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SESSION 719 -- hbar-chain dimensional class probe
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Dimensional analysis:
    [hbar] = J*s requires d=4 in L  (length appears as L^4 always)
    Free exponent in (c/v_SCM); no exponent eliminates the L^4 anchor

    => hbar requires an EXTERNAL length anchor L_DPM beyond the
       locked primitives + {c, v_SCM, rho_vac}.  This is a structural
       distinction from alpha (dimensionless), mu (dimensionless),
       and c (length/time ratio).

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Back-solve implied DPM length anchor (Form A, C_locked = 1):
    L_DPM^4 = hbar * v_SCM / rho_vac = 1.487407e+10 m^4
    L_DPM   = 349.226733 m
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Locked-rational structural search for L_DPM:

  candidate                                 value (m)      rel err vs L_DPM
  ----------------------------------------  -------------  -------------
  (c/v_SCM)^3 * 13                             350.272031  2.9932e-03 <-- closest
  (c/v_SCM)^3 * 12                             323.328029  7.4160e-02
  c_2 * 64                                     350.919268  4.8465e-03
  K_Mex * 168                                  350.000000  2.2142e-03 <-- closest
  pi^4 * 3.6                                   350.672728  4.1406e-03
  (D_crit/D_BSFG) * 81                         351.000000  5.0777e-03
  Phi_res * 420                                350.000000  2.2142e-03
  (c/v_SCM)^4 * 4.32                           348.952696  7.8470e-04 <-- closest
  c_2^2 * 11.63                                349.650534  1.2135e-03
  13/3 * 80.69                                 349.656667  1.2311e-03

  Closest locked candidate: (c/v_SCM)^4 * 4.32  (rel err 7.85e-04)

  Verdict: every candidate REQUIRES a non-locked numerical factor
           (13, 12, 64, 168, 3.6, 81, 420, 4.32, 11.63, 80.69 -- none
           are products of {F_TRZ, Phi_res, SSq, K_Mex, beta_i,
           D_phys, D_BSFG, D_crit, N_ch, SO5, A_5}).

  => L_DPM is NOT reachable from the 11 locked primitives.
     hbar-chain is CLASS IV: requires an external SCM length scale.

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UNIVERSALITY CLASSIFICATION (extended to 4 chains):
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  Class   Chain   Closure form                                      Anchor
  ------  ------  ------------------------------------------------  ------
  I       alpha   c_n = lambda_n * c_2^(n-1) / (n-1)!               per-loop locked rationals (15/7, 19/12)
  II      mu      c_n = c_2 * r^(n-2)                               single locked ratio r = 3*K_Mex = 25/4
  III     c       Borel + (D_crit/D_BSFG) * delta^3 * exp(-c_2*delta)  additive damped geom phase, rank 13/3
  IV      hbar    rho_vac * L_DPM^4 / v_SCM                         requires external length anchor L_DPM ~ 350 m

hbar_classIV_dimensional_identity: predicted=1.487407358251e+10 observed=1.487407358251e+10 error_pct=+0.000000e+00 status=EXACT
hbar_classIV_locked_rational_match: predicted=3.492267331920e+02 observed=3.489526964043e+02 error_pct=+0.078470 status=FAIL

Artifact written: C:/Users/tmsjd/source/repos/Daniel8Murphy0007/Star-Magic/_session719_hbar_dimensional_class_probe_result.json
