Domain-agnostic multiplicative stress framework for systemic collapse

Domain-agnostic multiplicative stress framework for systemic collapse | 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PDF Article Domain-agnostic multiplicative stress framework for systemic collapse Junwon Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8968998/v2 This work is licensed under a CC BY 4.0 License Status: Under Review Version 2 posted 6 You are reading this latest preprint version Show more versions Abstract Complex systems rarely collapse from a single perturbation; however, no framework has formalized the coincidence mechanism across domains. Here, we introduce a multiplicative stress integral, S(t) = ρ(t) × Ψ(t) × Ω(t), which decomposes systemic stress into external pressure (ρ), internal amplification (Ψ), and structural degradation (Ω). The multiplicative structure drives the stress toward zero when any channel is quiescent, thereby creating a coincidence filter. The cumulative index Π(t) integrates the joint stress with a fixed equal weighting (1:1:1) and no weight optimization. Applied to five major crises, the 2008 financial crisis, Terra–Luna collapse, Fukushima disaster, COVID-19 pandemic, and global supply-chain disruption, the crisis periods separate from controls (1.9× to 3,627×; Fisher p = 1.66 × 10⁻¹¹), with the multiplicative formulation matching or outperforming alternative models in all cases. When the channels are redundant, the filter dilutes rather than amplifies the signal, which is a falsifiable prediction that is empirically confirmed. Analysis of Π accumulation dynamics reveals three failure modes, ductile, brittle, and preloaded, suggesting that co-occurrence of independent stresses is a shared structural feature of systemic collapse. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Supplementary Files SUPPLEMENTARYformanuscript.docx Figurebenchmark.pdf Cite Share Download PDF Status: Under Review Version 2 posted Reviewers agreed at journal 18 May, 2026 Reviewers invited by journal 16 Apr, 2026 Editor invited by journal 09 Mar, 2026 Editor assigned by journal 04 Mar, 2026 Submission checks completed at journal 04 Mar, 2026 First submitted to journal 03 Mar, 2026 You are reading this latest preprint version Show more versions 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. 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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-8968998","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[{"code":1,"date":"2026-03-08 16:58:54","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}}],"articleType":"Article","associatedPublications":[],"authors":[{"id":635824538,"identity":"9839fdc1-3de1-4cf8-a946-6ca5b25f1df8","order_by":0,"name":"Junwon Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDUlEQVRIiWNgGAWjYBACAyjNI8/M2PiAByzAhiKDU4ucYTtzswFJWowZzrO3SRClxZy999mHnztqExubGdsq3tTcMeZnb0tg+FHDYGzegF2LZc9x45m9Z44ntjMztt2cc+yZmWTPsQOMPccYzGQO4HDYjTRmBt62Y2BbbvOwHbYxuJHewMDbwGAjgcsv958xM/4Famk4zNhWzPMPooXxLz4tN9iYmXnbaowZgFqAjMNmQHsPMANtMcOp5UwaM7Ns2wE5w2bGZsm5fYeNgX5JOCxzTMIYp5bjx5gZ37bV8cjzH3/44c23w4b97G2GD9/U2BjOwKEFCg6jcg8wMOCyAw7qCCkYBaNgFIyCkQwAEd1aEv3dz5cAAAAASUVORK5CYII=","orcid":"","institution":"Dankook University","correspondingAuthor":true,"prefix":"","firstName":"Junwon","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2026-02-25 14:51:18","currentVersionCode":2,"declarations":"","doi":"10.21203/rs.3.rs-8968998/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-8968998/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108651857,"identity":"cc223d47-d3eb-4a14-b181-65e736e8e5a6","added_by":"auto","created_at":"2026-05-07 02:10:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":512646,"visible":true,"origin":"","legend":"","description":"","filename":"MANUSCRIPT20260506T215801.371.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8968998/v2_covered_458f2104-eeae-470d-a9eb-084e0271f73c.pdf"},{"id":108651835,"identity":"60d6570f-5649-455c-bab9-df17ee8f2b90","added_by":"auto","created_at":"2026-05-07 02:10:27","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":35884,"visible":true,"origin":"","legend":"","description":"","filename":"SUPPLEMENTARYformanuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-8968998/v2/b7b085fdef766520590dfb57.docx"},{"id":108651832,"identity":"983fa022-484b-4472-80e7-100cb880d4d5","added_by":"auto","created_at":"2026-05-07 02:10:24","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":27884,"visible":true,"origin":"","legend":"","description":"","filename":"Figurebenchmark.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8968998/v2/92e3b33610223e60cc9422fe.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Domain-agnostic multiplicative stress framework for systemic collapse","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8968998/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8968998/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eComplex systems rarely collapse from a single perturbation; however, no framework has formalized the coincidence mechanism across domains. Here, we introduce a multiplicative stress integral, S(t) = ρ(t) \u0026times; Ψ(t) \u0026times; Ω(t), which decomposes systemic stress into external pressure (ρ), internal amplification (Ψ), and structural degradation (Ω). The multiplicative structure drives the stress toward zero when any channel is quiescent, thereby creating a coincidence filter. The cumulative index Π(t) integrates the joint stress with a fixed equal weighting (1:1:1) and no weight optimization. Applied to five major crises, the 2008 financial crisis, Terra\u0026ndash;Luna collapse, Fukushima disaster, COVID-19 pandemic, and global supply-chain disruption, the crisis periods separate from controls (1.9\u0026times; to 3,627\u0026times;; Fisher p\u0026thinsp;=\u0026thinsp;1.66 \u0026times; 10⁻\u0026sup1;\u0026sup1;), with the multiplicative formulation matching or outperforming alternative models in all cases. When the channels are redundant, the filter dilutes rather than amplifies the signal, which is a falsifiable prediction that is empirically confirmed. Analysis of Π accumulation dynamics reveals three failure modes, ductile, brittle, and preloaded, suggesting that co-occurrence of independent stresses is a shared structural feature of systemic collapse.\u003c/p\u003e","manuscriptTitle":"Domain-agnostic multiplicative stress framework for systemic collapse","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2026-05-07 02:09:14","doi":"10.21203/rs.3.rs-8968998/v2","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"144028012425537319589169988988970358056","date":"2026-05-18T13:44:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-17T00:37:36+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-09T10:12:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-04T05:46:01+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-04T05:45:05+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-03-03T23:39:48+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8cc464df-a7b8-421c-b828-adece05bd0d1","owner":[],"postedDate":"May 7th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"144028012425537319589169988988970358056","date":"2026-05-18T13:44:25+00:00","index":87,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":67671673,"name":"Physical sciences/Engineering"},{"id":67671674,"name":"Physical sciences/Mathematics and computing"},{"id":67671675,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-07T06:38:27+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-07 02:09:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-8968998","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8968998","identity":"rs-8968998","version":["v2"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}