Deterministic Clock

Anti-entropy maintenance on the BULK Network.

Overview

BULK requires every validator to independently derive the same timestamp for each consensus round, without a central clock. This timestamp is used as the seed for the deterministic shuffle and is embedded in the committed batch. The system achieves this through a formula-based approach with a Phase-Locked Loop (PLL) correction mechanism.

The Timestamp Formula

Each batch timestamp is computed deterministically:

$$T_{\text{batch}} = T_{\text{anchor}} + (R - R_{\text{anchor}}) \times \Delta t$$

Where $T_{\text{anchor}}$ is a known reference timestamp, $R_{\text{anchor}}$ is the round number at the anchor point, $R$ is the current round, and $\Delta t$ is the nanoseconds per consensus round (the tick rate).

Given the same anchor parameters and rate, every validator computes the same timestamp for any given round. No communication is needed for timestamp agreement - it falls directly out of the consensus round number.

Beacon PLL (Phase-Locked Loop)

Over time, the formula’s rate will drift from real wall-clock time due to variance in consensus round duration. The PLL corrects this using beacons - wall-clock timestamps embedded in committed transactions.

How Beacons Work

1. Beacon collection. Committed transactions include wall-clock timestamps from the validators that processed them.
2. Median extraction. For each round with beacons, the system takes the median of all beacon timestamps. The median is robust to outliers and Byzantine actors - even if some validators report incorrect times, the median reflects the honest majority.
3. Drift computation. The system compares the median beacon time against the formula’s predicted time for that round, computing a drift value.
4. Rate correction. If drift accumulates beyond a threshold, the PLL adjusts $\Delta t$ to bring the formula back into alignment with real time. The anchor point is also updated to prevent accumulated error.

Byzantine Resistance

The median-based approach is inherently resistant to Byzantine clocks. The system tolerates up to $\lfloor(n-1)/2\rfloor$ faulty clocks when computing the median. Rogue validators reporting wildly incorrect times are neutralized without any explicit detection mechanism - the median naturally converges on the honest majority.

Drift and Phase Correction

The PLL operates in two modes:

• Rate correction adjusts $\Delta t$ when consensus rounds consistently take longer or shorter than expected. This handles systematic drift (e.g., network conditions changing average round time).
• Phase correction adjusts the anchor point when the formula has accumulated a large offset from wall-clock time. This handles step changes (e.g., after a period of network instability).

Both corrections are applied deterministically based on committed data, so every validator applies the same correction at the same round.