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

Cryptocurrencies like Bitcoin rely on a proof-of-work system to validate transactions and prevent attacks or double-spending. Reliance on a few standard proofs-of-work such as hashcash, Ethash or Scrypt increases systemic risk of the whole crypto-economy. Diversification of proofs-of-work is a strategy to counter potential threats to the stability of electronic payment systems. To this end, another proof-of-work is introduced: it is based on a new metric associated to the algorithmically undecidable Collatz algorithm: 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 $0.714 \approx \frac{(\pi - 1)}{3}$ as the sample size increases. This pseudo-randomness opens the door to a new class of proofs-of-work based on congruential graphs.