Consensus Mechanism Geometry: A Frozen Phase-Coherence Probe Across Five Blockchain Architectures

Abstract

The frozen SUPT-CA phase-coherence probe (α = 0.01, zero free parameters) was applied to live blockchain data from Bitcoin, Ethereum, Solana, Cardano, and Polkadot. Consensus mechanism design directly determines geometric regime: deterministic hardware clocking (Solana, Polkadot) produces deep-lock distributions; regulated proof-of-stake with fee targeting (Ethereum, Cardano) produces coherence-zone distributions; probabilistic proof-of-work (Bitcoin) produces clutch-band timing with sub-floor transaction variability. A validated congestion oracle signal is identified for Ethereum: transaction count d_ij crossing 1.0 in a rolling 150-block window marks network congestion onset, confirmed against the May 2024 memecoin congestion event. All data from live public RPC endpoints, April 15, 2026. No parameters adjusted.