A KumKum Framework for Problem Resolution: A Mathematical and Learning-Based Model for Adaptive Solution Generation

A KumKum Framework for Problem Resolution: A Mathematical and Learning-Based Model for Adaptive Solution Generation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A KumKum Framework for Problem Resolution: A Mathematical and Learning-Based Model for Adaptive Solution Generation Nnaemeka Kingsley Ugwumba, Peter Sunday Jaja This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9248018/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study introduces the KumKum model, a novel framework for problem resolution based on the principle of adaptive interaction among the constituent elements of a system. The model is motivated by the observation that complex problems often arise from conflicting or constrained relationships between their internal components. Rather than treating these components as passive variables, the KumKum framework models them as interacting entities whose states can be adjusted in a manner that facilitates the emergence of a solution. The proposed approach consists of two complementary layers. The first is a mathematical model that represents problem elements as state variables within a continuous system. A transformation function is defined to regulate the interactions among these variables, guiding the system toward a stable configuration corresponding to a feasible solution. The second layer introduces a learning-based architecture that operationalizes the mathematical model within a decision-making pipeline. This component enables the system to adaptively learn optimal strategies for adjusting element states based on prior outcomes. Analytical properties of the mathematical formulation are examined, including stability conditions, convergence behavior, and the role of interaction parameters. The learning-based component is designed to integrate seamlessly with standard computational pipelines, allowing the model to be applied to a wide range of problem-solving contexts. The combined framework provides a structured approach to solution generation in complex systems, offering both theoretical insight and practical applicability. Artificial Intelligence and Machine Learning KumKum model mathematical modeling problem resolution nonlinear systems adaptive systems machine learning framework optimization dynamics system stability interaction modeling decision systems Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9248018","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":613511734,"identity":"12f890a7-4a94-4646-9c15-2a858747c81c","order_by":0,"name":"Nnaemeka Kingsley Ugwumba","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0000-2493-9846","institution":"Laskenta Technologies Limited","correspondingAuthor":true,"prefix":"","firstName":"Nnaemeka","middleName":"Kingsley","lastName":"Ugwumba","suffix":""},{"id":613511735,"identity":"14493b92-3341-43fb-914e-5df8955c0f58","order_by":1,"name":"Peter Sunday Jaja","email":"data:image/png;base64,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","orcid":"","institution":"Laskenta Technologies Limited","correspondingAuthor":true,"prefix":"","firstName":"Peter","middleName":"Sunday","lastName":"Jaja","suffix":""}],"badges":[],"createdAt":"2026-03-27 19:59:11","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-9248018/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9248018/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106088363,"identity":"68eea807-b793-45df-b799-3a5f28021467","added_by":"auto","created_at":"2026-04-03 10:11:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":373968,"visible":true,"origin":"","legend":"","description":"","filename":"KumKumFramework.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9248018/v1_covered_9d4abcb9-c2ca-4faf-b083-36e011bb56ef.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eA KumKum Framework for Problem Resolution: A Mathematical and Learning-Based Model for Adaptive Solution Generation\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Laskenta Technologies Limited","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"KumKum model, mathematical modeling, problem resolution, nonlinear systems, adaptive systems, machine learning framework, optimization dynamics, system stability, interaction modeling, decision systems","lastPublishedDoi":"10.21203/rs.3.rs-9248018/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9248018/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study introduces the KumKum model, a novel framework for problem resolution based on the principle of adaptive interaction among the constituent elements of a system. 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