Ciphertext-only family enumeration, and checks that reproduce off a GPU

check_family_enum.py measures the attack the manuscript now states in
Section III-A: the winning correlation is an index-free verifier, so
ranking the 63 non-constant Walsh rows by mean winning correlation
recovers the user set from one frame in 0.905 of 200 trials at 10 dB
and from four frames in 0.990, using nothing outside the stated threat
model. Under the invariance refresh it recovers it in none, because the
entry permutation relabels the codebook the adversary must align
against.

V8 and V9 read the trained codebook through main_model(), which
retrains on every call, and a codebook trained on CUDA is not the one
trained on CPU. The shipped verify_math.csv therefore read PASS here
and FAIL for anyone running this package without a GPU. model_main.pt
is 7 KB and fixes the codebook, which is what both checks are about;
delete it to retrain. V1-V11 now pass on both.

New checks: V10, the format-matched OMA reference Section VI-B quotes,
and V11, the closed-form against Monte Carlo comparison the manuscript
claimed and never stored. V3a's bias-linearity result was computed and
printed but never written to the CSV, so the one linearity claim the
paper quotes was the one this package could not show.

check_consistency.py gains 21 assertions, covering five data files that
no assertion read (users, csi, semantic, cov_attack, sec_jam) and the
trend claims it structurally could not see, since it compared values
and not shapes.

README: the figure map named stages that do not write the artifacts
they list, so following it did not reproduce Figs. 4 and 6; the
reproduction block was five scripts short; and the refresh numbers were
from a superseded run (nearly three, 15.0 to 64.8 bits) against the
manuscript's 2.3 and 23.8 to 364.6.

README.md

@@ -31,7 +31,7 @@ code/
   exp_permkpa.py        permutation-key known-plaintext attack (Fig. 7)
   check_cov_*.py        ciphertext-only covariance-attack checks (referee M1)
   exp_real_sec.py       stage G: real BERT WordPiece token streams
-  verify_math.py        closed-form checks V1-V5, PASS/FAIL and verify_math.csv
+  verify_math.py        closed-form checks V1-V11, PASS/FAIL and verify_math.csv
   replot_security.py    every result figure, from data/ to fig/
   make_tables.py        LaTeX rows of every result table, from data/
   feasibility_security.py   early CPU-sized study, kept for the record
@@ -53,6 +53,12 @@ python exp_full.py           # stages A-F and L
 python exp_kpa.py            # known-plaintext attack
 python exp_refresh.py        # the key-refresh layer
 python exp_real_sec.py       # real token streams
+python exp_permkpa.py        # permutation-key known plaintext
+python exp_infotheory.py     # mutual information and equivocation
+python exp_semantic.py       # semantic-similarity leakage
+python exp_users_csi.py      # load and channel-estimate sweeps
+python check_cov_attack.py   # ciphertext-only covariance attack
+python check_family_enum.py  # ciphertext-only enumeration of the key family
 python replot_security.py    # all figures from the CSVs
 python make_tables.py        # LaTeX rows of the result tables
 ```
@@ -77,9 +83,9 @@ Logarithms in an entropy or an information rate are base two.
 |---|---|---|
 | Fig. 2 SER against SNR | `exp_full.stage_A` | `sec_snr.csv` |
 | Fig. 3 key length | `exp_full.stage_B` | `sec_keylen.csv` |
-| Fig. 4 jamming (4 schemes) | `exp_full.stage_L` | `sec_jam_cmp.csv`, `sec_jam.csv` |
+| Fig. 4 jamming (4 schemes) | `exp_full.stage_C`, `stage_L` | `sec_jam_cmp.csv`, `sec_jam.csv` |
 | Fig. 5 key sensitivity | `exp_full.stage_I` | `sec_sens_cmp.csv` |
-| Fig. 6 brute-force search | `exp_full.stage_J` | `sec_brute_cmp.csv`, `sec_brute.csv` |
+| Fig. 6 brute-force search | `exp_full.stage_I`, `stage_F`, `stage_J` | `sec_brute_cmp.csv`, `sec_brute.csv` |
 | Fig. 7 known-plaintext attack | `exp_kpa`, `exp_permkpa` | `kpa.csv`, `pkpa.csv` |
 | Fig. 8 real token streams | `exp_real_sec` | `real_sec_ter.csv` |
 | Scheme comparison table | `exp_full.stage_E` | `sec_compare.csv` |
@@ -103,8 +109,8 @@ measures. The key must therefore be refreshed per coherence block from a shared
 seed. `exp_refresh.py` implements that layer and shows why it has to
 draw from the transformations that leave the decision statistic
 invariant: a refresh that installs fresh orthogonal keys instead costs
-the legitimate users a factor of nearly three, while the invariant
+the legitimate users a factor of 2.3, while the invariant
-refresh costs nothing and raises the per-block key from 15.0 to 64.8
+refresh costs nothing and raises the per-block key from 23.8 to 364.6
 bits.
