{
 "def2_beta": {
  "theory": 0.39,
  "empirical": 0.3870348174861091,
  "abs_err": 0.0029651825138909405
 },
 "lemma1_rho2_gamma1": {
  "theory": 0.07605,
  "empirical": 0.07755907030722882,
  "abs_err": 0.001509070307228813
 },
 "lemma1_rho2_gamma10": {
  "theory": 0.1382727272727273,
  "empirical": 0.13549989449940597,
  "abs_err": 0.0027728327733213265
 },
 "ofdma_ceiling": {
  "theory": 0.5,
  "empirical_mean": 0.49424545065943004,
  "empirical_std": 0.07545276320615535
 },
 "prop3_lmmse": {
  "mse_closed_form": 0.4824921051778264,
  "mse_empirical_wiener": 0.4821083056134569,
  "rel_diff": 0.0007960857755419693
 },
 "prop3_blind_eq_ofdma": {
  "max_abs_cos_diff": 4.440892098500626e-16
 },
 "appendix_f_bound": {
  "claimed_c1": 0.97,
  "holds_on_grid": true,
  "achieved_c1": 0.9710759305294567
 },
 "appendix_exp_ineq": {
  "holds": true
 },
 "concentration_residual": {
  "d64_residual": 0.125,
  "claimed_max": 0.13
 }
}