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

Fabian Bocart
Additional contact information
Fabian Bocart: Independent Researcher, Jackson Height, NY 11372, USA

JRFM, 2018, vol. 11, issue 4, 1-18

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.

Keywords: geometric distribution; collatz conjecture; inflation propensity; systemic risk; cryptocurrency; blockchain; proof-of-work (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/1911-8074/11/4/83/pdf (application/pdf)
https://www.mdpi.com/1911-8074/11/4/83/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jjrfmx:v:11:y:2018:i:4:p:83-:d:185990

Access Statistics for this article

JRFM is currently edited by Ms. Chelthy Cheng

More articles in JRFM from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().