Collaborative transaction notarization in a byzantine computing environment

A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform a method comprising:

• receiving a set of digital transactions at a collaboration of multiple miners;
• assigning to each miner a distinct slice of a solution space for discovering a solution for notarizing the set of digital transactions;
• during each of one or more rounds:
• determining whether the solution was discovered;
• and
• when the solution is not discovered during the round, shifting the solution space to assign each miner a different slice of the solution space;
• and
• when the solution is discovered:
• storing the set of digital transactions in a distributed ledger;
• and
• if the solution space was shifted at least once, penalizing one or more miners that failed to discover the solution.

A distributed computing system, comprising:

• multiple collaborative miner systems, each miner system comprising:
• one or more processors;
• and
• memory storing instructions that, when executed by the one or more processors, cause the miner system to:
• receive a set of digital transactions;
• adopt a distinct slice of a solution space for discovering a solution for notarizing the set of digital transactions;
• during each of one or more rounds:
• determine whether the solution was discovered;
• and
• when the solution is not discovered during the round, shift the solution space to adopt a different slice of the solution space;
• and
• when the solution is discovered:
• store the set of digital transactions in a distributed ledger;
• and
• if the solution space was shifted at least once, penalize one or more miner systems that failed to discover the solution.