Mining Difficulty
How BTQ difficulty retargeting holds up: the mathematics, a 293-trial Monte Carlo campaign, and live multi-node fork-resolution runs on regtest.
Mining Difficulty
Published: May 7, 2026 · Length: 25 pages · Format: PDF (≈ 791 KB)
Overview
This whitepaper studies how the BTQ protocol behaves under stress in two complementary regimes: the algorithmic regime, via a 293-trial Monte Carlo simulation campaign over three candidate difficulty algorithms, and the operational regime, via live multi-node experiments on a five-node btqd regtest cluster.
BTQ differs from Bitcoin in three ways that matter for proof-of-work: a one-minute target block spacing, a 20,160-block retarget window, and Dilithium-sized transactions that drive blocks toward an 8 MWU capacity ceiling. The interaction of those choices with the inherited difficulty-adjustment policy, gossip, mempool, and fork resolution is exactly what this study isolates.
Headline Findings
- The legacy retargeter is unfit for
T = 60 s. Under a −95% catastrophic hashrate event the Bitcoin-style retarget that BTQ inherits leaves mean block intervals at ≈ 678 s (11.3× target) for thousands of post-shock blocks. LWMA-1 (N = 45) returns to nominal within ∼ 80 blocks. ASERT (τ = 2 d) returns asymptotically. This is the single strongest quantitative argument for BTQ to migrate off the legacy retarget. MAX_FUTURE_BLOCK_TIMEis a faithful drift bound. Across all three algorithms, MFBT bounds adversarially induced timestamp drift with slope indistinguishable from 1 on log–log axes, independent of the retarget family in use.- Fork resolution on
btqdis decisive. A deliberately constructed two-tip fork at height 56,273 resolved by chain reorg to the longer minority branch within a single 2 s polling tick on reconnection, with all five nodes converging to a single best-block hash.
Scope
- Simulation campaign (E1–E6): 293 runs spanning three retarget algorithms (legacy windowed, BTQ-style LWMA-1, ASERT), seven hashrate scenarios, an LWMA-1 window sweep, an ASERT half-life sweep, adversarial-clock fraction sweeps, MFBT sweeps, and a soft-minimum block-interval hardening, with multiple seeds per cell.
- Live cluster experiments: Peer connectivity matrix, 50-block mining storm, 400 ms transaction storm, three-minute Prometheus rollup, and a deliberately induced network partition that produced a clean two-tip fork and a verifiable chain reorg on reconnection.
Recommendations Matrix (Summary)
| Decision | Recommendation |
|---|---|
| Difficulty algorithm | Migrate off legacy windowed retarget. Default LWMA-1 (N = 45); evaluate ASERT (τ ∈ [6, 24] h) as an alternative. |
MAX_FUTURE_BLOCK_TIME | Pick against an explicit drift budget; do not inherit Bitcoin's 7200 s as a default. |
| MTP rule | Adequate as-is at all examined adversarial clock fractions. |
| Soft-minimum block interval | Conditional — no measurable benefit on stationary or sinusoidal hashrate; do not enable by default. |
Deployed btqd network primitives | Trust within scope — block propagation, mempool gossip, and fork resolution all behaved correctly on regtest. |
Scope limits: the cluster experiments are regtest-only on a single kind host with sub-millisecond intra-cluster RTT. WAN-scale gossip tails and mainnet-scale Dilithium-signed block sizes are out of scope for the live experiments. The simulation hashrate is dimensionless, calibrated only to the genesis target.