The Scale-Emergent Unification Law (SEUL): Discrete Spacetime Geometry, Quantized Curvature, and Cross-Scale Empirical Footprints from DNA to Galaxies

The Scale-Emergent Unification Law (SEUL): Discrete Spacetime Geometry, Quantized Curvature, and Cross-Scale Empirical Footprints from DNA to Galaxies | 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 The Scale-Emergent Unification Law (SEUL): Discrete Spacetime Geometry, Quantized Curvature, and Cross-Scale Empirical Footprints from DNA to Galaxies Wisdom Qiao, MacArthur Watson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9600742/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 The order of the cosmos and the order of life arise from the same set of spacetime geometric rules. The second law of thermodynamics describes the one-way increase of entropy in isolated systems, but it does not explain what determines the direction of entropy . Here we manifest that entropy is a consequence , not a cause. The fundamental force that determines the direction of entropy is the intrinsic directional evolution of spacetime geometry itself —a direction conferred by the topological stability charge \(\:\zeta\:=4\) . We propose a fundamental law derived from discrete spacetime geometry—the Scale-Emergent Unification Law (SEUL) —precisely expressed by a unified spacetime geometric kinetic energy density formula: \(\:\mathcal{ℰ}=\kappa\:\cdot\:\nu\:\cdot\:{R}^{3}\cdot\:\zeta\:\) , where \(\:\:\zeta\:=4\) is the topological stability charge. This law reveals that the intrinsic directional evolution of spacetime geometry determines the trajectory of a system—either toward stable order (local entropy reduction) or toward disorder (entropy increase) . Its regulatory mechanism is the Scale-Emergent Unification Law , a spacetime-ordained principle that both life and the cosmos must jointly follow. The physical projection of this law manifests as a discrete spacetime geometric framework with \(\:{\mathbb{\mathbb{Z}}}_{7}\times\:{\mathbb{\mathbb{Z}}}_{9}\) gauge symmetry. Its intrinsic directional evolution appears across different scales as recursive geometric superposition, yielding the following cross-scale, parameter-free quantitative predictions supported by empirical footprints: ● Nanoscale (P1) : Stable curvature radius of 94 bp DNA minicircle = 9.4 nm (AFM: 9.42 ± 0.28 nm, 0.2% deviation); ● Subcellular scale (P2) : In HeLa cells, specific mechanical wave patterns significantly elongate telomeres, reduce harmful genomic structural variants by approximately 100-fold (drastic reduction in genomic entropy), and reprogram metabolic networks; ● Astronomical scale (P3) : Preference for 9:4 planetary orbital frequency ratios (TRAPPIST-1 g/h: 2.26 vs. 2.25, 0.44% deviation); ● Cosmological scale (P4) : Modulo-9 periodicity in the galaxy two-point correlation function (SDSS DR17, p < 0.005). These empirical footprints spanning over twelve orders of magnitude—from a single DNA helix to the distribution of millions of galaxies—provide multi-angle evidence for the existence of this law. Crucially, the ~ 100-fold reduction in harmful structural variants in HeLa cells is a direct manifestation of the intrinsic directional evolution conferred by the \(\:\zeta\:=4\) topological charge establishing local order in living matter —measurable evidence that spacetime geometric rules determine the direction of entropy. The core superiority of SEUL lies in providing a specific physical realization mechanism for Schrödinger‘s famous assertion that “life feeds on negative entropy”: local order originates from the intrinsic directional evolution of discrete spacetime geometry ( \(\:\zeta\:=4\) ), not from accidental chemical evolution. In the continuum limit, this law recovers the classical results of general relativity. Thus, it is not a negation of existing physics but an extension —providing a testable experimental handle for quantum gravity phenomenology. Scale-Emergent Unification Law discrete spacetime intrinsic directional evolution of spacetime geometry regulatory mechanism of entropy topological charge genomic entropy reduction cross-scale unification 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. We do this by developing innovative software and high quality services for the global research community. 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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-9600742","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":634011288,"identity":"0f72ce93-654b-48a7-87b2-7948663a1b2f","order_by":0,"name":"Wisdom Qiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYDACZgYGCSDFw8/MfPABaVok29mSDYi2CKSFweA8j5kAUcoNjrM/vPExx1rG+DCDGQNDjU00YS2HeYwtZ25L5zE7zJD2gOFYWm4DIS1mh3nYpHm3HQZpOW7A2HCYGC3sz8BajJsZ2ySI1MJgBtZiwMzMRpwWe5hfJA6zMRskEOMXyf7jwBDbZm3P33/+44MPNTaEtUABM4RKIFI5kpZRMApGwSgYBdgAAJbhOHS79LF0AAAAAElFTkSuQmCC","orcid":"","institution":"Amchi Digital Life Technology Co., Ltd.","correspondingAuthor":true,"prefix":"","firstName":"Wisdom","middleName":"","lastName":"Qiao","suffix":""},{"id":634011290,"identity":"1b69aedb-7b16-456a-988d-0752c783540c","order_by":1,"name":"MacArthur Watson","email":"","orcid":"","institution":"Amchi Digital Life Technology Co., Ltd.","correspondingAuthor":false,"prefix":"","firstName":"MacArthur","middleName":"","lastName":"Watson","suffix":""}],"badges":[],"createdAt":"2026-05-03 14:40:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9600742/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9600742/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108804237,"identity":"590d24b2-f46f-44b0-bd59-3b6b1cf4b82b","added_by":"auto","created_at":"2026-05-08 15:18:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":357145,"visible":true,"origin":"","legend":"","description":"","filename":"TheScaleEmergentUnificationLaw.