Kadena's public blockchain, Chainweb, is the only sharded and scalable layer-1 PoW network in production today. It utilizes a PoW (Proof of Work) consensus mechanism that improves throughput and scalalability without sacraficing security.
Kadena public summary paper
William Martino and Stuart Popejoy, November 2018
William Martino, Stuart Popejoy, Monica Quaintance, January 2018
Chainweb protocol security calculations
Monica Quaintance, William Martino, January 2018
Chainweb updated security analysis: agent-based simulations
Monica Quaintance, William Martino, Stuart Haber, Tarun Chitra, April 2019