The Distributed-Consensus Witness Problem: Distributed Consensus as the Fourth Domain

Abstract

The witness/extractability framework was established in the General Witness Theorem across three otherwise-disjoint domains: combinatorial mathematics, common-law evidence, and economic ledgers. The framework’s predictive content licenses a stronger claim: any domain admitting a valid instantiation of the abstract setup is governed by the framework, whether or not the domain’s practitioners have noticed. This paper instantiates the framework in a fourth domain: distributed consensus under Byzantine fault tolerance. We prove the BFT Witness Asymmetry Theorem: the structural cost of operating without standing on Byzantine nodes is super-linear, exhibited at single-level non-extractability as the standard O(n²) communication lower bound (Dolev–Reischuk 1985). We then state the Hierarchical-Coalition Cost-Asymmetry Conjecture: under recursive Byzantine sub-coalitions of adversarially-chosen depth k, the communication lower bound grows as Ω(n^{k+1}).