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Preserved in Portico This version is not peer-reviewed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)
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.
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.
Keywords
geometric distribution; collatz conjecture; inflation propensity; systemic risk; cryptocurrency; blockchain; proof-of-work
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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