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9600742/v1_covered_60f1bcb6-1e51-4deb-abda-be9da15cccfb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Scale-Emergent Unification Law (SEUL): Discrete Spacetime Geometry, Quantized Curvature, and Cross-Scale Empirical Footprints from DNA to Galaxies","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"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":"Scale-Emergent Unification Law, discrete spacetime, intrinsic directional evolution of spacetime geometry, regulatory mechanism of entropy, topological charge, genomic entropy reduction, cross-scale unification","lastPublishedDoi":"10.21203/rs.3.rs-9600742/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9600742/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe order of the cosmos and the order of life arise from the same set of spacetime geometric rules. The second law of thermodynamics describes the one-way increase of entropy in isolated systems, but it does not explain \u003cb\u003ewhat determines the direction of entropy\u003c/b\u003e. Here we manifest that entropy is a \u003cb\u003econsequence\u003c/b\u003e, not a cause. The fundamental force that determines the direction of entropy is the \u003cb\u003eintrinsic directional evolution of spacetime geometry itself\u003c/b\u003e\u0026mdash;a direction conferred by the topological stability charge \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\zeta\\:=4\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eWe propose a fundamental law derived from discrete spacetime geometry\u0026mdash;the \u003cb\u003eScale-Emergent Unification Law (SEUL)\u003c/b\u003e\u0026mdash;precisely expressed by a unified spacetime geometric kinetic energy density formula: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mathcal{ℰ}=\\kappa\\:\\cdot\\:\\nu\\:\\cdot\\:{R}^{3}\\cdot\\:\\zeta\\:\\)\u003c/span\u003e\u003c/span\u003e, where\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\zeta\\:=4\\)\u003c/span\u003e\u003c/span\u003e is the topological stability charge. This law reveals that \u003cb\u003ethe intrinsic directional evolution of spacetime geometry determines the trajectory of a system\u0026mdash;either toward stable order (local entropy reduction) or toward disorder (entropy increase)\u003c/b\u003e. Its regulatory mechanism is the \u003cb\u003eScale-Emergent Unification Law\u003c/b\u003e, a spacetime-ordained principle that both life and the cosmos must jointly follow.\u003c/p\u003e \u003cp\u003eThe physical projection of this law manifests as a discrete spacetime geometric framework with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mathbb{\\mathbb{Z}}}_{7}\\times\\:{\\mathbb{\\mathbb{Z}}}_{9}\\)\u003c/span\u003e\u003c/span\u003e gauge symmetry. Its intrinsic directional evolution appears across different scales as recursive geometric superposition, yielding the following cross-scale, parameter-free quantitative predictions supported by empirical footprints:\u003c/p\u003e \u003cp\u003e● \u003cb\u003eNanoscale (P1)\u003c/b\u003e: Stable curvature radius of 94 bp DNA minicircle\u0026thinsp;=\u0026thinsp;9.4 nm (AFM: 9.42\u0026thinsp;\u0026plusmn;\u0026thinsp;0.28 nm, 0.2% deviation);\u003c/p\u003e \u003cp\u003e● \u003cb\u003eSubcellular scale (P2)\u003c/b\u003e: In HeLa cells, specific mechanical wave patterns significantly elongate telomeres, reduce harmful genomic structural variants by approximately 100-fold (drastic reduction in genomic entropy), and reprogram metabolic networks;\u003c/p\u003e \u003cp\u003e● \u003cb\u003eAstronomical scale (P3)\u003c/b\u003e: Preference for 9:4 planetary orbital frequency ratios (TRAPPIST-1 g/h: 2.26 vs. 2.25, 0.44% deviation);\u003c/p\u003e \u003cp\u003e● \u003cb\u003eCosmological scale (P4)\u003c/b\u003e: Modulo-9 periodicity in the galaxy two-point correlation function (SDSS DR17, p\u0026thinsp;\u0026lt;\u0026thinsp;0.005).\u003c/p\u003e \u003cp\u003eThese empirical footprints spanning over twelve orders of magnitude\u0026mdash;from a single DNA helix to the distribution of millions of galaxies\u0026mdash;provide multi-angle evidence for the existence of this law. \u003cb\u003eCrucially, the ~\u0026thinsp;100-fold reduction in harmful structural variants in HeLa cells is a direct manifestation of the intrinsic directional evolution conferred by the\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\zeta\\:=4\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003etopological charge establishing local order in living matter\u003c/b\u003e\u0026mdash;measurable evidence that spacetime geometric rules determine the direction of entropy.\u003c/p\u003e \u003cp\u003eThe core superiority of SEUL lies in providing a specific physical realization mechanism for Schr\u0026ouml;dinger\u0026lsquo;s famous assertion that \u0026ldquo;life feeds on negative entropy\u0026rdquo;: local order originates from the intrinsic directional evolution of discrete spacetime geometry (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\zeta\\:=4\\)\u003c/span\u003e\u003c/span\u003e), not from accidental chemical evolution. In the continuum limit, this law recovers the classical results of general relativity. Thus, it is not a negation of existing physics but an \u003cb\u003eextension\u003c/b\u003e\u0026mdash;providing a testable experimental handle for quantum gravity phenomenology.\u003c/p\u003e","manuscriptTitle":"The Scale-Emergent Unification Law (SEUL): Discrete Spacetime Geometry, Quantized Curvature, and Cross-Scale Empirical Footprints from DNA to Galaxies","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-05 12:01:29","doi":"10.21203/rs.3.rs-9600742/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":"ca5cf5bb-6087-402f-9e14-d780d618acd2","owner":[],"postedDate":"May 5th, 2026","published":true,"recentEditorialEvents":[{"type":"checksComplete","content":"","date":"2026-05-04T09:15:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"Foundations of Physics","date":"2026-05-03T14:29:20+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-05-05T12:01:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-05 12:01:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9600742","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9600742","identity":"rs-9600742","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}