 
 ## License

code/check_consistency.py

@@ -268,6 +268,92 @@ chk("secrecy rate 14.87 of 14.93",
     "%s of %s" % (it["secrecy_rate_refresh_bits"], it["mi_legit_bits"]))
 
 
+_fe = {(float(r["snr_db"]), int(r["n_frames"]), r["keying"]): float(r["recovery"])
+       for r in rows("family_enum.csv")}
+chk("family enumeration recovers the user set at 10 dB",
+    abs(_fe[(10.0, 1, "fixed")] - 0.905) < 5e-3
+    and abs(_fe[(10.0, 4, "fixed")] - 0.990) < 5e-3,
+    "N=1 %.3f, N=4 %.3f" % (_fe[(10.0, 1, "fixed")],
+                            _fe[(10.0, 4, "fixed")]))
+chk("the refresh defeats the family enumeration",
+    _fe[(10.0, 2, "refreshed")] == 0.0,
+    "%.3f over 200 blocks" % _fe[(10.0, 2, "refreshed")])
+
+# --- trends, which the value assertions above cannot see ---------------
+_snr = rows("sec_snr.csv")
+_lg = [float(r["legit"]) for r in _snr]
+chk("legitimate SER falls monotonically with SNR",
+    all(a > b for a, b in zip(_lg, _lg[1:])), "%d points" % len(_lg))
+chk("legitimate below the binary OMA reference at every SNR",
+    all(float(r["legit"]) < float(r["oma"]) for r in _snr),
+    "min margin %.3f" % min(1 - float(r["legit"]) / float(r["oma"])
+                            for r in _snr))
+_kl = rows("sec_keylen.csv")
+chk("legitimate SER falls monotonically with key length",
+    all(float(a["legit_ser"]) > float(b["legit_ser"]) for a, b in zip(_kl, _kl[1:])),
+    "%d lengths" % len(_kl))
+chk("legitimate surpasses the reference from L=16 onward",
+    all(float(r["legit_ser"]) < float(r["oma"]) for r in _kl
+        if r["oma"] != "nan" and int(float(r["L"])) >= 16),
+    "checked L>=16")
+_ter = rows("real_sec_ter.csv")
+chk("legitimate TER below OMA over the whole range",
+    all(float(r["ter_legit"]) < float(r["ter_oma"]) for r in _ter),
+    "%d points" % len(_ter))
+chk("outsider TER stays above 0.9991",
+    min(float(r["ter_eve"]) for r in _ter) > 0.9991,
+    "min %.6f" % min(float(r["ter_eve"]) for r in _ter))
+
+# --- files no assertion read ------------------------------------------
+_us = rows("users.csv")
+chk("keys stay exactly orthogonal at every load",
+    all(float(r["mask_xcorr"]) == 0.0 for r in _us),
+    "U up to %s" % _us[-1]["users"])
+chk("eavesdropper never leaves chance across the load sweep",
+    all(float(r["eve_ser"]) > 0.999 for r in _us),
+    "min %.6f" % min(float(r["eve_ser"]) for r in _us))
+_u = {r["users"]: r for r in _us}
+chk("load endpoints 0.027 and 0.946",
+    abs(float(_u["2"]["legit_ser"]) - 0.027) < 5e-4
+    and abs(float(_u["32"]["legit_ser"]) - 0.946) < 5e-4,
+    "%.4f, %.4f" % (float(_u["2"]["legit_ser"]),
+                    float(_u["32"]["legit_ser"])))
+chk("the OMA crossing lies between U=16 and U=32",
+    float(_u["16"]["legit_ser"]) < float(_u["16"]["oma"])
+    and float(_u["32"]["legit_ser"]) > float(_u["32"]["oma"]),
+    "16: %.3f<%.3f, 32: %.3f>%.3f"
+    % (float(_u["16"]["legit_ser"]), float(_u["16"]["oma"]),
+       float(_u["32"]["legit_ser"]), float(_u["32"]["oma"])))
+_csi = rows("csi.csv")
+chk("phase residual moves the rate to 0.057 at 0.2 rad",
+    any(abs(float(r["legit_ser"]) - 0.057) < 1e-3 for r in _csi),
+    "%d rows" % len(_csi))
+_sem = rows("semantic.csv")
+chk("legitimate similarity at least 0.96 in both spaces",
+    all(float(r["legit"]) >= 0.96 for r in _sem if r["snr_db"] == "10.0"),
+    "%d rows" % len(_sem))
+_cov = rows("cov_attack.csv")
+chk("covariance attack reaches 0.26 at 300 same-key frames",
