{ "all_ok": true, "citations": { "exact_constant": "Bloch 2016; Wang, Wornell, Zheng 2016 (covert capacity constant)", "fading_mimo": "arXiv:2603.29645 (covert FBL over fading MIMO)", "srl": "Bash, Goeckel, Towsley \u2014 IEEE JSAC 2013 (square-root law)" }, "declared_model": { "covertness_metric": "block relative entropy D_n = n*d(g_w P) <= delta (nats)", "fading": "quasi-static normalized Rician power (unit mean, K-factor), CSIR; inverse-CDF quadrature, no RNG", "per_symbol_kl": "d(a) = a/sw2 - ln(1+a/sw2), a = g_w P (exact, complex Gaussian)", "regime": "low-SNR covert (P->0); dispersion vanishes -> no sqrt(V/n) penalty", "warden": "Gaussian (Neyman-Pearson optimal detector on Y_w=sqrt(g_w)X+N_w)" }, "detection_kl_budget": { "exact_quad_converges": true, "kl_at_budget_tight_all": true, "rows": [ { "exact_over_quad": 1.0296772533388117, "kl_at_budget_tight": true, "n": 256, "p_exact": 0.09101147103367654, "p_quad": 0.08838834764831845 }, { "exact_over_quad": 1.0147853259480448, "kl_at_budget_tight": true, "n": 1024, "p_exact": 0.04484759908915397, "p_quad": 0.04419417382415922 }, { "exact_over_quad": 1.0073792190994535, "kl_at_budget_tight": true, "n": 4096, "p_exact": 0.022260146157863512, "p_quad": 0.02209708691207961 }, { "exact_over_quad": 1.0036862336689734, "kl_at_budget_tight": true, "n": 16384, "p_exact": 0.011089270968920574, "p_quad": 0.011048543456039806 } ] }, "executed": true, "explicit_non_claim": "Leading order in 1/sqrt(n): the O(log n / n) higher-order term is DROPPED and disclosed, not claimed. NOT the fully-general MIMO converse of arXiv:2603.29645 (this implements the SISO / receive-diversity square-root law with the fading-quantile covert constant). CONVERSE SEMANTICS: kappa_eps bounds any covert scheme's rate OUTSIDE an eps channel outage IN THE MODEL; the achievability side is the exact-log capacity at the covert-feasible power (a leading-order sandwich, tight as n->inf), NOT a finite-n achievability certificate. Not OTA, not a product claim, not an FTO opinion.", "fading_outage_constant": { "by_k_and_diversity": { "K0": { "L1": { "kappa_eps": 0.10738309964176737, "kappa_median": 2.0402788931935794 }, "L2": { "kappa_eps": 0.29380746025449256, "kappa_median": 2.462834487485781 }, "L4": { "kappa_eps": 0.4575672955848276, "kappa_median": 2.695827391538946 } }, "K10": { "L1": { "kappa_eps": 0.7090866971302584, "kappa_median": 2.0402788931935785 }, "L2": { "kappa_eps": 0.9110465266676705, "kappa_median": 2.088856383627436 }, "L4": { "kappa_eps": 1.029463355504708, "kappa_median": 2.1128519207509138 } }, "K3": { "L1": { "kappa_eps": 0.2961309797106274, "kappa_median": 2.040278893193579 }, "L2": { "kappa_eps": 0.5533822093651009, "kappa_median": 2.1843259814440636 }, "L4": { "kappa_eps": 0.7158667460362607, "kappa_median": 2.2541669843421968 } } }, "diversity_raises_kappa_eps": true, "eps": 0.05 }, "flagship": { "covert_bits_ceiling": 65.8856547523013, "delta": 1.0, "eps": 0.05, "headline": "over quasi-static Rician-K10 fading with 4 Rx branches, at n=4096 uses and a 1-nat covertness budget, NO scheme covertly conveys more than ~65.89 bits outside a 5% channel outage \u2014 the square-root-law converse (a DETECTION limit, not a decoding one)", "k_factor": 10.0, "kappa_eps": 1.029463355504708, "n": 4096, "rx_diversity": 4 }, "honest_scope": "The covert square-root law converse is EXACT within the declared model (Gaussian warden, quasi-static Rician fading, low-SNR covert regime): the per-symbol KL is exact, the SRL constant is the LEADING-ORDER converse, the order is z3-certified, the fading outage constant is deterministic quadrature (no RNG), and the naive fixed-power twin is provably detected. MODEL, NOT OTA.", "naive_twin": { "block_kl_grows_linearly": true, "fixed_power": 0.05, "note": "a fixed-per-symbol-power scheme lets the block detection KL grow linearly in n, so it exceeds ANY covertness budget delta at large n -> Willie's optimal detector error ->0 -> DETECTED (the negative control the covert sqrt(1/n) power schedule avoids)", "provably_detected": true, "rows": [ { "block_kl_nats": 0.3097179726254069, "exceeds_delta": false, "n": 256 }, { "block_kl_nats": 1.2388718905016276, "exceeds_delta": true, "n": 1024 }, { "block_kl_nats": 4.95548756200651, "exceeds_delta": true, "n": 4096 }, { "block_kl_nats": 19.82195024802604, "exceeds_delta": true, "n": 16384 } ] }, "schema": "covert-fbl-v98c", "skipped": false, "square_root_law": { "kappa_awgn_unit": 2.0402788931935794, "per_use_rate_halves_per_4x_n": true, "rows": [ { "covert_bits_ceiling": 32.64446229109727, "n": 256, "per_use_rate_ceiling": 0.1275174308245987 }, { "covert_bits_ceiling": 65.28892458219454, "n": 1024, "per_use_rate_ceiling": 0.06375871541229935 }, { "covert_bits_ceiling": 130.57784916438908, "n": 4096, "per_use_rate_ceiling": 0.03187935770614968 }, { "covert_bits_ceiling": 261.15569832877816, "n": 16384, "per_use_rate_ceiling": 0.01593967885307484 } ], "total_covert_bits_double_per_4x_n": true }, "two_sided_band": { "band_nonempty_ach_below_conv": true, "band_tightens_with_n": true, "rows": [ { "band_ratio_ach_over_conv": 0.9570795861704656, "n": 256, "r_achievability_exactlog": 0.12566627042082207, "r_converse_linearized": 0.1313017979242947 }, { "band_ratio_ach_over_conv": 0.9782248655483494, "n": 1024, "r_achievability_exactlog": 0.06329252692583064, "r_converse_linearized": 0.06470140880169883 }, { "band_ratio_ach_over_conv": 0.9890323889489049, "n": 4096, "r_achievability_exactlog": 0.0317623820024462, "r_converse_linearized": 0.0321146024714132 }, { "band_ratio_ach_over_conv": 0.9944960172385455, "n": 16384, "r_achievability_exactlog": 0.015910381116693854, "r_converse_linearized": 0.015998436233935664 } ] }, "wall_banner_untouched": { "checked": true, "reference": { "slope": 5.673, "wall_1e5": 18.7858, "wall_1e6": 26.4421 }, "slope_db_per_decade": 5.673, "unchanged": true, "wall_1e5_db": 18.7858, "wall_1e6_db": 26.4421 }, "z3_ordering_lemma": { "name": "covert_srl_ordering", "proven": true, "tier": "z3-lra" } }