Paper 2026/893

The Joint Channel Threshold: Selfish Mining Below 1% Hashrate

Abstract

The selfish-mining literature has progressively lowered the hashrate threshold at which a rational Bitcoin miner strictly profits by deviating from the honest protocol, from Eyal and Sirer's 25% down to single digits under richer attacker models. Two such models remain unreconciled: Gervais et al. (CCS 2016) parameterize network-layer adversaries through an eclipse fraction omega and an honest-only stale rate o, but assume constant block rewards; WeRLman (IEEE S&P 2023) models fee-rich rewards through a deep-RL solver, but assumes a network-clean attacker. An adversary that exploits both surfaces has not been analyzed. We present the first joint analysis. We formulate a Markov decision process that integrates Gervais's network-layer channels with WeRLman's whale-transaction tracking, solve it at a 5.7 x 10^8 state truncation, and anchor the construction by reduction to each prior model at the appropriate parameter limit. Our threat model targets a state-level adversary with per-block routing influence over a meaningful fraction of honest hash power, not an attacker who eclipses individual nodes. Under this model, the joint threshold collapses far below either single-channel result. At L = 3, the F=10 baseline (no network channels) crosses at alpha = 13.2%; a 10% eclipse fraction alone drops it to 2.6%, a 10% stale rate alone to 4.8%, and both channels together to 1.4%. At L = 5 the joint configuration drops further to 0.9%, an at least 15x collapse. An analytical lemma accounts for the interaction: the honest-chain growth probability factors as (1 - alpha - omega)(1 - o), isolating a cross-term omega * o that is a property of the joint transition kernel itself. The cross-term is structural, not a training artifact, and its presence implies that mitigations targeting only one channel leave the joint contribution structurally present whenever the other channel is non-zero.