+    any(r["n_frames"] == "300" and abs(float(r["eve_ser"]) - 0.26) < 0.01
+        for r in _cov),
+    "%d rows" % len(_cov))
+chk("unjammed reference is 0.053",
+    abs(col("sec_jam.csv", "nojam")[0] - 0.053) < 0.05, "sec_jam.csv read")
+
+# --- the closed-form checks the manuscript quotes ----------------------
+_vm = {r["check"]: r for r in rows("verify_math.csv")}
+for _k, _c in [("V8 cross-period remainder", 0.0005),
+               ("V9 score-variance ratio", 0.05),
+               ("V10 format-matched OMA at 10 dB", 0.001),
+               ("V3a bias slope in kappa", 0.03)]:
+    chk("stored check %s passes" % _k.split()[0],
+        _k in _vm and _vm[_k]["verdict"] == "PASS"
+        and float(_vm[_k]["abs_err"]) <= _c,
+        _vm[_k]["empirical"] if _k in _vm else "row missing")
+chk("format-matched OMA quoted as 0.055",
+    "$0.055$ at $10$~dB against the proposed" in tex, "Section VI-B",
+    needs_tex=True)
+
 # --- tables against their generator -----------------------------------
 # Every printed table cell must be the one make_tables.py derives from
 # data/, so a rerun that moves a number cannot leave the manuscript behind.

code/check_family_enum.py

@@ -0,0 +1,113 @@
+# -*- coding: utf-8 -*-
+"""Ciphertext-only enumeration of the structured key family.
+
+Section III-A states that the winning correlation is itself an
+index-free verifier: with the right key the winning score is of order
+1/c, with a wrong key of order 1/sqrt(L). That makes the finite
+structured family exhaustible by an adversary that never sees a
+transmitted index, which is why the refresh of Section V-C is required
+rather than optional. This script is the measurement behind that
+claim.
+
+The attack. The threat model grants the adversary the public codebook,
+the key family and its distribution, the channel model and the
+normalizer, and it uses exactly those. For each of the L-1 non-constant
+Walsh-Hadamard rows the adversary de-masks the received frame with that
+row and records the mean winning per-digit correlation over N frames,
+then keeps the U highest-scoring rows. It reads only the size of the
+peak, never which candidate won, so no transmitted index is touched.
+
+It also runs the same attack against a refreshed key. The per-block
+sign draw and entry permutation relabel the codebook the adversary
+would have to align against, and the attack fails there.
+
+Writes data/family_enum.csv.
+"""
+from __future__ import annotations
+
+import math
+from pathlib import Path
+
+import torch
+
+from exp_full import base_keys, main_model
+from sse_lib import DEVICE, rayleigh_gain, snr_to_sigma2, write_csv
+
+DATA = Path(__file__).resolve().parents[1] / "data"
+TRIALS = 200
+SEED = 8131
+
+
+@torch.no_grad()
+def _observe(m, keys, snr_db, n, g):
+    """n superposed frames under the given key set, seen by Eve.
+
+    Eve has her own flat-fading gain and knows it, which is the
+    strongest reading of the threat model.
+    """
+    Bn = m.unit_codebook()
+    idx = torch.randint(m.vu, (n, m.users, m.P), generator=g, device=DEVICE)
+    e = Bn[idx] / math.sqrt(m.P)                     # (n,U,P,L)
+    y = (e * keys[None, :, None, :]).sum(dim=1) / m.c   # (n,P,L)
+    h = rayleigh_gain((n, 1, 1), device=DEVICE)
+    sig = float(snr_to_sigma2(torch.tensor(snr_db), m.d).sqrt())
+    rx = h * y + sig * torch.randn(n, m.P, m.L, generator=g, device=DEVICE)
+    return rx / h
+
+
+@torch.no_grad()
+def _peak_scores(m, r, cand, Bn):
+    """Mean winning per-digit correlation for every candidate row."""
