Informational Black–Hole Networks: A Minimal Microdynamics for Dimensional Emergence

Informational Black–Hole Networks: A Minimal Microdynamics for Dimensional Emergence | 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 Informational Black–Hole Networks: A Minimal Microdynamics for Dimensional Emergence Moisés Fernández Pérez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8368503/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 introduce the Informational Black–Hole Network (IBHN), a minimal microdynamic model in which spacetime is treated as an emergent structure built from discrete nodes carrying a finite integer load n of bits. Each node is subject to a dimension-dependent capacity K(D), interpreted as the maximal relational coordination implied by the Principle of Minimal Information (PMI). Dynamics is defined by four local rules—creation at frontier holes (C), one-bit transfer between neighbours (T), fusion of mutually selected neighbours (F), and an optional split channel for terminal 4D saturation (S)—combined with an activation law p_flip(n) = 2^{1 − n} implementing informational inertia. A dimensional bootstrap is enabled by the coordination ladder K(2) = 6, K(3) = 12, K(4) = 24: saturated 2D nodes (n = 6) can fuse into 3D nodes (n = 12), and saturated 3D nodes can fuse into 4D nodes (n = 24), while no analogous uplift is supported beyond 4D. We implement a 2D open-boundary hexagonal cellular automaton instantiation of the microdynamics and obtain a statistically stationary bulk with a nontrivial load distribution and a persistent saturated fraction. Rare mutual-selection events inside saturated clusters generate sustained 6 + 6→12 bootstrap events, providing constructive evidence that the rules self-organize the conditions required for dimensional uplift. The framework is intended as a minimal informational substrate suitable for analytic coarse-graining and higher-dimensional extensions. informational microdynamics emergent spacetime discrete networks Principle of Minimal Information cellular automata dimensional bootstrap Full Text Additional Declarations No competing interests reported. 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. 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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-8368503","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":562767531,"identity":"86b7b9a0-d487-451c-af1d-4414082ac828","order_by":0,"name":"Moisés Fernández 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cellular automata, dimensional bootstrap","lastPublishedDoi":"10.21203/rs.3.rs-8368503/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8368503/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe introduce the Informational Black\u0026ndash;Hole Network (IBHN), a minimal microdynamic model in which spacetime is treated as an emergent structure built from discrete nodes carrying a finite integer load n of bits. Each node is subject to a dimension-dependent capacity K(D), interpreted as the maximal relational coordination implied by the Principle of Minimal Information (PMI). Dynamics is defined by four local rules\u0026mdash;creation at frontier holes (C), one-bit transfer between neighbours (T), fusion of mutually selected neighbours (F), and an optional split channel for terminal 4D saturation (S)\u0026mdash;combined with an activation law p_flip(n)\u0026thinsp;=\u0026thinsp;2^{1\u0026thinsp;\u0026minus;\u0026thinsp;n} implementing informational inertia. A dimensional bootstrap is enabled by the coordination ladder K(2)\u0026thinsp;=\u0026thinsp;6, K(3)\u0026thinsp;=\u0026thinsp;12, K(4)\u0026thinsp;=\u0026thinsp;24: saturated 2D nodes (n\u0026thinsp;=\u0026thinsp;6) can fuse into 3D nodes (n\u0026thinsp;=\u0026thinsp;12), and saturated 3D nodes can fuse into 4D nodes (n\u0026thinsp;=\u0026thinsp;24), while no analogous uplift is supported beyond 4D. We implement a 2D open-boundary hexagonal cellular automaton instantiation of the microdynamics and obtain a statistically stationary bulk with a nontrivial load distribution and a persistent saturated fraction. Rare mutual-selection events inside saturated clusters generate sustained 6\u0026thinsp;+\u0026thinsp;6\u0026rarr;12 bootstrap events, providing constructive evidence that the rules self-organize the conditions required for dimensional uplift. The framework is intended as a minimal informational substrate suitable for analytic coarse-graining and higher-dimensional extensions.\u003c/p\u003e","manuscriptTitle":"Informational Black–Hole Networks: A Minimal Microdynamics for Dimensional Emergence","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-23 07:45:49","doi":"10.21203/rs.3.rs-8368503/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":"1a53efdf-ce53-435e-8bbd-cb197d73c959","owner":[],"postedDate":"December 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-20T18:16:05+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-23 07:45:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8368503","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8368503","identity":"rs-8368503","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}