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To protect participants' confidentiality, blockchains can be outfitted with anonymization methods. Observations of the underlying network traffic can identify the author of a transaction request, although these mechanisms often only consider the abstraction layer of blockchains. Previous systems either give topological confidentiality that may be compromised by an attacker in control of a large number of nodes, or provide strong cryptographic confidentiality but are so inefficient as to be practically unusable. In addition, there is no flexible mechanism to swap confidentiality for efficiency in order to accommodate practical demands. We propose a novel approach, the neural fairness protocol, which is a blockchain-based distributed ledger secured using neural networks and machine learning algorithms, enabling permissionless participation in the process of transition validation while concurrently providing strong assurance about the correct functioning of the entire network. Using cryptography and a custom implementation of elliptic curves, the protocol is designed to ensure the confidentiality of each transaction phase and peer-to-peer data exchange. [ABSTRACT FROM AUTHOR]

Fibonacci numbers are the basis of a new geometric construction that leads to the definition of a family { C n : n ∈ N } of octagons that come very close to the regular octagon. Such octagons, in some previous articles, have been given the name of Carboncettus octagons for historical reasons. Going further, in this paper we want to introduce and investigate some algebraic constructs that arise from the family { C n : n ∈ N } and therefore from Fibonacci numbers: From each Carboncettus octagon C n , it is possible to obtain an infinite (right) word W n on the binary alphabet { 0 , 1 } , which we will call the nth Carboncettus word. The main theorem shows that all the Carboncettus words thus defined are Sturmian words except in the case n = 5 . The fifth Carboncettus word W 5 is in fact the only word of the family to be purely periodic: It has period 17 and periodic factor 000 100 100 010 010 01. Finally, we also define a further word W ∞ named the Carboncettus limit word and, as second main result, we prove that the limit of the sequence of Carboncettus words is W ∞ itself. [ABSTRACT FROM AUTHOR]