Memory as Spatiotemporal Delay: A Unified Hybrid Framework for Quantum-cosmic Energetics and Astrobiological Dynamics

Memory as Spatiotemporal Delay: A Unified Hybrid Framework for Quantum-cosmic Energetics and Astrobiological Dynamics | 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 Memory as Spatiotemporal Delay: A Unified Hybrid Framework for Quantum-cosmic Energetics and Astrobiological Dynamics Hasan Hüseyin Tosunoğlu, Taylan Demir, Abdoul Karenzo, Niaz Ali Shah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8970251/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 We develop a unified dynamical framework in which memory is modeled as a state dependent spatiotemporal delay field embedded in De lay Differential and Volterra type Integro Differential Equations. The result ing non Markovian structure allows past states to influence present dynamics through weighted delay kernels and associated energy functionals. Spectral analysis of the transcendental characteristic equation identifies regimes of as ymptotic stability, critical slowing down, and delay induced oscillations con sistent with Hopf type transitions. To address computational challenges, we implement a Hybrid Physics Informed Neural Network (PINN) with attention based mechanisms to approximate state dependent delay operators. Numerical simulations validate the theoretical stability criteria and demonstrate transi tions between equilibrium and oscillatory dynamics. The framework provides a common delay driven structure linking curved spacetime effects and astro biological latency phenomena. Applied Mathematics Analysis Mathematical Physics Computational Mathematics Mathematical and Theoretical Biology Spatiotemporal Memory Delay Differential Equations (DDEs) Spatiotemporal Delay Invariance Quantum-Cosmic Energetics Astrobiologi cal Dynamics Hybrid Physics-Informed Neural Networks (PINN) Transformer based Attention Mechanism Metabolic Latency General Relativity and Time Dilation Non-Markovian Dynamics Martian Regolith Simulation 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-8970251","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":597106712,"identity":"389a1927-d107-49bf-97eb-44ac5f31d65d","order_by":0,"name":"Hasan Hüseyin Tosunoğlu","email":"","orcid":"https://orcid.org/0009-0004-8735-4289","institution":"Istanbul University","correspondingAuthor":false,"prefix":"","firstName":"Hasan","middleName":"Hüseyin","lastName":"Tosunoğlu","suffix":""},{"id":597106713,"identity":"b47bd830-7bb3-4983-9c95-0a8d4066cebd","order_by":1,"name":"Taylan Demir","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-7402-4468","institution":"Ankara University","correspondingAuthor":true,"prefix":"","firstName":"Taylan","middleName":"","lastName":"Demir","suffix":""},{"id":597106714,"identity":"85d59fe8-db3d-460b-ba27-7ea973d27d25","order_by":2,"name":"Abdoul Karenzo","email":"","orcid":"","institution":"Ankara University","correspondingAuthor":false,"prefix":"","firstName":"Abdoul","middleName":"","lastName":"Karenzo","suffix":""},{"id":597106844,"identity":"9cd98e68-43f9-4035-8424-dc13bf9c0316","order_by":3,"name":"Niaz Ali Shah","email":"","orcid":"https://orcid.org/0000-0002-1967-1176","institution":"Abbottabad University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Niaz","middleName":"Ali","lastName":"Shah","suffix":""}],"badges":[],"createdAt":"2026-02-25 17:34:50","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8970251/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8970251/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103622264,"identity":"e899554a-9773-4a5c-9e7f-51847e30298f","added_by":"auto","created_at":"2026-02-27 18:40:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":563168,"visible":true,"origin":"","legend":"","description":"","filename":"HasanHseyinTosunoluTaylanDemirAbdoulKarenzoNiazAlishah12.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8970251/v1_covered_308fe87e-34c8-422d-b042-99169ec11e86.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eMemory as Spatiotemporal Delay: A Unified Hybrid Framework for Quantum-cosmic Energetics and Astrobiological Dynamics\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Ankara University","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":"Spatiotemporal Memory, Delay Differential Equations (DDEs), Spatiotemporal Delay Invariance, Quantum-Cosmic Energetics, Astrobiologi cal Dynamics, Hybrid Physics-Informed Neural Networks (PINN), Transformer based Attention Mechanism, Metabolic Latency, General Relativity and Time Dilation, Non-Markovian Dynamics, Martian Regolith Simulation","lastPublishedDoi":"10.21203/rs.3.rs-8970251/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8970251/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe develop a unified dynamical framework in which memory is modeled as a state dependent spatiotemporal delay field embedded in De lay Differential and Volterra type Integro Differential Equations. The result ing non Markovian structure allows past states to influence present dynamics through weighted delay kernels and associated energy functionals. Spectral analysis of the transcendental characteristic equation identifies regimes of as ymptotic stability, critical slowing down, and delay induced oscillations con sistent with Hopf type transitions. To address computational challenges, we implement a Hybrid Physics Informed Neural Network (PINN) with attention based mechanisms to approximate state dependent delay operators. Numerical simulations validate the theoretical stability criteria and demonstrate transi tions between equilibrium and oscillatory dynamics. The framework provides a common delay driven structure linking curved spacetime effects and astro biological latency phenomena.\u003c/p\u003e","manuscriptTitle":"Memory as Spatiotemporal Delay: A Unified Hybrid Framework for Quantum-cosmic Energetics and Astrobiological Dynamics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-27 18:39:29","doi":"10.21203/rs.3.rs-8970251/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"14da3057-d7e8-4411-b6ad-a993671390f8","owner":[],"postedDate":"February 27th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63675186,"name":"Applied Mathematics"},{"id":63675187,"name":"Analysis"},{"id":63675188,"name":"Mathematical Physics"},{"id":63675189,"name":"Computational Mathematics"},{"id":63675190,"name":"Mathematical and Theoretical Biology"}],"tags":[],"updatedAt":"2026-02-27T18:39:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-27 18:39:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8970251","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8970251","identity":"rs-8970251","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}