BitCell: Cellular Automaton Tournaments and the Mathematics of Anti-Cartel Consensus

The consensus problem in distributed ledger systems has two distinct dimensions that existing protocols systematically conflate. The first is the Byzantine fault-tolerance question: can a network reach agreement in the presence of arbitrary failures? The second — less formalised but no less fundamental — is the anti-cartel question: can the incentive structure of the consensus mechanism structurally resist the formation of cartels that reconstitute centralised authority under a nominally decentralised banner? Bitcoin's proof-of-work has produced a system where a small number of industrial mining pools control the majority of hash power. BitCell is a proposal that takes the anti-cartel question seriously as an engineering problem rather than an economic folk theorem. BitCell replaces hash-grinding and stake-weighting with cellular automaton tournaments as the computational substrate for block proposal rights. In each round, miners commit to a pattern in a bounded Conway's Game of Life grid, are verifiably randomly paired via a VRF-based pairing mechanism, and compete in a deterministic single-elimination tournament whose outcome depends on strategic pattern design rather than raw computational expenditure or capital size. Victory rights are not transferable and are not enhanced by pooling strategies: a cartel of sub-majority miners cannot coordinate to construct a jointly optimal pattern that dominates unilateral honest play, because the tournament's pairwise structure, hidden identities (via ring signatures), non-shareable rewards, and reputation-gated eligibility remove each of the primary economic motivations that make mining pools attractive. Under a simple Bayesian model of miner incentives, collusive strategies for sub-majority cartels yield strictly lower expected payoffs than unilateral honest participation. Tournament eligibility and reward weighting are governed by an Evidence-Based Subjective Logic (EBSL) reputation layer. All state transitions are proven using succinct zero-knowledge proofs, enabling a ZKVM-backed smart contract layer with native privacy. BitCell makes three primary contributions: (i) a proof-of-computation consensus mechanism whose computational task is verifiable, bounded, non-parallelisable by pooling, and intellectually non-trivial; (ii) a game-theoretic proof that the combination of pairwise tournaments, anonymised pairing, non-transferable victory rights, and reputation gating renders cartel coordination strictly dominated in a Bayesian Nash equilibrium; and (iii) a native ZKVM execution environment for privacy-preserving smart contracts.