Preprint Article Version 2 This version is not peer-reviewed

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

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)

A peer-reviewed article of this Preprint also exists.

Bocart, F. Inflation Propensity of Collatz Orbits: A New Proof-of-Work for Blockchain Applications. J. Risk Financial Manag. 2018, 11, 83. Bocart, F. Inflation Propensity of Collatz Orbits: A New Proof-of-Work for Blockchain Applications. J. Risk Financial Manag. 2018, 11, 83.

Journal reference: J. Risk Financial Manag. 2018, 11, 83
DOI: 10.3390/jrfm11040083

## Abstract

Cryptocurrencies like 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 $0.714 \approx \frac{(\pi - 1)}{3}$ as the sample size increases. This pseudo-randomness opens the door to a new class of proofs-of-work based on congruential graphs.

## Subject Areas

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