Closes the two open items from the review.
3.9 correlated (AS/region) outages, from configs/correlated-churn.yaml at 6400
rounds/cell: clustered failure does NOT fragment the network -- the live coverage
holds at 1.000 at every degree through 80% churn, and the percolation threshold
of 3.5 never appears, because removing a failure domain removes a whole
neighbourhood and leaves every surviving one intact. At degree 4 and 70% churn,
scattered failure annihilates the network (live coverage 0.001, delivery 0.000)
while the same number of clustered failures still delivers 30% of messages. The
cost is that dead domains become unreachable islands, so all-node coverage falls
instead. This reverses the caveat previously written, which asserted correlated
outages would degrade coverage faster; 3.5 uncorrelated threshold is in fact the
conservative case for the operating network.
10^6: the fullscale run confirms the results carry -- adversary closed forms
reproduced to 1.6e-4 at a million nodes, coverage under churn indistinguishable
from 10^5, delivery still tracking (1-u)^hops, and full delay up only 5.8% from
10^5. It samples 192 rounds/cell against 8000, so it is recorded as a scaling
check rather than a source of headline numbers, and the tables are not restated
from it.
Remaining churn caveat is now the honest one: adversarially placed churn (a cut
set rather than a random or clustered set) is still unmodelled, as are
heavy-tailed AS sizes.
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>
