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KiHoLee 81c2be1d78 Verify the appendix bound against its stated constant
The check tested f(gamma) >= gamma/(gamma+1), but the manuscript claims
f(gamma) >= c1*gamma/(gamma+1) with c1 >= 0.97. It now tests the stated
constant and records the achieved one, 0.9711.
2026-08-26 13:53:55 +09:00

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{
"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
}
}