+    out = torch.empty(cand.shape[0])
+    for k in range(cand.shape[0]):
+        z = torch.einsum("npl,vl->npv", r * cand[k][None, None, :], Bn)
+        out[k] = z.max(dim=2).values.mean()
+    return out
+
+
+def run():
+    torch.manual_seed(SEED)
+    m = main_model()   # trains, so not under no_grad
+    _attack(m)
+
+
+@torch.no_grad()
+def _attack(m):
+    keys = m.masks()                                 # (U,L) the true rows
+    cand = base_keys(m.L - 1, m.L).to(DEVICE)        # every non-constant row
+    Bn = m.unit_codebook() / math.sqrt(m.P)
+    rows = []
+
+    for snr in (0.0, 10.0, 20.0):
+        for n in (1, 2, 4):
+            hit = 0
+            for t in range(TRIALS):
+                g = torch.Generator(device=DEVICE).manual_seed(
+                    SEED + 1000 * int(snr) + 10 * n + t)
+                r = _observe(m, keys, snr, n, g)
+                top = _peak_scores(m, r, cand, Bn).topk(m.users).indices
+                hit += int(set(int(i) for i in top) == set(range(m.users)))
+            rows.append((snr, n, "fixed", hit / TRIALS))
+            print("  %4.0f dB  N=%d  fixed      recovery %.3f"
+                  % (snr, n, hit / TRIALS))
+
+    hit = 0
+    for t in range(TRIALS):
+        g = torch.Generator(device=DEVICE).manual_seed(SEED + 77 + t)
+        perm = torch.randperm(m.L, generator=g, device=DEVICE)
+        sign = torch.randint(2, (m.L,), generator=g,
+                             device=DEVICE) * 2.0 - 1.0
+        rk = (keys * sign[None, :])[:, perm]
+        r = _observe(m, rk, 10.0, 2, g)
+        top = _peak_scores(m, r, cand, Bn).topk(m.users).indices
+        hit += int(set(int(i) for i in top) == set(range(m.users)))
+    rows.append((10.0, 2, "refreshed", hit / TRIALS))
+    print("    10 dB  N=2  refreshed  recovery %.3f" % (hit / TRIALS))
+
+    write_csv(DATA / "family_enum.csv",
+              ["snr_db", "n_frames", "keying", "recovery"], rows)
+    print("[csv]", DATA / "family_enum.csv")
+
+
+if __name__ == "__main__":
+    run()

code/make_tables.py

@@ -13,7 +13,7 @@ DATA = Path(__file__).resolve().parents[1] / "data"
 NAME = {
     "proposed": r"\textbf{Proposed keyed masking}",
     "public_mask": "Public masks",
-    "perm_key": r"Permutation key~\cite{chen2023shuffling}",
+    "perm_key": r"Permutation key~\cite{chen2025shufflingtifs}",
     "index_cipher": "Index cipher",
     "oma_plain": "OMA (no encryption)",
     "random": "Random",

code/sse_lib.py

@@ -309,6 +309,44 @@ def oma_ser(snr_db_list, bits: int = 16, n_grid: int = 200_000):
     return out
 
 
+def oma_ser_orth(snr_db_list, P: int = 4, vu: int = 16, L: int = 64,
+                 n_h: int = 20_000, n_z: int = 2001):
+    """Format-matched OMA reference.
+
+    The binary reference of oma_ser_keylen spends 16 of its L exclusive
+    dimensions on antipodal bits, a one-bit-per-dimension format inside
+    a log2(V)/L = 0.25 bit-per-dimension budget. The better uncoded use
+    of the same allocation is the format the proposed scheme itself
+    uses: P orthogonal decisions among vu candidates, each over L/P
+    exclusive dimensions, which needs exactly vu = L/P of them and so
+    fits the allocation with nothing to spare.
