Hyper-complex Binary Superposition Algebra: A Commutative and Associative Product

Hyper-complex Binary Superposition Algebra: A Commutative and Associative Product | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 17 June 2025 V1 Latest version Share on Hyper-complex Binary Superposition Algebra: A Commutative and Associative Product Author : José Antoine SEQUEIRA 0009-0008-4860-1450 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175016330.09338854/v1 151 views 63 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this article, we introduce a hyper complex algebra based on a binary superposition structure. Each algebraic unit is defined by a pair (f; S) where f ∈ {0; 1} encodes the logical presence of a base component, and S ∈ {-1; 1} encodes a geometric phase or orientation. This framework allows us to define an imaginary product that is both commutative and associative, properties rarely combined in higher-dimensional algebras. We demonstrate the consistency of this product through a binary and superposed formalism. This result provides a solid foundation for representing multi-level logic states, with potential applications in quantum information processing. Supplementary Material File (alg com ass jas wiley.docx) Download 53.55 KB Information & Authors Information Version history V1 Version 1 17 June 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords associativity binary logic commutativity hyper complex algebra qbit superposition Authors Affiliations José Antoine SEQUEIRA 0009-0008-4860-1450 [email protected] Record Researcher Publications View all articles by this author Metrics & Citations Metrics Article Usage 151 views 63 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation José Antoine SEQUEIRA. Hyper-complex Binary Superposition Algebra: A Commutative and Associative Product. Authorea . 17 June 2025. DOI: https://doi.org/10.22541/au.175016330.09338854/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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