Fixed-Point Traps and Identity Emergence in Educational Feedback Systems

Fixed-Point Traps and Identity Emergence in Educational Feedback Systems | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 27 May 2025 V1 Latest version Share on Fixed-Point Traps and Identity Emergence in Educational Feedback Systems Author : Faruk Alpay 0009-0009-2207-6528 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.174837868.87734182/v1 175 views 99 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract I present a categorical framework for analyzing fixed-point emergence in educational feedback systems, where exam-grade collapse mechanisms prevent the formation of stable learner identities. Using endofunctors and initial algebras from category theory, I model learning processes as generative functors φ that would naturally converge to fixed-point identities under transfinite iteration. However, when educational assessment introduces entropy-reducing collapse functors E, I prove that no nontrivial initial algebra can exist for the composite functor F = E • φ. This mathematical obstruction categorically blocks creativity-driven identity emergence, creating what I term "fixed-point traps" in educational systems. My results demonstrate that exam-driven feedback loops fundamentally prevent the stabilization of learner identities, offering a formal explanation for creativity suppression in assessment-heavy educational environments. Supplementary Material File (fixed_point_traps_and_identity_emergence_in_educational_feedback.pdf) Download 259.08 KB Information & Authors Information Version history V1 Version 1 27 May 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords academia academy alpay algebra category theory education exam sytem explainable ai fixed point theory fixed-point algebra system collapse Authors Affiliations Faruk Alpay 0009-0009-2207-6528 [email protected] Independent Researcher View all articles by this author Metrics & Citations Metrics Article Usage 175 views 99 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Faruk Alpay. Fixed-Point Traps and Identity Emergence in Educational Feedback Systems. Authorea . 27 May 2025. DOI: https://doi.org/10.22541/au.174837868.87734182/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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