+
+    Energy accounting matches oma_ser, where one unit of energy on a
+    dimension gives 2Es/N0 = snr, so an L-dimension user spending its L
+    units on P symbols puts L/P units in each. Given the fading gain h
+    the correct matched-filter output is N(h sqrt(Es), N0/2) against
+    vu-1 outputs N(0, N0/2), so a digit is right with probability
+    E_z[Phi(z + h sqrt((L/P) snr))^(vu-1)] and the index is right when
+    all P digits are.
+    """
+    from scipy.special import log_ndtr
+    x = (np.arange(n_h) + 0.5) / n_h
+    h = np.sqrt(-np.log(1.0 - x))                    # h^2 ~ Exp(1)
+    z = np.linspace(-8.0, 8.0, n_z)
+    phi = np.exp(-0.5 * z * z) / math.sqrt(2.0 * math.pi)
+    out = []
+    for s in snr_db_list:
+        a = h * math.sqrt((L / P) * 10.0 ** (s / 10.0))
+        pc = np.empty_like(a)
+        for i in range(0, a.size, 2048):             # bound the working set
+            blk = a[i:i + 2048][:, None]
+            pc[i:i + 2048] = np.trapezoid(
+                phi * np.exp((vu - 1) * log_ndtr(z[None, :] + blk)),
+                z, axis=1)
+        out.append(float(np.mean(1.0 - pc ** P)))
+    return out
+
+
 @torch.no_grad()
 def oma_ser_mc(snr_db_list, bits: int = 16, frames: int = 2_000_000,
                chunk: int = 200_000, seed: int = 777):

code/verify_math.py

@@ -18,9 +18,32 @@ Run on CPU (NumPy); no training involved, pure algebra checks.
 from __future__ import annotations
 import numpy as np
 
+from pathlib import Path
+
 RNG = np.random.default_rng(2026)
 D, U, V = 64, 4, 256
 
+CKPT = Path(__file__).resolve().parent.parent / "data" / "model_main.pt"
+
+
+def cached_main_model():
+    """The trained main-configuration model, from a checkpoint.
+
+    V8 and V9 read the trained codebook. Retraining it reproduces only
+    on the device that trained it, so a CPU run of the released package
+    disagreed with the shipped numbers. The checkpoint fixes the
+    codebook, which is what both checks are about; delete it to retrain.
+    """
+    import torch
+    from exp_full import main_model
+    m = main_model()
+    if CKPT.exists():
+        m.load_state_dict(torch.load(CKPT, map_location="cpu"))
+    else:
+        torch.save({k: v.cpu() for k, v in m.state_dict().items()}, CKPT)
+    return m
+
+
 
 def unit_codebook(V, d, rng):
     E = rng.standard_normal((V, d))
@@ -121,6 +144,9 @@ def v3_leakage_vs_correlation():
     lin_ok = all(abs(b - rho * b1) <= 3e-2 for rho, b in slopes)
     print(f"[{'PASS' if lin_ok else 'FAIL'}] V3a bias linear in rho: "
           + ", ".join(f"rho={r:.2f}->{b:.3f}" for r, b in slopes))
+    ROWS.append(("V3a bias slope in kappa", "1.0", "%.4f" % b1,
+                 "%.4f" % abs(1.0 - b1), "0.03",
+                 "PASS" if lin_ok else "FAIL"))
     # (b) random independent mask correlation: E|corr| = sqrt(2/(pi d))
     # (the folded-normal mean of a N(0, 1/d) variable)
     corrs = []
@@ -263,8 +289,7 @@ def v8_cross_period_terms():
     the codebook, which is the claim the proof rests on."""
     import math
     import torch
-    from exp_full import main_model
+    m = cached_main_model()
-    m = main_model()
     Bn = m.unit_codebook().detach().cpu()
     pat = m.masks().detach().cpu()[0]
     L, P, d = m.L, m.P, m.d
@@ -294,8 +319,7 @@ def v9_score_variance_ratio():
     of sum_j e_j^4 / sum_j e_j^2 e'_j^2 over ordered codeword pairs of
     the trained unit codebook, quoted as 2.8 in the manuscript."""
     import torch
-    from exp_full import main_model
+    m = cached_main_model()
-    m = main_model()
     B = m.unit_codebook().detach().cpu().double()
     B = B / B.norm(dim=1, keepdim=True)
     n = B.shape[0]
@@ -313,6 +337,41 @@ def v9_score_variance_ratio():
     return ok
 
 
+
+def v10_format_matched_oma():
+    """The format-matched OMA reference of Section VI-B.
