PoBU, measured on a running chain
In the last piece, we covered the threat model. The paper lists the main ways a PoBU system can fail or be weakened in practice: issuer concentration, compromise/coercion, availability, and privacy/linkability.
Now comes the part many readers care about most:
What can we actually measure on a live network?
Because PoBU verification of uniqueness and liveness is enforced off-chain, the paper focuses on what can be checked publicly: chain-derived measurements that anyone can reproduce.
What the paper measures
The paper uses two necessary, but not sufficient, signals to evaluate whether participation is broad and whether control is concentrating.
1) Validator-set breadth and dynamics
This is about the active validator set over time.
The paper measures things like:
- how many active validators exist per session
- how many enter and exit
- how much overlap there is between sessions
- and a churn rate
The point is simple: if participation stays broad at the key level, the validator set does not collapse into a tiny, fixed group. The paper treats validator-set collapse and near-zero churn as warning signs.
2) Block production concentration
Even if a chain has many validators, control can still concentrate if a small subset produces most blocks. So the paper also measures block production distribution.
It uses:
- top-k author share (top 1 / 5 / 10)
- HHI
- Gini
These metrics describe how spread out block production is across authors.
Why these measurements matter
PoBU’s core claim is about eligibility bounded by unique humans, but the paper stays careful: these measurements are computed over on-chain keys, not over verified unique humans.
So the paper treats these measurements as necessary signals at the chain boundary.
It also says what would look like failure in practice:
- validator-set collapse or near-zero churn
- high author concentration, where a small number of keys produce most blocks.
How the paper gets the data
The paper’s approach is simple and auditable.
It uses public chain data accessed via WebSocket RPC and extracts data via direct Substrate RPC.
The extraction process includes:
- converting timestamps to block ranges
- extracting block authors across block ranges
- extracting session validator sets
- computing concentration metrics from those datasets.
It also records endpoints, commands, datasets, and checksums so the measurements can be regenerated.
Multiple time windows, not one snapshot
The paper evaluates multiple windows to reduce cherry-picking and to separate recent behavior from longer-horizon regimes.
These are:
- W1: last 90 days
- W2: last 365 days
- W3: long-horizon snapshot.
The idea is to see how these participation and concentration signals look across different time ranges.
A few concrete results the paper reports
Here are a few of the headline numbers the paper gives.
Recent 90-day window (W1)
- top-10 block authors produced 4.5% of sampled blocks
- 405 unique block authors appeared in the sample
- average validators per session: 258.4 (min 169, max 367)
Mid-term window (W2)
- average validators per session: 1044.6 (min 169, max 1767)
These are key-level observations, but they are the kind of public evidence the paper uses to evaluate whether visible consensus control is concentrated or broadly distributed.
Limits the paper is clear about
The paper does not claim these measurements directly prove unique-human counts.
It states the limits clearly:
- the metrics are computed over on-chain keys, not verified unique humans
- block author statistics are computed from sampled blocks, and sampling can introduce bias, so step sizes are disclosed and treated as a limitation.
So the paper treats this as reproducible evidence at the chain boundary, not as a full measurement of identity-layer performance.
What comes next
The paper also notes that the evaluation would be strengthened by more publishable aggregates from the identity layer, but it keeps this draft grounded in what is publicly reproducible from chain data.
So the next theme after this one is simple:
What the chain can show today, and what the paper says, would further strengthen the evaluation if it can be published safely.