Bullet Cluster Path C Pipeline Summary
Charles Anthony Hyatt Battiste UM/FUM
USPTO 19/640,364 anchors

Locked framework constants:
  phi = 1.618033988749895
  alpha_struct = 0.0073032157
  Eidolon = 135.925985
  K_struct = 4*phi^3*Eidolon/3 = 767.7223
  g_critical = 1.0420e-10 m/s^2

Cluster-locus environmental parameters:
  eps_ext = 0.0
  eta_tid = 0.0
  Delta_ML = 0.05
  F_env = 1.0000
  F_ML^-1 = 0.9524

Lensing geometry:
  z_L = 0.296, z_S = 2.0
  Sigma_crit_lens = 4.7967e+00 kg/m^2

Sigma_baryon proxy:
  Source: JWST NIRCam F277W combined mosaic (Cha 2025 ICL filter)
  Conversion: 1 MJy/sr -> 6.50e+09 M_sun/Mpc^2 (stars * 6.5 baryon factor)
  Sigma range (kg/m^2): 0.000e+00 to 8.988e-04

kappa_pred stats:
  min = 0.0000e+00
  max = 2.9672e-03
  mean = 4.4526e-05

kappa_residual = kappa_observed - kappa_pred:
  min = 0.0387
  max = 2.8704
  RMS = 0.1822
  abs mean = 0.1449

Centroid separation: 17.72 arcsec