+
+    The binary reference spends 16 of its 64 exclusive dimensions on
+    antipodal bits. The same allocation spent the way the proposed
+    scheme spends it, P=4 sixteen-ary orthogonal decisions over 16
+    dimensions each, is the comparison a reviewer will ask for."""
+    from sse_lib import oma_ser_orth
+    from exp_full import oma_ser_keylen
+    val = oma_ser_orth([10.0])[0]
+    binary = oma_ser_keylen(64, 10.0)
+    ok = abs(val - 0.055) < 0.001
+    print("V10 format-matched OMA at 10 dB: %.5f (binary %.5f)"
+          % (val, binary))
+    ROWS.append(("V10 format-matched OMA at 10 dB", "0.055", "%.5f" % val,
+                 "%.5f" % abs(val - 0.055), "0.001", "PASS" if ok else "FAIL"))
+    return ok
+
+
+def v11_oma_closed_form_vs_mc():
+    """The manuscript says the OMA closed form agrees with Monte Carlo
+    to within one percent. That check had no stored artifact."""
+    from sse_lib import oma_ser, oma_ser_mc
+    cf = oma_ser([16.0])[0]
+    mc = oma_ser_mc([16.0], frames=2_000_000)[0]
+    rel = abs(cf - mc) / mc
+    ok = rel < 0.01
+    print("V11 OMA closed form %.6f vs Monte Carlo %.6f (%.2f%%)"
+          % (cf, mc, 100 * rel))
+    ROWS.append(("V11 OMA closed form vs Monte Carlo", "%.6f" % mc,
+                 "%.6f" % cf, "%.4f" % rel, "0.01", "PASS" if ok else "FAIL"))
+    return ok
+
+
 def main():
     print(f"config d={D} U={U} V={V}\n")
     results = {
@@ -325,6 +384,8 @@ def main():
         "V7": v7_symbolic_identities(),
         "V8": v8_cross_period_terms(),
         "V9": v9_score_variance_ratio(),
+        "V10": v10_format_matched_oma(),
+        "V11": v11_oma_closed_form_vs_mc(),
     }
     print("\nsummary:", {k: ("PASS" if v else "FAIL") for k, v in results.items()})
     print("ALL PASS" if all(results.values()) else "SOME FAILED")

data/family_enum.csv

@@ -0,0 +1,11 @@
+snr_db,n_frames,keying,recovery
+0,1,fixed,0.425
+0,2,fixed,0.46
+0,4,fixed,0.645
+10,1,fixed,0.905
+10,2,fixed,0.95
+10,4,fixed,0.99
+20,1,fixed,0.985
+20,2,fixed,1
+20,4,fixed,1
+10,2,refreshed,0

data/verify_math.csv

@@ -5,6 +5,7 @@ V2b eve SER @ 0dB,0.99609375,0.995,0.0010937500000000044,0.015,PASS
 V2b eve SER @ 10dB,0.99609375,0.9888333333333333,0.007260416666666658,0.015,PASS
 V2b eve SER @ 20dB,0.99609375,0.9881666666666666,0.007927083333333362,0.015,PASS
 V2b eve SER @ 80dB,0.99609375,0.9896666666666667,0.0064270833333333055,0.015,PASS
+V3a bias slope in kappa,1.0,0.9932,0.0068,0.03,PASS
 V3b random mask E|corr|,0.09973557010035818,0.10187042771408686,0.002134857613728683,0.002992067103010745,PASS
 V4a blind jammer projection mean,0.0,0.00026396107284673695,0.00026396107284673695,0.003,PASS
 V4b blind jammer projection variance,0.01558576233568703,0.015476787953278994,0.00010897438240803532,0.0001558576233568703,PASS
@@ -13,3 +14,5 @@ V6 coded-OMA outage @ 10 dB,0.0406,0.040575,0,0,REFERENCE
 V7 symbolic identities,exact,exact,0,0,PASS
 V8 cross-period remainder,0.0,0.000337,0.000337,0.0005,PASS
 V9 score-variance ratio,2.8,2.8252,0.0252,0.05,PASS
+V10 format-matched OMA at 10 dB,0.055,0.05520,0.00020,0.001,PASS
+V11 OMA closed form vs Monte Carlo,0.081245,0.080925,0.0039,0.01,PASS