engine gains a cover_rates axis: each rate plays a timeline through the same
graph and pairs it with the epoch emission budget, which needs no graph and so is
computed alongside rather than inside the window. Seeds are separate streams
(traffic_seedseq for the timeline and clocks, stake_seedseq for the stake draw
and budget), so the stake distribution is independent of the topology and of the
message schedule.
sweep writes traffic.parquet only when a cover-traffic study actually ran, so
every existing config keeps producing exactly three tables. quota_summary reports
the measured ceiling beside the predicted one in the same row, so a run can be
checked against the closed form instead of asked to be believed.
Two figures: blending against cover rate and release delay with the
rate*(2M+1)/3 law overlaid, and the quota ceiling with the measured transition
band against the prediction.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The quota ceiling was closed-form only. This adds per-node stake so a run can
show nodes actually breaking it.
- assign_stake: uniform, or heavy-tailed zipf (s ~ 1/rank^a), which is what makes
the ceiling bite -- the head sits orders of magnitude above it, the tail far below;
- inferred_alpha: converts true relative stake to the sigma/D_hat the lottery
actually weighs, so a low estimate inflates every node alpha;
- simulate_epoch_emissions: measures the budget over a full epoch. Overrun happens
at epoch scale and needs no graph, so this is cheap: proposals are Binomial over
the epoch slots, a proposal cancels the next cover, and a node stays at exactly
its quota until its wins no longer fit -- at which point it emits more often than
everyone else, which is the signal cover traffic exists to suppress.
Measured against the closed form at N=20,000, zipf stake, over an epoch: the
predicted ceiling falls inside the transition band every time, and at D_hat/D = 1
the smallest overrunning node sits at 0.1468% against a predicted 0.1475%. The
D_hat/D normalisation is confirmed empirically -- deflating the estimate to 0.64
pulls the measured ceiling down with it, as the (D_hat/D)*alpha_max form requires.
With heavy-tailed stake 99.7% of nodes comply and only the head breaks; the
largest holder at 9.5% stake is some 65x over its allowance.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
The key() coverage test enumerates every SimConfig field, so the five cover-
traffic knobs had to be given alternative values. Caught by the test itself
immediately after the previous commit.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
First half of the cover-traffic work: the two new modules and their tests.
quota.py -- the emission budget. Cover traffic gives every node the same number
of emissions per epoch, which only holds while a node block proposals fit inside
its quota. The bind is exact: alpha_max = ln(1-q)/ln(1-f), where alpha is stake
relative to the INFERRED total D_hat, since that is the denominator the lottery
threshold is derived from. In true stake the ceiling carries the estimator ratio,
s_max = (D_hat/D)*alpha_max, with D_hat/D an input rather than an assumption. The
familiar q/f is a small-q approximation that runs 1.7% high and so overstates the
tolerable stake. Sitting on the mean bind overruns the quota half the time, so
max_alpha_for_confidence gives the ceiling that holds with stated probability.
traffic.py -- the timeline. The rest of the simulator samples independent rounds
and draws each hold from the stationary residual, which has no notion of time and
so can never let two messages meet at a relay. Here every node owns one
free-running clock shared by all messages through it, extended lazily so only the
relays actually visited grow one. A clock sampled once still reproduces
mixclock.mix_wait, so single-message statistics are unchanged.
It separates two quantities that are easy to conflate: mixing (messages a relay
holds at once) and blending (messages it has SEEN between consecutive releases).
Blending is the anonymity set -- every broadcast reaches every node, so an
observer cannot tell which of them the relay forwarded. Gaps sampled at a release
are size-biased, so blending is rate*(2M+1)/3, twice the mean hold, not
rate*M/2 as a naive reading gives. Measured within 1-4% of that at M = 3, 10, 30
and linear in the cover rate.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Uncorrelated churn alone was incomplete: real outages take out a datacentre, AS
or region as a unit. Adds failure domains and a correlated churn mode, plus the
metric needed to tell the two apart.
- n_regions / region_locality: nodes belong to equal-sized failure domains, and
a configurable share of each node peers inside its own domain. Locality is what
makes a failure domain a connectivity domain -- with region-blind peering,
dropping whole regions removes a uniformly random set of nodes and is
indistinguishable from uniform churn. The locality matchings keep the graph
exactly d-regular (they change where peers are, never how many).
- churn_mode = uniform | regional, swept per topology so both modes are compared
on the same graph at an identical dead-node count.
- frac_reached_live: coverage of the *responsive* network, alongside coverage of
all nodes. The two move in opposite directions under correlated failure, so one
number could not express the result.
Measured (degree 4, 20 domains, 75% locality, half the network dead): clustered
failure leaves the survivors fully connected -- live coverage 1.000 and delivery
equal to the live-relay rate, i.e. nothing lost to routing -- where the same
number of scattered failures gives 0.857 live coverage and loses delivery to
broken routes. Correlated outages are gentler on the survivors than uniform
churn, while stranding the dead domains. Verify check 8 anchors this.
