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pd: verify anchors for the blending law and the emission ceiling

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Check 9 -- cover traffic on a timeline. Blending follows rate*(2M+1)/3 (7.39 vs
7.41 predicted), the mean hold is the renewal residual (2M+1)/6, and mixing is
nil at the baseline rate: 0.007 concurrent holds, max 2. That last one is the
substantive finding rather than a sanity check -- at one message per second a
relay has nothing to mix, so the anonymity comes entirely from what it has seen.

Check 10 -- the emission quota. The measured breakpoint brackets the closed form
(band [0.127%, 0.159%] against a predicted 0.1475%), and deflating D_hat/D to
0.64 pushes more nodes over their quota, as the (D_hat/D)*alpha_max form requires.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
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Marcin Pawlowski 2026-08-05 17:33:59 +02:00 committed by Marcin Pawlowski
parent 61d72bb5f5
commit 1865b4110d
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1 changed files with 42 additions and 1 deletions
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43
tools/simulators/blend/pd/src/pd/verify.py
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@ -14,7 +14,7 @@ import numpy as np
from .adversary import adversary_metrics, deanon_metrics, place_adversary
from .config import SimConfig
from .graph import build_graph
from .rng import placement_seedseq
from .rng import placement_seedseq, traffic_seedseq
def _check(name: str, ok: bool, detail: str) -> bool:
@ -217,6 +217,47 @@ def main(argv: list[str] | None = None) -> int:
f"delivery regional {res['regional']['delivery_rate']:.3f}"
f" vs uniform {res['uniform']['delivery_rate']:.3f}")
# 9. cover traffic. Blending -- the broadcasts a relay saw between consecutive releases, which
# is the anonymity set -- follows rate*(2M+1)/3: gaps sampled AT a release are size-biased,
# so it is twice the mean hold, not rate*M/2. Mixing (messages held at once) stays ~0 at the
# baseline rate, which is the point: at one message a second the relays have nothing to mix.
from .traffic import simulate_window, traffic_metrics
tc = SimConfig(n_nodes=2000, degree=8, blend_hops=3, max_blend_delay=10,
cover_rate_mult=1.0, graph_seed=0)
tg = build_graph(tc)
tw = simulate_window(tg, tc, np.random.default_rng(traffic_seedseq(tc, 3, 10, 1.0)), 1200)
tm = traffic_metrics(tw, tc)
rate = (tw.emitted_cover + tw.emitted_block) / tw.window_seconds
blend_th = rate * (2 * 10 + 1) / 3
ok &= _check("blending = rate*(2M+1)/3",
abs(tm["blending_mean"] - blend_th) < 0.15 * blend_th,
f"sim {tm['blending_mean']:.2f} vs theory {blend_th:.2f}")
ok &= _check("mean hold = (2M+1)/6", abs(tm["hold_seconds_mean"] - 21 / 6) < 0.3,
f"sim {tm['hold_seconds_mean']:.2f}s vs theory {21/6:.2f}s")
ok &= _check("mixing is nil at the baseline rate", tm["queue_mean"] < 0.05,
f"mean concurrent holds {tm['queue_mean']:.4f}, max {tm['queue_max']:.0f}")
ok &= _check("cover between blocks = rate x block interval",
abs(tm["cover_per_block_interval"] - rate * 30) < 8,
f"sim {tm['cover_per_block_interval']:.1f} vs theory {rate*30:.1f}")
# 10. the emission quota. The ceiling binds on stake relative to the INFERRED total, and the
# measured breakpoint must bracket the closed form ln(1-q)/ln(1-f).
from .quota import alpha_max, assign_stake, simulate_epoch_emissions
fq, nq, sq = 1.0 / 30.0, 20_000, 648_000
st = assign_stake(nq, "zipf", np.random.default_rng(11), 1.0)
qr = simulate_epoch_emissions(st, fq, nq, sq, np.random.default_rng(12))
pred = alpha_max(nq, fq)
ok &= _check("quota ceiling brackets the closed form",
qr["min_overrun_stake"] <= pred * 1.5 and qr["max_compliant_stake"] >= pred * 0.5,
f"measured band [{qr['min_overrun_stake']*100:.4f}%, "
f"{qr['max_compliant_stake']*100:.4f}%] vs predicted {pred*100:.4f}%")
lowd = simulate_epoch_emissions(st, fq, nq, sq, np.random.default_rng(12),
stake_inference_ratio=0.64)
ok &= _check("a low D_hat/D tightens the true-stake ceiling",
lowd["compliant_frac"] < qr["compliant_frac"],
f"compliant {qr['compliant_frac']*100:.2f}% at 1.00 -> "
f"{lowd['compliant_frac']*100:.2f}% at 0.64")
print("OK" if ok else "FAILURES PRESENT")
return 0 if ok else 1