Inflation Propensity of Collatz Orbits: A New Proof-of-Work for Blockchain Applications

Abstract

Cryptocurrencies such as Bitcoin rely on a proof-of-work system to validate transactions and prevent attacks or double-spending. A new proof-of-work is introduced which seems to be the first number theoretic proof-of-work unrelated to primes: it is based on a new metric associated to the Collatz algorithm whose natural generalization is algorithmically undecidable: the inflation propensity is defined as the cardinality of new maxima in a developing Collatz orbit. It is numerically verified that the distribution of inflation propensity slowly converges to a geometric distribution of parameter 0.714 ≈ ( π − 1 ) 3 as the sample size increases. This pseudo-randomness opens the door to a new class of proofs-of-work based on congruential graphs.