========================================================================
  D2 COMPANION: MEASURED REGGE TRIANGULATION OF deSITTER
THIS LETS US EXAMINE CONVERGENCE TO A NONZERO EH ACTION
========================================================================
   (k = 1/9, G = c = 1), proper window s = 0.8 
  levels n = [4, 6, 8, 10, 12, 14, 16]  (mesh scale h = s/n)

FLAT-SPACE NULL TEST (identity metric, same pipeline):
    n = 6: interior hinges = 16064, max|delta| = 7.11e-15
    [PASS] interior deficits vanish in flat space (threshold 1e-9)

deSITTER SERIES (outer window, r0 = 2.0=2/3 R_Lambda):
  r in [1.702, 2.298] R_Lambda/3, Kretschmann K = 2.9630e-01, sqrt(K) = 5.4433e-01
    n =   4: interior hinges =     1232, median|delta| = 3.283e-04, max|delta| = 5.218e-03   (0.0 s)volume = 4.023e-02,
    n =   6: interior hinges =    16064, median|delta| = 1.405e-04, max|delta| = 2.450e-03   (0.1 s)volume = 1.026e-01,
    n =   8: interior hinges =    75600, median|delta| = 7.661e-05, max|delta| = 1.417e-03   (0.3 s)volume = 1.523e-01,
    n =  10: interior hinges =   230144, median|delta| = 4.787e-05, max|delta| = 9.224e-04   (0.7 s)volume = 1.895e-01,
    n =  12: interior hinges =   549200, median|delta| = 3.312e-05, max|delta| = 6.479e-04   (1.5 s)volume = 2.179e-01,
    n =  14: interior hinges =  1121472, median|delta| = 2.422e-05, max|delta| = 4.799e-04   (2.7 s)volume = 2.401e-01,
    n =  16: interior hinges =  2054864, median|delta| = 1.831e-05, max|delta| = 3.697e-04   (4.8 s)volume = 2.577e-01,

  h      median|delta|   median|sur|   max|sur|    C3(abs)   C2(signed)        C1(Regge)
  0.2000     3.2833e-04      7.4559e-03     1.1697e-02     1.182e-07   +1.1807e-07     +3.7943e-02
  0.1333     1.4052e-04      3.3539e-03     5.3402e-03     2.021e-08   +2.0180e-08     +3.2696e-02
  0.1000     7.6612e-05      1.8987e-03     3.0470e-03     6.034e-09   +6.0246e-09     +3.0744e-02
  0.0800     4.7873e-05      1.2199e-03     1.9675e-03     2.396e-09   +2.3921e-09     +2.9729e-02
  0.0667     3.3124e-05      8.4808e-04     1.3746e-03     1.134e-09   +1.1315e-09     +2.9107e-02
  0.0571     2.4220e-05      6.2409e-04     1.0144e-03     6.039e-10   +6.0276e-10     +2.8687e-02
  0.0500     1.8307e-05      4.7829e-04     7.7929e-04     3.507e-10   +3.4998e-10     +2.8385e-02

  Doubling ratios log2[dens(h)/dens(h/2)]:
    n =  4 ->  8:  +4.292
    n =  6 -> 12:  +4.156
    n =  8 -> 16:  +4.105

  MEASURED exponents (least-squares over all levels):
    median|delta|        ~ h^2.08   (power counting: 2)
    |S_RS - S_Regge|/Vol ~ h^4.19   (power counting: 4)

deSITTER SERIES (inner window, r0 = 1.5= 1/2 R_Lambda):
  r in [1.154, 1.846] R_Lambda/3, Kretschmann K = 2.9630e-01, sqrt(K) = 5.4433e-01
    n =   4: interior hinges =     1232, median|delta| = 5.974e-04, max|delta| = 5.738e-03   (0.0 s)volume = 4.019e-02,
    n =   6: interior hinges =    16064, median|delta| = 2.600e-04, max|delta| = 2.806e-03   (0.1 s)volume = 1.027e-01,
    n =   8: interior hinges =    75600, median|delta| = 1.474e-04, max|delta| = 1.649e-03   (0.3 s)volume = 1.526e-01,
    n =  10: interior hinges =   230144, median|delta| = 9.323e-05, max|delta| = 1.082e-03   (0.7 s)volume = 1.901e-01,
    n =  12: interior hinges =   549200, median|delta| = 6.535e-05, max|delta| = 7.639e-04   (1.5 s)volume = 2.187e-01,
    n =  14: interior hinges =  1121472, median|delta| = 4.786e-05, max|delta| = 5.677e-04   (2.8 s)volume = 2.409e-01,
    n =  16: interior hinges =  2054864, median|delta| = 3.662e-05, max|delta| = 4.383e-04   (4.8 s)volume = 2.587e-01,

  h      median|delta|   median|sur|   max|sur|    C3(abs)   C2(signed)        C1(Regge)
  0.2000     5.9736e-04      7.5245e-03     1.2114e-02     1.175e-07   +1.1667e-07     +3.7973e-02
  0.1333     2.6002e-04      3.3670e-03     5.5864e-03     2.046e-08   +2.0238e-08     +3.2716e-02
  0.1000     1.4738e-04      1.9002e-03     3.2002e-03     6.168e-09   +6.0875e-09     +3.0759e-02
  0.0800     9.3225e-05      1.2207e-03     2.0706e-03     2.464e-09   +2.4280e-09     +2.9740e-02
  0.0667     6.5351e-05      8.4774e-04     1.4501e-03     1.170e-09   +1.1520e-09     +2.9115e-02
  0.0571     4.7860e-05      6.2429e-04     1.0733e-03     6.252e-10   +6.1501e-10     +2.8694e-02
  0.0500     3.6620e-05      4.7842e-04     8.2637e-04     3.638e-10   +3.5767e-10     +2.8390e-02

  Doubling ratios log2[dens(h)/dens(h/2)]:
    n =  4 ->  8:  +4.251
    n =  6 -> 12:  +4.128
    n =  8 -> 16:  +4.083

  MEASURED exponents (least-squares over all levels):
    median|delta|        ~ h^2.01   (power counting: 2)
    |S_RS - S_Regge|/Vol ~ h^4.16   (power counting: 4)

========================================================================
  Interpretation:
  * The deficit exponent ~2 and residual-density exponent ~4 are the
    D2 power-counting claims, now measured on a real triangulation
    with geometric dihedral angles, not generated by construction.
  * Coefficients are mesh/method dependent (chord-length edges);
    the exponent is the invariant content. Flat-space null test
    confirms zero curvature-independent artifact.
  * Regge -> EH convergence itself stays the external CMS input.
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