preprints.org > computer science and mathematics > computational mathematics > doi: 10.20944/preprints201809.0472.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 20 September 2018 / Approved: 25 September 2018 / Online: 25 September 2018 (03:58:07 CEST)
Version 2 : Received: 25 November 2018 / Approved: 26 November 2018 / Online: 26 November 2018 (07:25:04 CET)

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.

geometric distribution; collatz conjecture; inflation propensity; systemic risk; cryptocurrency; blockchain; proof-of-work

Computer Science and Mathematics, Computational Mathematics