Also, per review of the caveats: exact d-regularity is a protocol requirement
rather than a modelling simplification, and the timing-correlation adversary is
deferred because it is only meaningful once the network emits cover traffic,
which this simulator does not yet do.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Extends the pd Blend simulator along two axes the deanonymization model
opened up, adds the reports/blend/pd report of record, and fixes three
correctness defects found while reviewing the result.
Linkability over time (pd.linkability):
- time to link an emitter ~ 30s*ln(1/(1-alpha))/(stake*q): inversely
proportional to stake, so a 5% staker is linked in ~2 days and a 0.001%
staker only after ~27 years;
- time to certify a node's stake >= theta from the count of attributable
observations (relative precision ~1/sqrt(N)): sizing a node costs 100-400x
more than identifying it, and sub-0.1% stake is practically unlearnable.
Both are closed forms over the exact deanonymization rates and a
stake-proportional 30 s emission cadence, checked against a Monte-Carlo of
the emission process in verify.
Messaging redundancy (R independent cascades per emission, R = 1..4):
- `redundancy` knob threaded through config/rng/propagation/engine/metrics/
sweep; a node receives from whichever cascade reaches it first, so arrival
times combine element-wise. Delivery and capture both follow 1-(1-x)^R, so
redundancy trades reliability against anonymity and divides time-to-link
by ~R. Measured: delivery 0.34 -> 0.81 at 30% churn for R = 1 -> 4, while a
1%-staker's time to link falls 10 d -> 2.5 d.
- Redundancy buys NO coverage: a cascade only delivers if the sender could
already route to its relay, so every delivered cascade floods the sender's
own component. Coverage is flat in R to four decimals at every degree.
- Near the percolation threshold the cascades fail together rather than
independently, so redundancy under-delivers against 1-(1-p1)^R there.
Churn percolation (configs/percolation.yaml, verify check 7):
- the flood only crosses responsive nodes, so it lives on the responsive
sub-graph -- site percolation on a d-regular graph. A network survives churn
only up to u_c = 1 - 1/(degree-1); measured collapse lands on the predicted
threshold for every degree (3 -> 0.50, 6 -> 0.80, 16 -> 0.93), which inverts
into the sizing rule degree > 1 + 1/(1-u).
Correctness fixes:
- redundancy delay used the fastest cascade's own full delay, which
over-states it (min-max vs max-min); now the element-wise earliest arrival,
reducing exactly to the single-cascade model at R = 1 (test);
- the "redundancy improves coverage" claim was false in both the report and
the simulator README -- removed and replaced with the measured result;
- per-hop latency is degree-dependent (1.5 s at degree 16 to 2.7 s at degree
3), not a flat 1.6 s; and the worst-case observation figure was averaged
over degrees -- at degree 8 and f_adv = 0.2 it is 0.83 -> 1.000.
Statistics: round counts raised for resolution rather than speed -- 8000
rounds per cell in the main sweep, 9600 in the redundancy study, 6400 in the
percolation study, giving SEM <= 0.009 on every delivery rate and <= 0.04 s
on every delay mean. The previous redundancy grid (144 rounds/cell) produced a
non-monotonic delivery curve; it is now monotonic and within 0.015 of theory.
Adversary and deanonymization metrics remain closed-form and exact.
reports/blend/pd: the report of record -- peering-degree trade-offs across
speed, observation, eclipse, deanonymization and reliability, plus the
time-to-link, stake-inference, redundancy and churn-threshold sections, with
21 figures of record and an explicit sampling-error statement.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Static-graph simulator quantifying how a node's peering degree trades off
propagation speed, adversary exposure, deanonymization, and reliability in the
Blend network. Scales to 1e6 nodes (sparse CSR + sampled Dijkstra); the
adversary and deanonymization metrics are exact at every N.
Model (ms): seeded d-regular peer graph (matching-union), Blend cascade
(sender -> blend_hops timed-release mix relays -> final flood), geographic link
base + exponential transport jitter, per-node processing lag, free-running
release-clock mixing.
Metrics:
- propagation: full-delay mean/p50/p90/p99, path/broadcast split, coverage times
- reliability: message success-delivery-rate ~ (1-unresponsive_frac)^blend_hops
and flood coverage, with unresponsive nodes modelled as routing holes
- adversary (exact): observed/eclipsed fractions, random + worst-case placement
- deanonymization (exact): P(whole blend path adversarial) ~ f_adv^blend_hops,
and full deanonymization (path adversarial AND honest sender peered with an
adversary) = deanon_rate * observed_frac
Deterministic blake2b seed streams, three parquet tables, joblib parallelism,
memguard, an analytic verify harness, 50 unit tests, and an auto-installing
Makefile.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
