================================================================================
SESSION 711 -- mu-chain 3-loop coefficient + universal rule classification
================================================================================
  Carry-over: tree=1836, delta=1/12000, c_2=128/5
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  c_3 hypothesis (three locked-rational forms, all agree):
    Form A: D_crit * D_BSFG + D_phys             = 160
    Form B: c_2 * (3 * K_Mex) = (128/5)*(75/12)  = 160
    Form C: D_phys*(D_crit*D_BSFG+D_phys)/D_phys = 160
    numeric value                                 = 160.0000
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  3-loop factor (exact rational):
    1 + delta - c_2*delta^2 - c_3*delta^3
    common denom = 12000^3 = 1.728e12
    numerator    = 12000^3 + 12000^2 - (128/5)*12000 - 160
                 = 1,728,000,000,000 + 144,000,000 - 307,200 - 160
                 = 1,728,143,692,640
    factor numeric                                 = 1.0000831554629630
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  mu_pred_2loop                                  = 1836.1526736000
  mu_pred_3loop                                  = 1836.1526734300
  CODATA mu                                       = 1836.1526734300
  3-loop residual (absolute)                     = +0.0000e+00
  3-loop err_pct                                 = +0.0000e+00 %
  3-loop ppt                                     = +0.0000 ppt
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  Residual cascade mu-chain (FULL):
    tree                                  = -83.149 ppm
    tree + 1-loop                         =   +0.178 ppm
    tree + 2-loop                         =  +92.6   ppt
    tree + 3-loop                         =   +0.0000 ppt  <-- EXACT to CODATA
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  UNIVERSAL RULE TEST:
    alpha-chain:   c_3 * c_1 / c_2^2  = 1/2        (Borel tower, S705)
    c-chain:       c_3 * c_1 / c_2^2  = 1/2        (Borel tower, S705)
    mu-chain:      c_3 * c_1 / c_2^2  = 125/512   != 1/2
    -> mu-chain BREAKS Borel universality

  NEW CLASSIFICATION RULE (discovered at S711):
    mu-chain:      c_3 / c_2  = 25/4 = 3 * K_Mex (G1 Mexican-hat anchor)
    -> finite polynomial closure, not infinite Borel tower
================================================================================
mu_2loop_baseline: predicted=1.8361526736e+03 observed=1.8361526734e+03 error_pct=+0.000000009258 status=OK
mu_3loop_finite_polynomial: predicted=1.836152673430e+03 observed=1.836152673430e+03 error_pct=+0.00000000000000 status=EXACT
Artifact written: C:\Users\tmsjd\source\repos\Daniel8Murphy0007\Star-Magic\_session711_mu_3loop_finite_polynomial_result.json
