Filtered Diagonals and Divergent Fixed-Point Paradigms

Filtered Diagonals and Divergent Fixed-Point Paradigms | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 3 July 2025 V1 Latest version Share on Filtered Diagonals and Divergent Fixed-Point Paradigms Author : Faruk Alpay 0009-0009-2207-6528 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175156626.67215412/v1 201 views 125 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We introduce a novel filtered diagonal operator that bridges two fundamental paradigms in fixed-point theory: logical self-reference (as exemplified by Lawvere's fixed-point theorem) and topological contraction (as in Banach's fixed-point theorem). While Lawvere's theorem shows that self-referential constructions in categorical logic inevitably lead to fixed points that often yield paradoxes, classical fixed-point theorems in analysis guarantee well-behaved fixed points through topological or metric properties. We construct a filtered diagonal operator ∆ F that acts on continuous self-maps of compact Hausdorff spaces, producing a unique fixed point through a form of topological self-reference. This fixed point exists within standard mathematics without paradox, yet we prove it is distinct from the fixed point that would arise from Lawvere's diagonal argument. Our results formally demonstrate that self-reference manifests in fundamentally different ways depending on the mathematical framework, suggesting that the paradoxical nature of self-reference is not inherent but rather depends on the structural context in which it appears. Supplementary Material File (filtered_diagonals_and_divergent_fixed_point_paradigms.pdf) Download 241.35 KB Information & Authors Information Version history V1 Version 1 03 July 2025 Copyright This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License Keywords alpay algebra category theory diagonal arguments fixed-point theorems lawvere's theorem mathematical paradoxes self-reference topological spaces Authors Affiliations Faruk Alpay 0009-0009-2207-6528 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 201 views 125 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Faruk Alpay. Filtered Diagonals and Divergent Fixed-Point Paradigms. Authorea . 03 July 2025. DOI: https://doi.org/10.22541/au.175156626.67215412/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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