100000      8.3486e+09    -0.0772% <-- SUB-0.1%
  9      10    3  1-F_TRZ*N_ch                      8.100000      8.3486e+09    -0.0772% <-- SUB-0.1%
  10     12    4  K_Mex/A_5                         0.034722      8.3628e+09    +0.0925% <-- SUB-0.1%
  11     14    3  beta_i/D_BSFG                     0.100483      8.3657e+09    +0.1282% *
  12     11    4  F_TRZ*27/26                       0.103846      8.3428e+09    -0.1464% *
  13     11    4  27/26*F_TRZ                       0.103846      8.3428e+09    -0.1464% *
  14     11    4  27/26/SO5                         0.103846      8.3428e+09    -0.1464% *
  15     19   -1  A_5/K_G                         189.090909      8.3424e+09    -0.1512% *
  16     19   -1  A_5*1/K_G                       189.090909      8.3424e+09    -0.1512% *
  17     19   -1  1/K_G*A_5                       189.090909      8.3424e+09    -0.1512% *
  18     25    0  beta_i/A_5                        0.010048      8.3678e+09    +0.1530% *
  19     22   -1  D_phys/SSq                        7.017544      8.3419e+09    -0.1565% *
  20      0    7  27/26                             1.038462      8.3407e+09    -0.1711% *

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DECISION GATE
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  Track (a): 10 integer-locked derivations of '42' found.
  Track (b): best Lambda-ratio closure = -0.0081%; sub-0.1% count = 10.

  VERDICT: FRAMEWORK CLOSED at 14 constants (3 dimensional + 11 dimensionless)

L_H_exponent_42_derivation_count: predicted=1.000000e+01 observed=1.000000e+01 error_pct=+0.000000e+00 status=EXACT
rhoLambda_ratio_best_locked: predicted=8.354350e+09 observed=8.355022e+09 error_pct=-8.052621e-03 status=OK
L_H_p42_parsimony: predicted=4.200000e+01 observed=4.200000e+01 error_pct=+0.000000e+00 status=EXACT
locked_FTRZ_Phires_invariant: predicted=8.333333e-02 observed=8.333333e-02 error_pct=+0.000000e+00 status=EXACT
locked_K_G_value: predicted=3.173077e-01 observed=3.173077e-01 error_pct=+0.000000e+00 status=EXACT

Artifact written: C:/Users/tmsjd/source/repos/Daniel8Murphy0007/Star-Magic/_session727_LH42_Lambda_closure_result.json
